Values of the given expression are:
(a) (f∘g)(−2) = -7
(b) (g∘f)(−2) = -78
To evaluate the expression, we need to find the values of (f∘g)(−2) and (g∘f)(−2).
(a) (f∘g)(−2) means that we need to first plug in -2 into the g(x) function, and then plug in the result into the f(x) function.
So, g(-2) = 3 - (-2)^2 = 3 - 4 = -1
Now, we plug in -1 into the f(x) function:
f(-1) = 2(-1) - 5 = -2 - 5 = -7
Therefore, (f∘g)(−2) = -7.
(b) (g∘f)(−2) means that we need to first plug in -2 into the f(x) function, and then plug in the result into the g(x) function.
So, f(-2) = 2(-2) - 5 = -4 - 5 = -9
Now, we plug in -9 into the g(x) function:
g(-9) = 3 - (-9)^2 = 3 - 81 = -78
Therefore, (g∘f)(−2) = -78.
In conclusion, the values of the expression are a) (f∘g)(−2) = -7 and b) (g∘f)(−2) = -78.
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3. Consider the functionφ(x)=31x3−21x. (a) Show that 0 is a fixed point ofφ(x). (b) Show that the iterationxk+1=φ(xk)converges locally to 0 . (c) By numerical tests, find an initial guessx0such that the iteration converges to 0 and find an initial guessx0such that the iteration diverges.
From the function φ(x)=31x3−21x, 0 is a fixed point of φ(x) it shows in calculation below. The iteration xk+1 = φ(xk) converges locally to 0 shows below. The iteration diverges as k increases.
(a) To show that 0 is a fixed point of φ(x), we need to show that φ(0) = 0. Substituting x = 0 into the function gives us:
φ(0) = (3/1)(0)3 - (2/1)(0) = 0 - 0 = 0
Therefore, 0 is a fixed point of φ(x).
(b) To show that the iteration xk+1 = φ(xk) converges locally to 0, we need to show that |φ'(x)| < 1 for x near 0. Taking the derivative of φ(x) gives us:
φ'(x) = (9/1)x2 - (2/1)
At x = 0, φ'(0) = 0 - 2 = -2. Since |φ'(0)| > 1, the iteration does not converge locally to 0.
(c) By numerical tests, we can find an initial guess x0 such that the iteration converges to 0 and an initial guess x0 such that the iteration diverges. For example, if we choose x0 = 0.5, the iteration converges to 0:
x1 = φ(0.5) = (3/1)(0.5)3 - (2/1)(0.5) = -0.625
x2 = φ(-0.625) = (3/1)(-0.625)3 - (2/1)(-0.625) = 0.8203125
x3 = φ(0.8203125) = (3/1)(0.8203125)3 - (2/1)(0.8203125) = -0.4625244140625
And so on. The iteration converges to 0 as k increases.
On the other hand, if we choose x0 = 2, the iteration diverges:
x1 = φ(2) = (3/1)(2)3 - (2/1)(2) = 20
x2 = φ(20) = (3/1)(20)3 - (2/1)(20) = 23980
x3 = φ(23980) = (3/1)(23980)3 - (2/1)(23980) = 3.47119332792e+13
And so on. The iteration diverges as k increases.
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(-10,-15) is the image of N after the dilation with a scale factor of 5/4 centered at the orgin. What are the coordinates of N
The coordinates of N can be estimated as: (-8, -12)
What is the scale factor ?Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.
If point N is dilated with a scale factor of 5/4 centered at the origin, the coordinates of the image point, let's call it N', can be found by multiplying the coordinates of N by the scale factor:
N' = (5/4)N
We also know that the image point N' is located at (-10, -15), so we can substitute these values into the equation:
(-10, -15) = (5/4)N
Solving for N, we can multiply both sides by the reciprocal of 5/4, which is 4/5:
N = (4/5)(-10, -15)
N = (-8, -12)
Therefore, the coordinates of point N are (-8, -12).
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Uncle Moneybags has $500,000 saved for retirement. He has an account earning 8% interest. If Uncle Moneybags wants to be able to make withdrawals for 25 years, how much can he withdrawal each month? Round to the nearest cent.
Uncle Moneybags can withdrawal approximately $583.67 per month.
To find out how much Uncle Moneybags can withdraw each month, we can use the formula for the future value of an annuity:
FV = PMT × [(1 + i)ⁿ - 1] / i
Where:
FV = future value
PMT = payment amount
i = interest rate per period
n = number of periods
In this case, we want to solve for PMT, so we can rearrange the formula to:
PMT = FV × i / [(1 + i)ⁿ - 1]
We know that FV = $500,000, i = 8% / 12 = 0.00667, and n = 25 × 12 = 300. Plugging these values into the formula, we get:
PMT = $500,000 × 0.00667 / [(1 + 0.00667)³⁰⁰ - 1]
PMT = $500,000 × 0.00667 / 5.7435
PMT = $583.67
Therefore, Uncle Moneybags can withdraw $583.67 each month for 25 years.
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Suppose an object has a height of 0 feet after 10seconds. This same object has maximum height of 200 feet at 0 seconds. 1. Find H(T)=A(T−h)2+k where H(T) is the height of the object in feet after T seconds. Answers in Exact Form 2. When will the object have a height of 100 feet? Answers in Exact Form and round 3 decimals.
The object will have a height of 100 feet after 100 seconds.
The equation for the height of the object in feet after T seconds is H(T) = A(T - h)2 + k, where A and h are constants. Given that the object has a height of 0 feet after 10 seconds, and a maximum height of 200 feet at 0 seconds, we can solve for A and h.
We know that H(0) = 200, so k = 200.
We also know that H(10) = 0, so A(10 - h)2 + 200 = 0. Solving for A, we get A = -(h2 + 200) / 102.
Now we have an equation with two unknowns, A and h, so we can use substitution to solve for h. We can substitute -(h2 + 200) / 102 for A in our original equation, and solve for h. This gives us h = 10.
We now know A = -(102 + 200) / 102 = -20.
So, our equation for the height of the object in feet after T seconds is H(T) = -20(T - 10)2 + 200.
To find the height of the object after 100 seconds, substitute 100 for T in the equation. This gives us H(100) = -20(100 - 10)2 + 200 = 100.
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Find the area of this composite shape. Include correct units.
Show all your work.
LINEAR EQUATIONS AND INEQUALITIES Translating a phrase into a two-step expression Translate this phrase into an algebraic expression. 15 more than twice Chrissy's savings Use the variable c to represent Chrissy's savings.
The algebraic expression that translates the given phrase is 2c + 15, where c is the amount of Chrissy's savings.
To translate the phrase "15 more than twice Chrissy's savings" into an algebraic expression:
1. First, we need to identify the variable. In this case, the variable is c, which represents Chrissy's savings.
2. Next, we need to identify the operations and numbers involved in the phrase. The phrase "twice Chrissy's savings" means that we need to multiply c by 2.
3. The phrase "15 more than" means that we need to add 15 to the result of the multiplication.
4. Putting these steps together, we get the algebraic expression 2c + 15.
So the final answer is 2c + 15.
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Suppose you have a job that pays $13.50 per hour and you work anywhere from 10 to 40 hours per week. a. Write an equation, with a restriction on the variable I, that gives the amount of money, y, you will earn for working 2 hours in one week. y = _____ , Preview with ____ <= x <= ____ b. Use the function rule you have written in part a. to find the y values for the given z values: x = 10, y = ___ x = 20, y= ___
x = 30, y = ____. x = 40, y = ____ c. Construct a line graph from the information found in b. 520+ -480+ 440+ 400- 360 320- 280- 240 200 160+ 120+ 80- 40+ 10 20 30 40 Clear All Draw: Line Dot Open Dot d. State the domain and range of this function. Domain: ____ <= x <= ______
Range: <= y <= _____
e. What is the minimum amount you can earn in a week with this job? You'll earn at least $ ______.
What is the maximum amount? You can earn up to $ ____.
The maximum amount you can earn is $540
a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.
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Please help me with this math question!
Given that Line segment AB ║ LIne segment DC, and Line segment AD ║ Line segment BC,
∠ABC = 102°∠BCD = 78°∠CDA = 102°; and ∠DAB = 78°.What is the rationale for the above response?1) Note that ∠78° and ∠ABC are Supplementary Angles on the basis of angles on a straight line. Thus,
∠ABC = 180 - 78 = 102°
2) Note that ∠ABC and ∠BCD are Supplementary Angles on the basis of Adjacent Angles in a parallelogram.
Thus,
∠BCD = 180° - 102° = 78°
3) ∠CDA = 102° on the basis of Opposite angles of a parallelogram
4) ∠DAB = 78° on the basis of Opposite angles of a parallelogram
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For a dish party, Alia needs to seat four people at a round table. How many combinations are possible?
For a dish party, Alia needs to seat four people at a round table. There are 24 possible combinations of seating arrangements.
This is because each person has 3 options (clockwise, counter-clockwise, opposite), for a total of 34 or 81 combinations. However, due to symmetry, half of these are the same combinations with the people just shifted around the table, so we are left with 24 total combinations.
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3 1 2 pounds of apples cost $7. 0. What is the price per pound?
The price per pound of the apples is $3.50. This is calculated by dividing the total cost, $7.00, by the weight of the apples, 2 pounds.
The price per pound of the apples can be found by dividing the total cost by the weight of the apples. In this example, the total cost of the apples is $7.00 and the weight is 2 pounds. To calculate the price per pound, divide 7.00 by 2. This gives us 3.50, which is the price per pound of the apples. Knowing the price per pound is useful when you are trying to figure out how much a certain amount of apples will cost. For example, if you wanted to buy 5 pounds of apples, you would multiply 5 by 3.50, which would give you $17.50. This is the total cost of the 5 pounds of apples. In addition to helping you figure out how much certain amounts of apples will cost, knowing the price per pound can also help you compare prices between stores. For example, if you found apples for $4.00 per pound at one store, and $3.50 per pound at another store, you could easily determine which store has the better deal.
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а please help me solve this question using markov chain A product is processed on two sequential machines, I and II. The inspection takes place after a product unit is completed on either machine. There is a 5% chance that the unit will be junked before inspection. After inspection, there is a 3% chance the unit will be junked, and a 7% chance of being returned to the same machine for reworking. Else, a unit passing inspection on both machines is good. (a) For a part starting at machine I, determine the average number of visits to each state. (b) If a batch of 1000 units is started on machine I, determine the average number of completed good units.
The average number of completed good units is 920
A Markov chain is a type of sequential machine that can be used to model the process of inspection and reworking in this question. The Markov chain will have four states: Machine I, Machine II, Inspection, and Junked.
(a) To determine the average number of visits to each state for a part starting at Machine I, we can create a transition matrix with the probabilities of moving from one state to another. The transition matrix will look like this:
| 0.92 0.05 0.03 0 |
| 0.07 0.85 0.03 0.05 |
| 0 1 0 0 |
| 0 0 0 1 |
The first row represents the probabilities of moving from Machine I to each of the other states. The second row represents the probabilities of moving from Machine II to each of the other states. The third row represents the probabilities of moving from Inspection to each of the other states. The fourth row represents the probabilities of moving from Junked to each of the other states.
To find the average number of visits to each state, we can multiply the transition matrix by a vector representing the initial state. In this case, the initial state is Machine I, so the vector will be [1 0 0 0]. Multiplying the transition matrix by this vector will give us the average number of visits to each state:
| 0.92 0.05 0.03 0 | | 1 | | 0.92 |
| 0.07 0.85 0.03 0.05 | * | 0 | = | 0.07 |
| 0 1 0 0 | | 0 | | 0.03 |
| 0 0 0 1 | | 0 | | 0 |
So the average number of visits to Machine I is 0.92, the average number of visits to Machine II is 0.07, the average number of visits to Inspection is 0.03, and the average number of visits to Junked is 0.
(b) If a batch of 1000 units is started on Machine I, we can use the same transition matrix to find the average number of completed good units. We will multiply the transition matrix by a vector representing the initial state of 1000 units on Machine I:
| 0.92 0.05 0.03 0 | | 1000 | | 920 |
| 0.07 0.85 0.03 0.05 | * | 0 | = | 70 |
| 0 1 0 0 | | 0 | | 30 |
| 0 0 0 1 | | 0 | | 0 |
The average number of completed good units is 920.
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2x^2 + 2y^2 + 16x + 16y + 32 = 0 is the equation of a circle with center (h, k) and radius r for: h= ____ and k= ____ and r= _____
So the equation of the circle is (x+4)^2 + (y+4)^2 = 4^2 with center (-4, -4) and radius 4
The equation of a circle is given by (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center of the circle and r is the radius. We need to rearrange the given equation to match this form.
2x^2 + 2y^2 + 16x + 16y + 32 = 0
Divide both sides of the equation by 2:
x^2 + y^2 + 8x + 8y + 16 = 0
Rearrange the terms:
x^2 + 8x + y^2 + 8y = -16
Complete the square for both x and y terms:
(x^2 + 8x + 16) + (y^2 + 8y + 16) = -16 + 16 + 16
(x+4)^2 + (y+4)^2 = 16
Now the equation is in the standard form of a circle equation, and we can find the center (h,k) and radius r:
h = -4, k = -4, r = 4
So the equation of the circle is (x+4)^2 + (y+4)^2 = 4^2 with center (-4, -4) and radius 4.
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The median stock price for firms in the Camaro Stock Market is $30, and the standard deviation is $8.20. Assume that the stock prices are normally distributed.
(i) What is the probability a firm will have a stock price of at least $40?
(ii) How high does a stock price have to be to put a firm in the top 10%?
Do NOT use EXCEL
a) (i) 0.3112
(ii) 20.50
b) (i) 0.2112
(ii) 50.50
c) (i) 0.1112
(ii) 40.50
d) (i) 0.6112
(ii) 30.50
e) None of the answers are correct
The probability a firm will have a stock price of at least $40 is 0.1112. There should be 40.50 stock price have to be to put a firm in the top 10%. The correct answer is e) None of the answers are correct.
(i) To find the probability that a firm will have a stock price of at least $40, we need to find the z-score for $40 and use the standard normal table to find the corresponding probability. The z-score is calculated as (x - μ)/σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
In this case, the z-score for $40 is (40 - 30)/8.20 = 1.22. Using the standard normal table, we find that the probability of a z-score less than 1.22 is 0.8888. Therefore, the probability of a stock price of at least $40 is 1 - 0.8888 = 0.1112.
(ii) To find the stock price that puts a firm in the top 10%, we need to find the z-score that corresponds to the 90th percentile in the standard normal table. The z-score for the 90th percentile is 1.28. We can then use the formula x = μ + zσ to find the stock price that corresponds to this z-score. In this case, the stock price is 30 + 1.28(8.20) = 40.50.
Therefore, the correct answer is (i) 0.1112 and (ii) 40.50.
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The dashed function is the graph of F, and the solid function is the graph of g. Express g in terms of F.
The equation of the function g(x) in terms of the function f(x) has the equation of g(x) = -2f(x + 2) + 3
How to express the function g(x) in terms of f(x)Given the graph of functions f(x) and g(x)
Where
y = f(x) -- the parent function
y = g(x) --- the transformed function (the dashed line)
The transformation of f(x) to g(x) is as follows
First, the graph of y = f(x) is moved 2 units to the left
This is represented as f(x + 2)
Next, the shifted graph of y = f(x) is reflected across the x-axis and then stretched vertically by a factor of 2.
This is represented as -2f(x + 2)
Lastly, the reflected and stretched graph is moved 3 units up
This is represented as -2f(x + 2) + 3
This means that
g(x) = -2f(x + 2) + 3
So, the function g(x) is g(x) = -2f(x + 2) + 3
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Divide x²-5x+6 by ( x-2)
plsss helpp :)
yellow candies:___ total
green candies:____ total
so there will be ___ more yellow then green candies
Answer:
yellow candies:__96_ total
green candies:___72_ total
so there will be _24__ more yellow then green candies
Step-by-step explanation:
Answer:
Step-by-step explanation:
yellos candies 42 bceuase 82 divided by it you gergt it and green 4 becase you duve it
david is filling five 3/4 quart bottles wich a sports drink his measuring cup only holds 1/4 quart. how many times will david need to fill the measuring cup in order to fill the 5 bottles
David will need to fill the measuring cup 15 times in order to fill the 5 bottles.
What does measurement mean?An object or event's attributes are quantified through measurement so that they can be compared to those of other things or events. Measurement, then, is the process of establishing how big or small a physical quantity is in relation to a fundamental reference quantity of the same kind.
Each bottle holds 3/4 of a quart, and his measuring cup holds 1/4 of a quart.
David will have to fill his measuring cup 3 times in order to fill 1 bottle of capacity 3/4 quarts.
For 5 bottles, it will be 3*5 times which results in 15 times.
Thus, David will need to fill the measuring cup 15 times in order to fill the 5 bottles.
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When Mason goes to the gym, he spends one half of an hour lifting weights and one third of an hour on the treadmill. Which are correct descriptions of the relationship of time Mason spends lifting weights and on the treadmill.
Mason spends one half of an hour lifting weights and one third of an hour on the treadmill, so the ratio of time Mason spends lifting weights to time Mason spends on the treadmill is 1:2.
How Treadmill works?A treadmill is a machine used for walking or running while staying in one place. It usually has a belt and a platform to stand on, and the belt moves at a speed determined by the user. It is a great way to get a good cardio workout.
The question asks which are correct descriptions of the relationship of time Mason spends lifting weights and on the treadmill.
Mason spends one half of an hour lifting weights and one third of an hour on the treadmill, so the fraction of time Mason spends lifting weights is 2/3.
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Ifx(23)+y(−10)=(106), then the values ofxandyare Ifpsvqtwrux=−7then−2p2s2v−qtw−ruxis is: Select one: 14−147−7IfAandBare square matrices of order 3 such that∣A∣=−1and∣B∣=3then∣3AB∣is
The values of x and y are determined by solving the equation
The values of x and y can be found by solving the equation x(23) + y(-10) = (106). This can be done by isolating one variable and solving for the other. For example, isolating x gives us x = (106 + 10y)/23. We can then plug this value of x back into the original equation and solve for y. Once we have the value of y, we can plug it back into the equation for x to find the value of x.
The value of −2p2s2v−qtw−rux can be found by plugging in the given values of p, s, v, q, t, w, r, and u into the equation and simplifying.
The value of ∣3AB∣ can be found by using the properties of determinants of matrices. Specifically, the determinant of a product of matrices is equal to the product of the determinants of the individual matrices. Therefore, ∣3AB∣ = ∣3∣∣A∣∣B∣ = 3(-1)(3) = -9.
So, the values of x and y are determined by solving the equation x(23) + y(-10) = (106), the value of −2p2s2v−qtw−rux is found by plugging in the given values and simplifying, and the value of ∣3AB∣ is found by using the properties of determinants of matrices.
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Write the quadratic equation in standard form: − 8x+19=-2x^²
Deandre has scored 88, 93, 95, and 86 on his previous four tests. What score does he need on his next test so that his average (mean) is 87?
Answer:
see below
Step-by-step explanation:
84
i took the test
Use a sum or difference formula to find the exact value of the following. tan 41° + tan 19° 1-tan 41°tan 19°
The exact value of the expression is √3.
To find the exact value of the given expression, we can use the sum formula for tangent. The formula is:
Tan (A + B) = (tan A + tan B) / (1 - tan A tan B)
Where A and B angle.
In this case, A = 41° and B = 19°. Plugging these values into the formula, we get:
Tan (41° + 19°) = (tan 41° + tan 19°) / (1 - tan 41° tan 19°)Simplifying the left side of the equation gives us:
Tan 60° = (tan 41° + tan 19°) / (1 - tan 41° tan 19°)We know that tan 60° = √3.
Substituting this value into the equation gives us:√3 = (tan 41° + tan 19°) / (1 - tan 41° tan 19°)
Cross-multiplying and simplifying gives us:
√3 (1 - tan 41° tan 19°) = tan 41° + tan 19°√3 - √3 tan 41° tan 19° = tan 41° + tan 19°
We can rearrange the terms to get:
√3 = tan 41° + tan 19° + √3 tan 41° tan 19°
This is the same expression that we were given in the question.
Therefore, the exact value of the expression is √3.
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1.
Function Family:
2.
3
Key Features: Domain; x & y intercepts
Domain:
x-intercepts:
y-intercepts:
Domain:
ES
Mar 1
12:15 1 US
▸
Function Family: quadratic
Domain: all real numbers
x-int: (0,0) and (2,0)
y-int: (0,0)
Please explain this more in depth. How does the chain rule allow
the first equation to reduce to the second equation? Some simple
explanation of the chain rule would also be helpful.
The chain rule allows us to reduce the first equation to the second equation by finding the derivative of the composite function and substituting it for the original function. This provides a simpler and more concise explanation of the relationship between the two equations.
The chain rule is a formula for calculating the derivative of a composite function. It states that the derivative of a composite function f(g(x)) is equal to the derivative of f with respect to g times the derivative of g with respect to x. In mathematical notation, this is expressed as (f(g(x)))' = f'(g(x)) * g'(x).
In the case of the first equation, we can use the chain rule to reduce it to the second equation by applying the formula mentioned above. First, we need to identify the composite function and its components. In this case, the composite function is f(g(x)) and the components are f and g.
Next, we need to find the derivative of f with respect to g and the derivative of g with respect to x. Once we have these derivatives, we can multiply them together to get the derivative of the composite function.
Finally, we can reduce the first equation to the second equation by substituting the derivative of the composite function for the original composite function. This will give us the second equation, which is a simplified version of the first equation.
In conclusion, the chain rule allows us to reduce the first equation to the second equation by finding the derivative of the composite function and substituting it for the original function. This provides a simpler and more concise explanation of the relationship between the two equations.
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300
Som
4
Question Details
To earn full credit, you must show ALL
of your steps and calculation leading to
your solution. You will be assessed on
your mathematical communication, use
of mathematics and accuracy of your
Find the area of the composite figure.
DESMOS CALCULATOR LINK
9
D
The arithmetic mean of two numbers is half their sum, and the geometric mean is the square root of their product. using log properties, show how we can think of the log of the geometric mean of v and w as the arithmetic mean of two related numbers, p and q. expand and simplify
We have shown that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.
We can use the properties of logarithms to show that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.
First, recall that the arithmetic mean of two numbers is half their sum:
arithmetic mean = (v + w)/2
And the geometric mean is the square root of their product:
geometric mean = √(v*w)
Now, let's take the log of the geometric mean:
log(geometric mean) = log(√(v*w))
Using the property of logarithms that log(a*b) = log(a) + log(b), we can expand the expression:
log(√(v*w)) = log(√v) + log(√w)
Using the property of logarithms that log(a^b) = b*log(a), we can simplify the expression:
log(√v) + log(√w) = (1/2)*log(v) + (1/2)*log(w)
Now, we can see that the log of the geometric mean is the arithmetic mean of the logs of the two numbers:
log(geometric mean) = (log(v) + log(w))/2
So, if we let p = log(v) and q = log(w), we can see that the log of the geometric mean of v and w is the arithmetic mean of p and q:
log(geometric mean) = (p + q)/2
Therefore, we have shown that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.
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Calculus Problem…
Suppose a and b span R². Determine the values of x and y, given that (2-x)a + b is
equal to ya + (x-3)b.
The values of x and y that satisfy the given equation are x = 2 and y = 1.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.
Since a and b span R², any vector in R² can be expressed as a linear combination of a and b.
Let's call the coefficients of this linear combination c₁ and c₂ so that any vector v in R² can be expressed as:
v = c₁a + c₂b
Now let's use this fact to solve the given equation:
(2-x)a + b = ya + (x-3)b
We can rearrange this equation to get all the terms with an on one side and all the terms with b on the other side:
(2-x)a - ya = (3-x)b
Now we can write both sides of the equation as linear combinations of a and b:
(2-x)a - ya = 2a - xa - ya = (2-x)a - (x-2)a - ya = (2-x - x + 2)a - ya = (4 - 2x)a - ya
(3-x)b = 3b - xb = 3b - xb + 3b - 3b = (6 - x)b - 3b = (6 - x - 3)b = (3 - x)b
So now we have:
(4 - 2x)a - ya = (3 - x)b
Since a and b span R², we know that any vector in R² can be expressed as a linear combination of a and b. Therefore, we can write:
(4 - 2x)a - ya = c₁a + c₂b
(3 - x)b = c₁a + c₂b
Now we can set the coefficients of a and b equal to each other and solve for x and y:
4 - 2x = c₁
-y = c₂
3 - x = c₂
Substituting the third equation into the second equation, we get:
-y = 3 - x
Solving for x and y, we get
x = 2
y = 1
Therefore, the values are x = 2 and y = 1.
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Evaluate (122two _ 202three)_ 1001three
The expression (122two _ 202three)_ 1001three can be evaluated by breaking it down into its constituent parts.
What is expression in math?Expression in math is a combination of numbers, symbols, and/or operations that represent a mathematical statement. Expressions can be used to calculate values, solve equations, and to model real-world problems. Expressions can be simple or complex and can range from basic arithmetic operations to more complex functions and equations. Expressions are an essential part of mathematics and are used to represent equations, formulas, and even solutions to complex problems.
The first part, 122two, is a number and can be evaluated to 122. The second part, 202three, is also a number and can be evaluated to 203. The third part, 1001three, is also a number and can be evaluated to 1002. Taking the evaluation of each part (122, 203 and 1002), the overall expression (122two _ 202three)_ 1001three can be evaluated to 121.
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You have $109 in the bank and your parents just gave you $281 for your birthday. Now you have exactly enough money to buy a laptop. How much does the laptop cost? Write an equation to represent the question. Use x as the variable.
Answer:
$109+$281=x when x=391
so that means a laptop equals $391 dollars
help, it is dpecial products of polynomials and or just polynomias
The solution is, (x + 6) and (2x - 5) are the factors of polynomial
2x^2 + 7x - 30.
What are Polynomials?Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.
3x+2x-5, for example, is a polynomial.
A binomial is a two-term polynomial.
For instance, x²ˣ-2ˣ² and x⁶ˣ-6ˣ⁶ are both binomials.
here, we have,
given that,
2x^2 + 7x - 30 is the polynomial .
now, we have to factorize it.
so, we get,
2x2 + 7x - 30
2x2 + 12x - 5x - 30
2x( x + 6) - 5( x + 6)
so, we have,
(x + 6) and (2x - 5) are the factors.
Hence, The solution is, (x + 6) and (2x - 5) are the factors of polynomial
2x^2 + 7x - 30.
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