The factorization of 81x² - 4 is (9x + 2)(9x - 2).
Factorization, also known as factoring, is the process of expressing a number or an algebraic expression as a product of two or more factors that are smaller than the original number or expression.
We can factorize 81x² - 4 by recognizing that it is a difference of squares, which can be factored as:
a² - b² = (a + b)(a - b)
In this case, a = 9x and b = 2, so we can write:
81x²- 4 = (9x + 2)(9x - 2)
Therefore, the factorization of 81x² - 4 is (9x + 2)(9x - 2).
To know more about factorization follow
https://brainly.com/question/25829061
#SPJ1
For each relation, indicate whether the relation is a partial order, a strict order, or neither. If the relation is a partial or strict order, indicate whether the relation is also a total order. Justify your answers.
(a) The domain is the set of all words in the English language (as defined by, say, Webster's dictionary). Word x is related to word y if x appears before y in alphabetical order. Assume that each word appears exactly once in the dictionary.
(b) The domain is the set of all words in the English language (as defined by, say, Webster's dictionary). Word x is related to word y if x appears as a substring of y. x is a substring of y if all the letters in x appear in consecutive order somewhere in y. For example, "logical" is substring of "topological" because the letters l-o-g-i-c-a-l appear consecutively in order in the word "topological". However, "local" is not a substring of "topological" because the letters l-o are separated from c-a-l by the letters g and i.
A. The relation is a partial order.
B. The relation is neither a partial nor a strict order.
(a) The relation is a partial order because it is reflexive (a word appears before itself in alphabetical order), antisymmetric (if word x appears before word y and word y appears before word x, then x and y must be the same word), and transitive (if x appears before y and y appears before z, then x must appear before z).
However, it is not a total order because some words are not comparable (e.g., "orange" and "pear").
(b) The relation is neither a partial nor a strict order because it is not reflexive (a word is not a substring of itself), not antisymmetric (e.g., "local" and "logical" are both substrings of "topological" but are not the same word), and not transitive (e.g., "logical" is a substring of "topological" and "topological" is a substring of "biological," but "logical" is not a substring of "biological").
Therefore, it cannot be a total order.
To learn more about substring, refer below:
https://brainly.com/question/30765811
#SPJ11
if `\frac{3}{4}` pound of nails fills a container `\frac{2}{3}` full, then how many pounds of nails will fill the container?
Let's use the proportion method to solve the problem. We know that \frac{3}{4} pound of nails fills \frac{2}{3} of the container. Let x be the total weight of nails that will fill the container. Then we can set up the proportion:
\frac{3}{4} / \frac{2}{3} = x / 1
To solve for x, we can cross-multiply and simplify:
\frac{3}{4} * \frac{3}{2} = x
x = \frac{9}{8} = 1.125 pounds of nails
Therefore, 1.125 pounds of nails will fill the container.
Learn more about Fraction here:- brainly.com/question/78672
#SPJ11
For a cost function C 100+ 10Q+ Q2, the average fixed cost of producing 10 units of output is: Multiple Choice 10. 5. None of the answers are correct.
a) The average fixed cost of producing 10 units of output is 10.
b) The average fixed cost is calculated by dividing the total fixed cost by the quantity of output produced. In this case, the cost function is given as C = 100 + 10Q + Q^2, where Q represents the quantity of output.
Since the fixed cost is constant and does not depend on the quantity of output, it remains the same regardless of the level of production. Therefore, the average fixed cost is simply equal to the fixed cost divided by the quantity of output. In this case, the fixed cost is 100, and when 10 units of output are produced, the average fixed cost is 100/10 = 10.
Learn more about fixed costs here:- brainly.com/question/17137250
#SPJ11
on a nationwide math test, the mean was 69 and the standard deviation was 7. if roberto scored 85, what was his z-score?
Roberto's z-score is approximately 2.29. This means that his score is about 2.29 standard deviations above the mean.
A z-score (also known as a standard score) is a measure of how many standard deviations a data point is away from the mean of a distribution. It is used to standardize data so that we can compare values from different distributions.
For example, if a student's score on a test is 80 and the mean score is 75 with a standard deviation of 5, the z-score for the student's score would be:
z = (80 - 75) / 5
z = 1
This means that the student's score is one standard deviation above the mean.
To find Roberto's z-score, we can use the formula:
(x - μ) / σ
where x is Roberto's score, μ is the mean of the test, and σ is the standard deviation of the test.
We are given that the mean was 69 and the standard deviation was 7. Roberto scored 85. So we can plug in these values into the formula and solve for z:
z = (85 - 69) / 7
z = 16 / 7
z ≈ 2.29
Therefore, Roberto's z-score is approximately 2.29.
To learn more about z-score visit:
https://brainly.com/question/15016913
#SPJ4
dren. what is the probability that an individual in this survey has fewer than three children? at least one child? five or more children?
Let's say that out of 100 individuals surveyed, 40 have fewer than three children. The probability of an individual in this survey having fewer than three children would be 40/100 or 0.4.
To calculate the probability of an individual in the survey having fewer than three children, we would need to know the total number of individuals surveyed and how many of those individuals have fewer than three children. Let's say that out of 100 individuals surveyed, 40 have fewer than three children. The probability of an individual in this survey having fewer than three children would be 40/100 or 0.4.
To calculate the probability of an individual in the survey having at least one child, we would need to know how many individuals in the survey have no children. Let's say that out of the 100 individuals surveyed, 20 have no children. The probability of an individual in this survey having at least one child would be (100-20)/100 or 0.8.
To calculate the probability of an individual in the survey having five or more children, we would need to know how many individuals in the survey have five or more children. Let's say that out of the 100 individuals surveyed, only 2 have five or more children. The probability of an individual in this survey having five or more children would be 2/100 or 0.02.
To determine the probability of an individual in this survey having fewer than three children, at least one child, or five or more children, you will need specific data or information about the distribution of children per family in the survey. Once you have that information, you can calculate the probabilities by dividing the number of individuals meeting each condition by the total number of individuals in the survey.
Visit here to learn more about probability : https://brainly.com/question/30034780
#SPJ11
calculate the solubility at 25˚c of bacro4 in pure water and in a 0.0180 m bacl2 solution.
The solubility of BaCrO4 in a 0.0180 M BaCl2 solution is 6.50 x 10^-6 M.
We are given that;
Temperature= 25
bacl2 solution= 0.0180
Now,
In a 0.0180 M BaCl2 solution, we have to consider that some of the Ba2+ ions come from the BaCl2 salt, which is highly soluble and dissociates completely in water. Therefore, the concentration of Ba2+ in the solution is not equal to x, but rather 0.0180 + x. The concentration of CrO4^2- is still equal to x, since it only comes from the dissolution of BaCrO4. Then we have:
Ksp = (0.0180 + x)x
Solving for x, we get:
(0.0180 + x)x = 1.17 x 10^-10 x^2 + 0.0180x - 1.17 x 10^-10 = 0 Using the quadratic formula, we get: x = [-0.0180 ± √(0.0180^2 + 4(1.17 x 10^-10))] / 2 x ≈ -0.0180 or x ≈ 6.50 x 10^-6 M
We reject the negative value of x, since it does not make sense for a concentration to be negative.
Therefore, by the solution the answer will be 6.50 x 10^-6 M.
Learn more about solutions;
https://brainly.com/question/16339562
#SPJ1
The radius of the Sun is about 700,000,000 meters, the radius of the planet Venus is about 6,000,000 meters, and the radius of the supergiant star Betelgeuse is about 500,000,000,000 meters. Which of these statements is correct? Select three that apply.
A
The radius of the Sun is about 7×107 meters, and the radius of Venus is about 6×106 meters.
B
The radius of the Sun is about 7×108 meters, and the radius of Betelgeuse is about 5×1011 meters.
C
The radius of Venus is about 6×106 meters, and the radius of the Sun is about 7×108 meters.
D
The radius of Venus is about 6×107 meters, and the radius of Betelgeuse is about 5×1011 meters.
E
The radius of Betelgeuse is about 5×1010 meters, and the radius of the Sun is about 7×108 meters.
F
The radius of Betelgeuse is about 5×1011 meters, and the radius of Venus is about 6×106 meters
The Sun has a radius of roughly 700,000,000 metres, Venus has a radius of about 6,000,000 metres, and the supergiant star Betelgeuse has a radius of about 500,000,000,000 metres. The appropriate answers are: a- false b- true c- true d- false e- false f- false.
Here radius of the sun = 700,000,000
radius of Venus = 6,000,000
radius of Betelheuse = 500,0000,000,000
a) This says the radius of the sun [tex]7 * 10^7[/tex]= 70,000,000 (having seven zeros) and this is not equal to what we were initially given in our question hence its false
b) This says the radius of the sun is [tex]7 * 10^8[/tex] = 700,000,000 (having seven zeros) while radius of Betelheuse is [tex]5 * 10^11[/tex] = 500,0000,000,000 (having eleven zeros) which is the same as the value we were given in the question.
c) This says the radius of Venus is [tex]6 * 10^6[/tex] = 6,000,000 (having seven zeros) while radius of the sun is [tex]7 * 10^8[/tex] = 700,000,000 (having eleven zeros) which is the same as the value we were given in the question.
d) This says the radius of Venus is [tex]6 * 10^7[/tex]= 60,000,000 (having seven zeros) while radius of Betelheuse is [tex]5 * 10^{11[/tex] = 500,0000,000,000 (having eleven zeros) which is not the same as the value we were given in the question. This applies for (e) and (f) also
Learn more about radius Visit: brainly.com/question/24375372
#SPJ4
Evaluate the line integral (CF. dr for the vector field F = sin(x)i+yvtj + zk along the curve given by r(t) = { i++j+tk,1
The line integral of the given vector field F along the curve r(t) is 0. To evaluate the line integral (CF. dr for the vector field F = sin(x)i+yvtj + zk along the curve given by r(t) = { i++j+tk,1, we need to parameterize the curve and then compute the integral.
First, let's find the derivative of r(t):
r'(t) = i + j + t k
Next, we need to find the limits of integration. The curve is given by r(t) = { i+j+tk,1 for 0 ≤ t ≤ 1. Therefore, our limits of integration are 0 and 1.
Now, we can compute the line integral using the formula:
CF.dr = ∫(CF).r'(t) dt
= ∫(sin(x)i+yvtj + zk).(i+j+tk) dt
= ∫(sin(i+j+tk) + vt) dt
= -cos(i+j+tk) + 1/2v(t^2)
Evaluating the integral from t=0 to t=1, we get:
CF.dr = [-cos(1+i+j+k) + 1/2v] - [-cos(1+i+j) + 1/2v(0)]
= [-cos(1+i+j+k) + cos(1+i+j)] + 1/2v
Therefore, the value of the line integral is:
CF.dr = [-cos(1+i+j+k) + cos(1+i+j)] + 1/2v.
To evaluate the line integral of the vector field F = sin(x)i + y√tj + zk along the curve r(t) = ti + tj + tk, where t is in the range [1, 1], follow these steps:
1. Differentiate r(t) with respect to t to obtain the tangent vector dr/dt:
dr/dt = (di/dt)i + (dj/dt)j + (dk/dt)k = 1i + 1j + 1k
2. Write the vector field F in terms of the parameter t by substituting x = t, y = t, and z = t:
F(t) = sin(t)i + t√tj + tk
3. Compute the dot product F(t)⋅(dr/dt):
F(t)⋅(dr/dt) = [sin(t)i + t√tj + tk]⋅[1i + 1j + 1k] = sin(t) + t√t + t
4. Evaluate the line integral ∫(CF. dr) over the range [1, 1]:
Since the integral range is [1, 1], the result of the integral will be 0, as there is no difference in the range.
So, the line integral of the given vector field F along the curve r(t) is 0.
Visit here to learn more about derivative brainly.com/question/30365299
#SPH11
4. a small grocery store has 10 cartoons of milk, 1 of which is sour. if you are going to buy the sixth carton of milk sold at random, compute the probability of selecting a carton of sour milk.
The probability of selecting a carton of sour milk when buying the sixth carton of milk sold at random is 1/10 or 0.1.To compute the probability of selecting a carton of sour milk when buying the sixth carton of milk sold at random, we can use the concept of conditional probability.
There are a total of 10 cartons of milk, with 1 sour carton and 9 fresh cartons. When the first 5 cartons are sold, there are 3 possible scenarios:
1) All 5 cartons sold are fresh, leaving 4 fresh and 1 sour carton.
2) 4 cartons sold are fresh and 1 sour, leaving 5 fresh cartons.
3) At least 2 sour cartons are sold, which is not possible as there's only 1 sour carton.
For Scenario 1, the probability of all 5 fresh cartons being sold is (9/10) * (8/9) * (7/8) * (6/7) * (5/6) = 5/10.
In this case, the probability of selecting the sour carton as the sixth carton is 1/5.
For Scenario 2, the probability of 4 fresh cartons and 1 sour carton being sold is 5 * [(9/10) * (8/9) * (7/8) * (6/7) * (1/6)] = 5/10.
In this case, the probability of selecting the sour carton as the sixth carton is 0, as the sour carton has already been sold.
Since Scenario 3 is not possible, we can ignore it.
Now, the overall probability of selecting a sour carton as the sixth carton can be computed as:
(Probability of Scenario 1) * (Probability of selecting sour in Scenario 1) + (Probability of Scenario 2) * (Probability of selecting sour in Scenario 2) = (5/10) * (1/5) + (5/10) * 0 = 1/10.
So, the probability of selecting a carton of sour milk when buying the sixth carton of milk sold at random is 1/10 or 0.1.
learn more about conditional probability here: brainly.com/question/18878381
#SPJ11
charlie draws a triangle with the dimensions shown. then he draws a second triangle in which the dimensions are halved. what is the relationship between the areas of the two triangles?
The area of a triangle is calculated using the formula A = 1/2bh, where b is the base and h is the height. If Charlie draws a second triangle with dimensions that are halved, then the base and height of the second triangle are half of the base and height of the first triangle.
This means that the area of the second triangle is 1/2(1/2bh) = 1/4bh, which is one-fourth of the area of the first triangle. In other words, the area of the second triangle is 25% of the area of the first triangle. Therefore, the relationship between the areas of the two triangles is that the area of the second triangle is one-fourth of the area of the first triangle.
When Charlie draws a triangle with given dimensions and then creates a second triangle with dimensions halved, the relationship between the areas of the two triangles is a ratio of 1:4. This is because the area of a triangle is calculated using the formula A = 0.5 * base * height. When both the base and height are halved, the new area becomes A = 0.5 * (base/2) * (height/2), which simplifies to A = 0.25 * base * height. Comparing the original area to the new area (1 * base * height versus 0.25 * base * height), we see that the area of the second triangle is one-fourth or 25% the area of the original triangle.
Visit here to learn more about area : https://brainly.com/question/27683633
#SPJ11
5x -5 = 35
—
2 What is the answer
Hello!
To solve the equation (5x - 5)/2 = 35, you need to isolate x on one side of the equation.
Start by multiplying both sides of the equation by 2 to eliminate the denominator:
(5x - 5)/2 * 2 = 35 * 2
This simplifies to: 5x - 5 = 70
Add 5 to both sides of the equation to isolate the variable term on one side:
5x - 5 + 5 = 70 + 5
This simplifies to: 5x = 75
Finally, divide both sides of the equation by 5 to solve for x:
5x/5 = 75/5
This simplifies to: x = 15
Therefore, the solution to the equation (5x - 5)/2 = 35 is x = 15.
Answer:
10 is the answer to the question
Step-by-step explanation:
2×5=10 is the answer
What two numbers
Add to -4 and multiply to 3
Answer: -3 and -1
Step-by-step explanation:
-3 + -1 is equal to -4, -3 * -1 is equal to 3, this is because the multiplication of two negative numbers is equal to a positive number, where if the two negative numbers had started positive, it would equal the same thing nonetheless.
2. Given the demand function is D(x) = (x - 5)2 and supply function is S(x) = x2 +x+3. Find each of the following: a) The equilibrium point. b) The consumer surplus at the equilibrium point. Explain what the answer means in a complete sentence using the definition of consumer surplus. c) The producer surplus at the equilibrium point. Explain what the answer means in a complete sentence using the definition of producer surplus.
A the equilibrium point is approximately x = 4.56. b The total amount paid by consumers is $20.94. , c the equilibrium point, producers are earning a total of $357.93 more from selling the good than they would be willing to sell it for.
a) To find the equilibrium point, we need to set the demand and supply functions equal to each other and solve for x:
D(x) = S(x)
(x - 5)2 = x2 + x + 3
x2 - 9x + 22 = 0
Using the quadratic formula, we get:
x = (9 ± sqrt(17))/2
Therefore, the equilibrium point is approximately x = 4.56.
b) To find the consumer surplus at the equilibrium point, we need to calculate the area between the demand curve and the equilibrium price (which is also the supply curve at the equilibrium point) up to the quantity demanded at that point.
First, we calculate the price at the equilibrium point by plugging in x = 4.56 into either the demand or supply function:
P = D(4.56) = S(4.56)
P = (4.56 - 5)2 = 4.56^2 + 4.56 + 3
P = 8.595
Next, we calculate the quantity demanded at the equilibrium point by plugging in the price we just found into the demand function:
Q = D(8.595)
Q = (8.595 - 5)2
Q = 12.098
Now we can calculate the consumer surplus by finding the area between the demand curve and the price line up to Q = 12.098:
Consumer Surplus = 1/2 * (8.595 - 5) * (12.098 - 0)
Consumer Surplus = $20.94
This means that at the equilibrium point, consumers are willing to pay a total of $20.94 more for the good than they actually have to pay.
c) To find the producer surplus at the equilibrium point, we need to calculate the area between the supply curve and the equilibrium price up to the quantity supplied at that point.
Using the price we calculated earlier (P = $8.595), we can find the quantity supplied at the equilibrium point by plugging it into the supply function:
Q = S(8.595)
Q = 8.595^2 + 8.595 + 3
Q = 83.846
Now we can calculate the producer surplus by finding the area between the supply curve and the price line up to Q = 83.846:
Producer Surplus = 1/2 * (8.595 - 0) * (83.846 - 0)
Producer Surplus = $357.93
This means that at the equilibrium point, producers are earning a total of $357.93 more from selling the good than they would be willing to sell it for.
Learn more about equilibrium here:
https://brainly.com/question/30807709
#SPJ11
if a fair coin is flipped, what is the probability that thethirdhead ap-pears on the eight trial? ninth? tenth?
The probability of flipping a head on a fair coin is 1/2. The probability of getting three heads in a row on the third, ninth, and tenth flips of a fair coin are 1/8, 1/32, and 1/32, respectively.
The probability of flipping a head on a fair coin is 1/2. If we flip a coin three times in a row, there are eight possible outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
Out of these eight outcomes, only one has three heads in a row, which is HHH. Therefore, the probability of getting three heads in a row on the third flip is 1/8.
If we flip the coin nine times in a row, there are 2⁹ = 512 possible outcomes. The probability of getting three heads in a row on the ninth flip can be found by breaking down the problem into smaller parts. We can consider the first six flips separately from the last three flips.
The probability of getting three heads in a row in the first six flips is 1/8. If this happens, the next three flips must be TTH or TTT, which has a probability of 1/4. Therefore, the probability of getting three heads in a row on the ninth flip is (1/8) x (1/4) = 1/32.
If we flip the coin ten times in a row, the probability of getting three heads in a row on the tenth flip can be similarly calculated. The probability of getting three heads in a row in the first seven flips is 1/8, and the probability of getting TTH or TTT on the last three flips is 1/4.
Therefore, the probability of getting three heads in a row on the tenth flip is (1/8) x (1/4) = 1/32.
In summary, the probability of getting three heads in a row on the third, ninth, and tenth flips of a fair coin are 1/8, 1/32, and 1/32, respectively.
To know more about probability refer here:
https://brainly.com/question/31120123#
#SPJ11
an animal shelter has 10 dogs and 10 cats. you adopt animals at random without looking. how many animals must you adopt to guarantee having at least 3 animals of the same type? how many animals must you adopt to guarantee having at least 3 cats?
To guarantee having at least 3 animals of the same type, you would need to adopt a total of 5 animals.
In the worst-case scenario, you would first adopt 2 cats and 2 dogs. By adopting a 5th animal, you would then have at least 3 animals of the same type, either 3 cats and 2 dogs, or 3 dogs and 2 cats. This is due to the Pigeonhole Principle, which states that if you have n categories and n+1 items, at least one category will contain more than one item.
In order to guarantee having at least 3 cats, you would need to adopt a total of 13 animals. This is because, in the worst-case scenario, you could first adopt all 10 dogs, followed by 3 cats. After adopting 13 animals, you would be certain to have at least 3 cats, as you would have exhausted the entire population of dogs in the shelter.
To learn more about Pigeonhole Principle click here
brainly.com/question/24491336
#SPJ11
If 3 pounds of kiwi fruit cost $3.99, how much will 4 pounds cost?
Answer:
5.32
Step-by-step explanation:
Divide the cost of the kiwi by 3 and then once divided, multiple divided number by 4
How is the graph of y = x - 8 obtained from
the graph of y=x?
Answer:
We must move the graph of y = x down by 8 units to generate the graph of y = x - 8. This may be accomplished by subtracting 8 from the y-coordinates of all the spots on the y = x graph.
For example, the point (0,0) on the y = x graph will change to (0, -8) on the y = x - 8 graph. Similarly, the point (1,1) on the y = x graph will shift to (1, -7) on the y = x - 8 graph, and so on for all other points on the graph.
As a result, the graph of y = x - 8 will be similar to the graph of y = x, but 8 units lower.
what is the answer to this please
The required value of the hypotenuse 'x' is 9.7.
To find out the measure of the hypotenuse or 'x' we are supposed to apply the Pythagoras theorem, as the given triangle is a right angle triangle.
So, following the Pythagorean theorem,
x²+10.1² = 14²
x = √[14²-10.1²]
x = 9.69
Thus, the requried value of the hypotenuse 'x' is 9.7.
Learn more about Pythagoras' theorem here:
https://brainly.com/question/343682
#SPJ1
sculpting a sculptor wants to remove stone from a cylindrical block that has a height of 3 feet to create a cone. the diameter of the base of the cone and cylinder is 2 feet. what is the volume of the stone that the sculptor must remove? round your answer to the nearest hundredth.
The volume of the stone that the sculptor must remove is 6.28 cubic feet of stone. Rounding to the nearest hundredth, the sculptor must remove approximately 6.28 cubic feet of stone.
To solve this problem, we need to use the formula for the volume of a cone, which is V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone. Since the diameter of the base of the cylinder and cone is 2 feet, the radius is 1 foot. First, we need to find the height of the cone. Since the height of the cylinder is 3 feet and the cone will have the same height, the height of the cone is also 3 feet. Next, we can plug in the values into the formula for the volume of the cone:
V = (1/3)π(1^2)(3)
V = π
So the volume of the cone is π cubic feet.
To find the volume of the stone that the sculptor must remove, we need to find the volume of the cylinder and subtract the volume of the cone from it. The formula for the volume of a cylinder is V = πr^2h.
V = π(1^2)(3)
V = 3π
So the volume of the cylinder is 3π cubic feet.
Now we can subtract the volume of the cone from the volume of the cylinder:
3π - π ≈ 6.28
Rounding to the nearest hundredth, the sculptor must remove approximately 6.28 cubic feet of stone.
Learn more about volume here
https://brainly.com/question/27710307
#SPJ11
band c please. thank you.dy dx x² + 4x+3 given that y = x² b) Find 1 y'given y=xVx+ x² y=xborot c) find
For part (b), we need to find y' or dy/dx. Using the power rule of differentiation, we can write: y = x² + 4x + 3, y' = 2x + 4
Therefore, the derivative of y with respect to x is 2x + 4. For part (c), we need to find y when y = x √(x + x²). The value of y is x^(3/2) √(1 + x).
a) For the function y = x², the derivative is found as follows:
Step 1: Identify the power rule for derivatives: (d/dx)(x^n) = nx^(n-1)
Step 2: Apply the power rule to y = x²: dy/dx = 2x^(2-1) = 2x
So, dy/dx for y = x² is 2x.
b) For the function y = x√x + x², the derivative is found as follows:
Step 1: Rewrite the function to simplify: y = x^(3/2) + x²
Step 2: Apply the power rule to each term: y' = (3/2)x^(1/2) + 2x
So, y' for y = x√x + x² is (3/2)x^(1/2) + 2x.
c) It seems that the third function may have missing or incorrect information (xborot). Please provide the correct function, and I'll be happy to help you find its derivative.
Learn more about power rule here: brainly.com/question/23418174
#SPJ11
Suppose 4x2 + 9y2 = 100, where x and y are functions of t. dy 1 (a) If find when x = 4 and y = 2. dt 위못 = dx 10) If = 3, find dy dt when x = -4 and y = 2. dy
So, when x = 4, y = 2, and dx/dt = 3, dy/dt = -8/3. we need to use the chain rule and implicit differentiation,
(a) If x = 4 and y = 2, we can substitute these values into the equation 4x^2 + 9y^2 = 100 to get:4(4)^2 + 9(2)^2 = 100 .
Simplifying, we get: 16 + 36 = 100, This is not true, so there is no solution for when x = 4 and y = 2. (b) To find dy/dt when x = -4 and y = 2 and dx/dt = 3, we first need to differentiate both sides of the equation 4x^2 + 9y^2 = 100 implicitly with respect to t: d/dt (4x^2 + 9y^2) = d/dt (100) .
Using the chain rule, we get: 8x (dx/dt) + 18y (dy/dt) = 0, We can substitute the given values to get: 8(-4) (3) + 18(2) (dy/dt) = 0, Simplifying, we get:
-96 + 36(dy/dt) = 0
Adding 96 to both sides and dividing by 36, we get:
dy/dt = 96/36
Simplifying, we get:
dy/dt = 8/3
Given the equation 4x^2 + 9y^2 = 100, where x and y are functions of t, let's find dy/dt when x = 4, y = 2, and dx/dt = 3.
First, differentiate both sides of the equation with respect to t:
8x(dx/dt) + 18y(dy/dt) = 0
Now, plug in the given values (x = 4, y = 2, and dx/dt = 3):
8(4)(3) + 18(2)(dy/dt) = 0,
Solve for dy/dt: 96 + 36(dy/dt) = 0
Divide by 36:
(dy/dt) = -96/36, Simplify: (dy/dt) = -8/3, So, when x = 4, y = 2, and dx/dt = 3, dy/dt = -8/3.
To know more about value click here
brainly.com/question/30760879
#SPJ11
Determine whether the pair of functions can be combined by function composition. If so, then
a. draw an input/output diagram for the new function.
b. write a statement for the new function complete with function notation and input and output units and descriptions.
Computer Chips The profit generated by the sale of c computer chips is P(c) dollars; The number of computer chips a manufacturer produces during t hours of production is C(t) chips.
The given functions are:
1. P(c) - the profit generated by the sale of c computer chips, in dollars.
2. C(t) - the number of computer chips produced during t hours of production, in chips.
Since the first function, P(c), takes the number of computer chips (c) as its input and the second function, C(t), outputs the number of computer chips (c) as a function of time (t), these functions can be combined by function composition.
a. Input/Output diagram for the new function:
t (hours) -> [C(t)] -> c (chips) -> [P(c)] -> P (dollars)
b. To write a statement for the new function using function notation, we need to express the profit function P(c) in terms of the time function C(t). This can be done by composing the functions as follows:
P(C(t)) - the profit generated by the sale of computer chips produced during t hours of production, in dollars.
This new function, P(C(t)), describes the relationship between the time spent on production (t) and the profit generated (P) in dollars.
refer, for more
https://brainly.com/question/10781304#
#SPJ11
two green balls, two red balls, and two yellow balls are placed in two green boxes, two red boxes, and two yellow boxes; one ball in each box. find the probability that no ball is in a box of the same color.
So the probability that no ball is in a box of the same color is 12/25.
Using the principle of inclusion-exclusion, we have:
P(not A_1 and not A_2 and not A_3) = P(not A_1) * P(not A_2 | not A_1) * P(not A_3 | not A_1 and not A_2)
To find these probabilities, we can use the following logic:
P(not A_1) = the first ball can be placed in any of the 5 remaining boxes (out of 5 boxes), so this probability is 5/5.
P(not A_2 | not A_1) = the second ball can be placed in any of the 4 remaining boxes of a different color (out of 5 boxes, with one color already taken by the first ball), so this probability is 4/5.
P(not A_3 | not A_1 and not A_2) = the third ball can be placed in any of the 3 remaining boxes of a different color (out of 5 boxes, with two colors already taken by the first two balls), so this probability is 3/5.
Therefore, we have:
P(not A_1 and not A_2 and not A_3) = (5/5) * (4/5) * (3/5) = 12/25
To know more about probability,
https://brainly.com/question/30034780
#SPJ11
If θ = and R = ,7squared 2 then F1 =
Answer:
im pretty sure the answer is 7
i need help
A circular cookie cake costs $12.56. If the diameter of the cookie cake is 8 inches, what is the approximate cost per square inch of the cookie cake? Use π = 3.14.
$0.04
$0.06
$0.16
$0.25
The approximate cost per square inch of the cookie cake is 0.25
What is the approximate cost per square inch of the cookie cake?From the question, we have the following parameters that can be used in our computation:
Diameter = 8 inches
So, the area is
Area = 3.14 * (8/2)^2
Evaluate
Area = 50.24
The approximate cost per square inch of the cookie cake is calcilaed as
Rate = 12.56/50.24
Evaluate
Rate = 0.25
Hence, the unit rate is 0.25
Read more about unit rate
https://brainly.com/question/4895463
#SPJ1
A circle has a center at point A ( 3, − 1 ) and a point on the circle is located at R ( 5,4 ). What is the location of S, on the diameter RS?
A circle has a center at point A ( 3, − 1 ) and a point on the circle is located at R ( 5,4 ). The location of S is (1, -6).
To find the location of S on the diameter RS, we need to first find the midpoint of RS, which will be the center of the circle. Then we can find the coordinates of S by using the distance formula.
The midpoint of RS is the average of the coordinates of R and S:
((5 + x)/2, (4 + y)/2)
Since the midpoint is the center of the circle, it has the same coordinates as point A:
((5 + x)/2, (4 + y)/2) = (3, -1)
We can solve this system of equations for x and y:
(5 + x)/2 = 3
(4 + y)/2 = -1
Solving for x and y, we get:
x = 1
y = -6
Therefore, the location of S is (1, -6).
To know more about circle here
https://brainly.com/question/24375372
#SPJ4
a metal rod of length 31 cm is placed in a magnetic field of strength 2.3 t, oriented perpendicular to the field.
Given a metal rod of length 31 cm placed in a magnetic field of strength 2.3 T, oriented perpendicular to the field, you need to consider the following:
1. The metal rod is 31 cm in length.
2. The magnetic field strength is 2.3 T (tesla).
3. The rod is positioned perpendicular to the magnetic field, which means that the angle between the rod and the magnetic field is 90 degrees.
In this scenario, the rod is placed in such a way that it experiences the full effect of the magnetic field due to its perpendicular orientation.
When a metal rod of length 31 cm is placed in a magnetic field of strength 2.3 T, oriented perpendicular to the field, it will experience a force. The force on the rod will be given by the formula F = BIL, where B is the magnetic field strength, I is the current flowing through the rod, and L is the length of the rod.
Since the rod is not connected to a circuit, there is no current flowing through it. Therefore, the force on the rod will be zero. However, if a current is passed through the rod, it will experience a force perpendicular to both the magnetic field and the direction of the current flow. The magnitude of the force will depend on the strength of the magnetic field, the current flowing through the rod, and the length of the rod.
Learn more about :
magnetic field : brainly.com/question/11514007
#SPJ11
A store sells T-shirts with logos on them. Last year, the store sold 500 of these T-shirts at $12 each. The sales manager is planning to increase the price. A survey indicates that for each $1 increase in price, 25 fewer T shirts will be sold per year.
What is the equation for this problem?
The equation for this problem, considering the increase in price and decrease in sales, is R = (12 + x) . (500 - 25x), as explained below.
How to find the equationFirst, let's establish the following:
R = revenueQ = quantityP = priceConsidering the information given in the prompt about the price of the shirts and the quantity sold, we have this equation, in which the price multiplied by the quantity equals the revenue:
P x Q = R
12 x 500 = 600
However, we are told that the company will increase the price in $1 and that, for each increase, 25 fewer shirts will be sold. Having x as the number of increases in price, the equation would be:
R = (12 + 1x) . (500 - 25x) or
R = 13 . (500 - 25x)
Learn more about equations here:
https://brainly.com/question/2972832
#SPJ1
Find the Distance between the two points (Round to the nearest tenth)
1. (0,1) (0,6)
2. (2,1) (5,6)
3. (4,6) (-2,-2)
here are the solutions to the distance problems:
To find the distance between the two points (0,1) and (0,6), we can use the distance formula:
Distance = √[(y2 - y1)² + (x2 - x1)²]
Substituting the values, we get:
Distance = √[(6 - 1)² + (0 - 0)²] = √25 = 5
Therefore, the distance between the two points is 5 units.
To find the distance between the two points (2,1) and (5,6), we can use the distance formula:
Distance = √[(y2 - y1)² + (x2 - x1)²]
Substituting the values, we get:
Distance = √[(6 - 1)² + (5 - 2)²] = √34 ≈ 5.8
Therefore, the distance between the two points is approximately 5.8 units (rounded to the nearest tenth).
To find the distance between the two points (4,6) and (-2,-2), we can use the distance formula:
Distance = √[(y2 - y1)² + (x2 - x1)²]
Substituting the values, we get:
Distance = √[(-2 - 6)² + (-2 - 4)²] = √80 ≈ 8.9
Therefore, the distance between the two points is approximately 8.9 units (rounded to the nearest tenth).
Find the indicated derivative and simplify. - 9x - 8 y' for y= x² + 7x 2 y' = = Find dy dt : y= (29+ e ') Int e 히 = dy dt (Type an exact answer.)
The derivative of y with respect to t is 2x + 7.
In our problem, we can see that y is a composite function of x, where y = f(g(x)), with f(x) = -8x and g(x) = x² + 7x. Therefore, we can apply the chain rule to find y' as follows:
y' = f'(g(x)) * g'(x) = -8 * (2x + 7) = -16x - 56
Substituting this value into the original expression, we get:
-9x - 8y' = -9x - 8(-16x - 56) = -9x + 128x + 448 = 119x + 448
Thus, the derivative of -9x - 8y' is 119x + 448.
Secondly, let us consider the problem of finding dy/dt, where y = x² + 7x and y' = 2x + 7. This problem involves the chain rule again, but this time we are dealing with the derivative of a function with respect to time, t. In this case, we need to apply the chain rule and multiply the derivative of y with respect to x (i.e., y') by the derivative of x with respect to t (i.e., dx/dt). This gives us:
dy/dt = dy/dx * dx/dt = (2x + 7) * dx/dt
To find dx/dt, we need to differentiate the function x = x(t) with respect to t. However, we are not given any information about the function x(t), so we cannot solve this problem exactly. Instead, we can use the chain rule to write:
dx/dt = dx/du * du/dt
where u is some other function of t. We can choose u = t, so that du/dt = 1 and dx/dt = dx/du. Since x = x(t), we have dx/du = 1, and hence dx/dt = 1. Substituting this value into the expression for dy/dt, we get:
dy/dt = (2x + 7) * dx/dt = (2x + 7) * 1 = 2x + 7
To know more about derivative here
https://brainly.com/question/30074964
#SPJ4