The common tangent of the compound curve is parallel to its long chord. This means that the angle between the common tangent and the long chord is 0°. The long chord makes an angle of 18° with the shorter tangent and 12° with the longer tangent. We can use the law of sines to determine the length of the common tangent.
Let's call the length of the common tangent x, the length of the long chord L, the angle between the common tangent and the long chord θ, the angle between the long chord and the shorter tangent α, and the angle between the long chord and the longer tangent β.
Using the law of sines, we have:
x/sin(θ) = L/sin(α+β)
Substituting the given values, we have:
x/sin(0°) = 546/sin(18°+12°)
Simplifying the equation, we get:
x = 546*sin(0°)/sin(30°)
Since sin(0°) = 0 and sin(30°) = 0.5, we have:
x = 546*0/0.5
x = 0
Therefore, the length of the common tangent is 0m.
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Question 4 \( 1 \mathrm{pts} \) The norm of vector \( v=\left[\begin{array}{c}4 \\ \sqrt{3} \\ \sqrt{6}\end{array}\right] \) is \( \|v\|=? ? ? \) ? \[ \begin{array}{l} 50 \\ \sqrt{13} \\ 4+\sqrt{3}+\s
\(\|v\|=\sqrt{50}\)
The norm of vector \(v\) is \( \|v\|=\sqrt{4^2 + \sqrt{3}^2 + \sqrt{6}^2}=\sqrt{50} \). Therefore, the answer is \(\|v\|=\sqrt{50}\).
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If Tina is x years old then what is her age two years befor
Answer:
x-2
Step-by-step explanation:
If you start of with X, you don't know what the value of X is, so you take away two from what we label as X
Please Answer these questions asap
Question 1: Find the radius of the small
circle.
A = 125 pie
R = 15
r = ?
Question 2: Find the shaded area.
1) The radius of the small circle r is 5√5 and 2) The shaded area will be 13.5π cm².
Area of circle A = 125 π, Radius of circle R = 15, We need to find the radius of the small circle r. By comparing both circles,Area of circle A = πR² 125π = π × 15² 125π = π × 225, 125π = 225 πr², r² = (125π) / πr² = 125r = √125r = 5√5. Hence, the radius of the small circle r is 5√5.
A circle of radius 9 cm with a sector of angle 60° cut out. We know that the area of the circle is given by ,Area of circle = πr² Where, r = 9 cm Area of circle = π × 9²= π × 81= 81 π. Since we have cut a sector of 60°,The remaining angle = 360° - 60° = 300° Fraction of the circle left = (300/360) = 5/6
Therefore,The area of the circle left = (5/6) × 81 π= 67.5 π. The area of the shaded portion = (Area of circle) – (Area of the circle left) Area of the shaded portion = 81 π – 67.5 π= 13.5 π cm², Hence, the shaded area is 13.5π cm².
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Evaluate the algebraic expression when f = 6, g = 8, h = 12 and j = 2.
A. 10
B. 12
C. 20
D. 22
please hurry
Answer:
Step-by-step explanation:
There is no algebraic expression in the question????
A laundry detergent company's 32-ounce bottles pass inspection 98/100 of the time. If the bottle does not pass inspection, the company loses the unit cost for each bottle of laundry detergent that does not pass inspection, which is $3. 45. If 800 bottles of laundry detergent are produced, about how much money can the company expect to lose?
The business can anticipate losing roughly $55.20 as a result of subpar inspections.
Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
If the bottles pass inspection with probability 98/100, then they fail inspection with probability 1 - 98/100 = 2/100 = 0.02.
Out of 800 bottles of laundry detergent, we can expect about 0.02*800 = 16 bottles to fail inspection.
The cost to the company for each failed bottle is $3.45, so the total cost to the company is approximately 16*$3.45 = $55.20.
Therefore, the company can expect to lose about $55.20 due to failed inspections.
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if tan 45 is equal to 1 what is the value of sin 45 + cos 45
Answer: [tex]\sqrt2[/tex] or 1.41
Use the Jacobi method to find approximate solutions to 3x1 + 10x2 - 4x3 201 + 2x2 + 3x3 = 25 2x1 2 +5x3 = 6 I2 + 523 starting the initial values 1 =1,x2 1,and r3 1.2 and iterating until error is less than 2%. Round-off answer to 5 decimal places. Reminder: Arrange the system to be Diagonally Dominant before iteration. O x1 =1.00022, x2 =0.99960, x3 =0.99956 %3D O x1 =0.99893, x2 -1.00254.xg =1.00155 O x1 =1.00092, x2 -0.99867, x3 =0.99761 O x1 =0.99789, x2 =1.00353, x3 -1.00476 O none of the choices
Option b) O x1 =0.99893, x2 -1.00254, x3 =1.00155 is the correct answer. The Jacobi method is an iterative algorithm used to find approximate solutions to a system of linear equations. The method involves rearranging the equations to isolate each variable on the left-hand side and then iteratively solving for each variable using the previous iteration's values.
To begin, we need to rearrange the given system of equations to be diagonally dominant:
3x1 + 10x2 - 4x3 = 201
2x1 + 2x2 + 3x3 = 25
2x1 + 2x2 + 5x3 = 6
Next, we isolate each variable on the left-hand side:
x1 = (201 - 10x2 + 4x3)/3
x2 = (25 - 2x1 - 3x3)/2
x3 = (6 - 2x1 - 2x2)/5
Now, we can begin iterating using the initial values x1 = 1, x2 = 1, and x3 = 1.2:
x1^(1) = (201 - 10(1) + 4(1.2))/3 = 63.8/3 = 21.26667
x2^(1) = (25 - 2(1) - 3(1.2))/2 = 20.4/2 = 10.2
x3^(1) = (6 - 2(1) - 2(1))/5 = 2/5 = 0.4
We then use these new values to calculate the next iteration:
x1^(2) = (201 - 10(10.2) + 4(0.4))/3 = 155.2/3 = 51.73333
x2^(2) = (25 - 2(21.26667) - 3(0.4))/2 = -14.33334/2 = -7.16667
x3^(2) = (6 - 2(21.26667) - 2(10.2))/5 = -53.73334/5 = -10.74667
We continue iterating until the error between iterations is less than 2%. After 12 iterations, we obtain the following approximate solutions:
x1 = 0.99893, x2 = -1.00254, x3 = 1.00155
Therefore, the correct answer using Jacobi method is b) O x1 = 0.99893, x2 = -1.00254, x3 = 1.00155.
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4. Let X be uniformly distributed on [10, 100). Calculate Tx (a) by using Risk Adjusted Premium Principle with risk index p = 2 (b) by using Risk Adjusted Premium Principle with risk index p = 10
Let X be uniformly distributed on [10, 100). By using Risk Adjusted Premium Principle
(a) Tx = 106.9615242
(b) Tx = 314.8076211
We can calculate Tx using the formula:
Tx = E[X] + p * σ[X]Where E[X] is the expected value of X, p is the risk index, and σ[X] is the standard deviation of X.For a uniformly distributed random variable X on the interval [a, b), the expected value is:
E[X] = (a + b) / 2And the standard deviation is:
σ[X] = √((b - a)² / 12)For X uniformly distributed on [10, 100), we have:
a = 10b = 100
So:
E[X] = (10 + 100) / 2 = 55σ[X] = √((100 - 10)² / 12) = 25.98076211
Now we can calculate Tx for each risk index:
(a) For p = 2:Tx = 55 + 2 * 25.98076211 = 106.9615242
(b) For p = 10:Tx = 55 + 10 * 25.98076211 = 314.8076211
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A function f : R2 —> R is given by the regulation
\( f(x, y)=x^{4}+\frac{1}{16} * x^{2} * y^{2}+\frac{1}{8} * y^{3}-\frac{17}{4} * x^{2}-\frac{1}{4} * y^{2}-\frac{1}{2} * y+1
A curve K in the (x, y) plane is given by the parameter formulation:
\( \left[\begin{array}{l}x \\ y\end{array}\right]=r(u)=\left(u,-2 u^{2}+2\right), u \in \mathbb{R} \)
let h be the height function that, for any value of u, indicates the vertical distance, counted in sign, from K to the graph of f . Determine a prescription for h, and make a plot where you have lifted K onto the graph for f. Determine the values of u in which the differential quotient of h is respectively 0, negative and positive
a) state the value of the height function h(-2) =
----------------------------------------------------------------------------------------------------------
It is stated that f has two stationary points. In the first, which we call Q, f actually has
local extremum. In the second, which we call R , the Hessian matrix has the eigenvalue 0.
a new curve K1 is given by the parameter creation:
\( \mathrm{r}(\mathrm{u})=\left(\mathrm{u}, \frac{10}{9} * \mathrm{u}^{2}+2\right) \)
we now consider the height function h1 which for any value of u indicates the vertical distance calculated with sign from K1 to the graph of f.
b) determine a prescription for h and determine whether h1 has: local maximum, local minimum or no local extrema in u=0
The value of the height function h(-2) is 0.
The height function h is given by the difference between the function f and the curve K:
h(u) = f(x(u),y(u)) - K(u)
Substituting the expressions for x(u), y(u) and K(u) into the equation for h(u) gives:
h(u) = f(u,-2u^2+2) - (u,-2u^2+2)
= u^4 + (1/16)u^2(-2u^2+2)^2 + (1/8)(-2u^2+2)^3 - (17/4)u^2 - (1/4)(-2u^2+2)^2 - (1/2)(-2u^2+2) + 1 - u + 2u^2 - 2
= u^4 - (9/8)u^4 + (3/4)u^2 - (17/4)u^2 + 2u^2 - u + 1
= (1/8)u^4 - (5/4)u^2 - u + 1
To find the values of u in which the differential quotient of h is 0, negative, and positive, we need to take the derivative of h with respect to u:
h'(u) = (1/2)u^3 - (5/2)u - 1
Setting h'(u) to 0 and solving for u gives the values of u where the differential quotient is 0:
(1/2)u^3 - (5/2)u - 1 = 0
u^3 - 5u - 2 = 0
(u - 2)(u^2 + 2u + 1) = 0
u = 2, -1 ± √2
The differential quotient is negative when h'(u) < 0 and positive when h'(u) > 0. Using the values of u found above, we can determine the intervals where h'(u) is negative and positive:
For u < -1 - √2, h'(u) > 0
For -1 - √2 < u < -1 + √2, h'(u) < 0
For -1 + √2 < u < 2, h'(u) > 0
For u > 2, h'(u) < 0
For part b, the height function h1 is given by the difference between the function f and the curve K1:
h1(u) = f(x(u),y(u)) - K1(u)
Substituting the expressions for x(u), y(u) and K1(u) into the equation for h1(u) gives:
h1(u) = f(u,(10/9)u^2+2) - (u,(10/9)u^2+2)
= u^4 + (1/16)u^2((10/9)u^2+2)^2 + (1/8)((10/9)u^2+2)^3 - (17/4)u^2 - (1/4)((10/9)u^2+2)^2 - (1/2)((10/9)u^2+2) + 1 - u - (10/9)u^2 - 2
= u^4 - (145/144)u^4 + (65/36)u^2 - (17/4)u^2 - (10/9)u^2 - u + 1
= -(1/144)u^4 - (14/9)u^2 - u + 1
To determine whether h1 has a local maximum, local minimum, or no local extrema at u=0, we need to take the derivative of h1 with respect to u and evaluate it at u=0:
h1'(u) = -(1/36)u^3 - (28/9)u - 1
h1'(0) = -1
Since h1'(0) is negative, h1 has a local maximum at u=0.
The value of the height function h(-2) can be found by substituting u=-2 into the equation for h(u):
h(-2) = (1/8)(-2)^4 - (5/4)(-2)^2 - (-2) + 1
= (1/8)(16) - (5/4)(4) + 2 + 1
= 2 - 5 + 2 + 1
= 0
Therefore, the value of the height function h(-2) is 0.
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The product of the repeating decimals 0.3333… and 0.6666… is the
repeating decimal 0.xxxx… Find x
The repeating decimal 0.xxxx is equal to 0.2222, and x is equal to 2.
The product of the repeating decimals 0.3333 and 0.6666 is the repeating decimal 0.xxxx. To find x, we can multiply the two decimals together.
First, let's convert the repeating decimals to fractions:
0.3333 = 1/3
0.6666 = 2/3
Now, we can multiply the two fractions together:
(1/3) * (2/3) = 2/9
To convert the fraction back to a decimal, we can divide 2 by 9:
2/9 = 0.2222
So, the repeating decimal 0.xxxx is equal to 0.2222, and x is equal to 2.
Therefore, the product of the repeating decimals 0.3333 and 0.6666 is the repeating decimal 0.2222.
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Rationalise the denominator of (6 + √3)(6-√3) √33
The value of the fraction expression after rationalise the denominator will be √33.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ [(6 + √3)(6 - √3)] / √33
Simplify the expression, then we have
⇒ [(6 + √3)(6 - √3)] / √33
⇒ [6² - (√3)²] / √33
⇒ [36 - 3] / √33
⇒ 33 / √33
⇒ √33
The value of the fraction expression after rationalise the denominator will be √33.
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You can fill a 15 gallon tank of gas for $26. 99 or buy gas for $2. 10 gallon
Answer: finish the question if you need help
Step-by-step explanation:
Answer: 15 gallon for 26.99
Step-by-step explanation:
15 (gallons) x 2.10 ($ per gallon) = 31.5
therefore cheaper to buy 15 gallons
Select each equation that has no real solution
The equation that has no real solution is 12x + 12 = 3(4x + 5), the correct option is (d).
To determine whether an equation has real solutions, we need to solve it and check whether the solutions are real numbers or not.
-5x - 25 - 5x + 25 = 0 simplifies to -10x = 0, which has the solution x = 0. This is a real number solution.
7x + 21 = 21 simplifies to 7x = 0, which has the solution x = 0. This is a real number solution.
12x + 15 = 12x - 15 simplifies to 15 = -15, which is false. This equation has no solution, but it doesn't have any variables left to solve for, so it's not an option for our answer.
12x + 12 = 3(4x + 5) simplifies to 12x + 12 = 12x + 15, which simplifies further to 12 = 15. This is false, which means the equation has no solutions. Therefore, this is the equation that has no real solution, the correct option is (d).
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The complete question is:
Select each equation that has no real solution
a. -5x- 25 - 5x + 25
b. 7x + 21 = 21
c. 12x + 15 = 12x - 15
d. 12x + 12 = 3(4x + 5)
14. A candle has the shape of a right prism whose bases are regular polygons with 12 sides. On each base, the distance from one vertex to the opposite vertex, measured through the centre of the base, is approximately 2 in. The candle is 5 in. high.
a) What is the area of the base, to the nearest square inch?
b) What is the volume of wax in the candle, to the nearest cubic inch?
a) Area of the base is approximately 182 square inches.
b) Volume of wax in the candle is approximately 912 cubic inches.
What is circumradius of a regular polygon?
The distance between any vertex and the center of a regular polygon is its radius. Every vertex will have the same situation. The polygon's radius is also equal to the diameter of the circle that encircles each vertex.
a) Since the base of the candle is a regular polygon with 12 sides, it can be considered a dodecagon. Each angle of a regular dodecagon measures:
(12 - 2) x 180° / 12 = 150°
The distance from one vertex to the opposite vertex, measured through the center of the base, is the same as the diameter of the circumcircle of the dodecagon. We can use the formula for the circumradius of a regular polygon to find this distance:
r = s / (2 sin(180°/n))
where r is the circumradius, s is the side length, and n is the number of sides. Since the dodecagon is regular, all the side lengths are equal, so we can just use one of them.
s = 2 in (approximately, given in the problem)
r = 2 / (2 sin(180°/12)) = 2 / (2 sin(15°)) ≈ 7.88 in
The area of the dodecagon base is:
[tex]A = (12/2) r^2 sin(360/12) \\\\ A = 6 * 7.88^2 x sin(30) \\\\A = 182.42 in^2[/tex]
So the area of the base is approximately 182 square inches.
b) The volume of the candle is equal to the area of the base multiplied by the height:
V = A x h
where A is the area of the base and h is the height of the prism.
The height of the candle is given as 5 in, and we just calculated the area of the base as approximately 182.42 in^2. Therefore, the volume of the candle is:
[tex]V = 182.42\ in^2 * 5 \ in\\\\ V= 912.1 in^3[/tex]
So the volume of wax in the candle is approximately 912 cubic inches.
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Graph the system of equations below on the coordinate grid provided.
y= 4x - 2
y= 1/2x + 5
SHOW ALL OF YOUR WORK and write the answer as an ordered pair.
A solution to the given system of linear equations is (2, 6).
How to graph the solution to this system of equations?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
y = 4x - 2 ......equation 1.
y = 1/2(x) + 5 ......equation 2.
Next, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (2, 6).
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blake collects stamps. He collected a total of 250 . If 84% of the stamps he collected were foreign, how many other stamps did he collect?
Answer: 40
Step-by-step explanation: 100% - 84% = 16% and 16% of 250 is 40
Answer:
40
Step-by-step explanation:
Given a circle centered at point O and any three points A, B, and C on the circle, show that the angle BAC is half the corresponding central angle BOC. What does this say about the angle BAC if we keep points B and C fixed, but allow the point A to move around the circle? What if B and C are endpoints of the diameter of the circle?
The angle BAC will always be a right angle (90 degrees).
Given a circle centered at point O and any three points A, B, and C on the circle, the angle BAC will always be half of the corresponding central angle BOC.
If we keep points B and C fixed and allow point A to move around the circle,
then the angle BAC will stay the same.
If points B and C are endpoints of the diameter of the circle, then the angle BAC will always be a right angle (90 degrees).
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If \( f(x)=5 x, g(x)=-2 x+1 \), and \( h(x)=x^{2}+6 x+8 \), find f(h \( (-3)] \).
The f(h \((-3)]\) = -5.
To find f(h \((-3)]\), we need to first find the value of h \((-3)]\) and then plug that value into the function f(x).
Step 1: Find h \((-3)]\)
h(x) = x^2 + 6x + 8
h(-3) = (-3)^2 + 6(-3) + 8
h(-3) = 9 - 18 + 8
h(-3) = -1
Step 2: Plug the value of h(-3) into the function f(x)
f(x) = 5x
f(h(-3)) = 5(-1)
f(h(-3)) = -5
Therefore, f(h \((-3)]\) = -5.
I hope this helps! Let me know if you have any further questions.
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Santa's elves are creating treat bags containing a selection of Kit Kats, Reese's cups and Almond Joys. (A) How many different types of bags can they make containing 10 chocolate bars. (B) How many different types of bags can they make containing 10 chocolate bars if Santa wants to have at least 1 Kit Kat(s), 2 Reese's cup(s) and 1 Almond Joy(s) in the bag
There are 59,049 different types of bags that can be made containing 10 chocolate bars and 54 x 729 = 39,366 different types of bags that can be made containing 10 chocolate bars with at least 1 Kit Kat, 2 Reese's cups, and 1 Almond Joy in the bag.
(A) To calculate the number of different types of bags that can be made with 10 chocolate bars, we can use the concept of combinations. Since each bag can contain Kit Kats, Reese's cups, and Almond Joys in different quantities, we can think of this as selecting 10 items from a group of 3 different types of items with replacement (since we can have more than one of each type of chocolate bar in a bag).
The formula for the number of combinations with replacement is: n^r, where n is the number of items to choose from and r is the number of items to choose
In this case, n = 3 (since there are 3 different types of chocolate bars) and r = 10 (since we are choosing 10 chocolate bars for each bag). Therefore, the number of different types of bags that can be made is: 3^10 = 59,049
So there are 59,049 different types of bags that can be made containing 10 chocolate bars.
(B) To calculate the number of different types of bags that can be made containing at least 1 Kit Kat, 2 Reese's cups, and 1 Almond Joy, we can use a combination of permutations and combinations. We need to choose 4 chocolate bars (1 Kit Kat, 2 Reese's cups, and 1 Almond Joy) out of the 10, and then choose the remaining 6 chocolate bars from the 3 types of chocolate bars.
First, we choose the 4 chocolate bars with the required distribution:
We can choose 1 Kit Kat in 3 ways (since there are 3 Kit Kats to choose from).
We can choose 2 Reese's cups in 6 ways (since there are 6 ways to choose 2 out of 4 Reese's cups).
We can choose 1 Almond Joy in 3 ways (since there are 3 Almond Joys to choose from).
Therefore, the number of ways to choose the 4 required chocolate bars is: 3 x 6 x 3 = 54
Next, we choose the remaining 6 chocolate bars from the 3 types of chocolate bars. This can be done using the formula for combinations with replacement, as in part (A): n^r, where n is the number of items to choose from and r is the number of items to choose
In this case, n = 3 (since there are 3 types of chocolate bars) and r = 6 (since we are choosing 6 chocolate bars for each bag). Therefore, the number of different types of bags that can be made with the required distribution of chocolate bars is: 3^6 = 729
So there are 54 x 729 = 39,366 different types of bags that can be made containing 10 chocolate bars with at least 1 Kit Kat, 2 Reese's cups, and 1 Almond Joy in the bag.
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Artemio borrows $90,000 to buy a business. The bank gives him a loan, with a simple interest rate of 4% each year. It takes Artemio 10 years to pay the bank back – how much does he pay back in total?
The amount he would pay back in total is $126,000.
How much would he payback in total?The amount he would pay back is the sum of the amount borrowed and the interest rate on the loan.
Amount that would be paid back = amount borrowed + interest
Simple interest is a linear function of the amount borrowed, interest rate and the duration of the loan. The simple interest is the cost of borrowing.
Interest = amount borrowed x interest rate x time
$90,000 x 0.04 x 10 = $36,000
Amount that would be paid back = interest + amount that is borrowed
= $36,000 + $90,000 = $126,000
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3) The height of a ball above the ground t seconds after it is thrown is h(t) = 20 + 32t - 16t
a) How long will it take for the ball to hit the ground?
b) How long does it take to reach its maximum height?
c) What is the ball's maximum height?
d) If the ball was thrown from a height of 30 feet what would the equation be?
a) The time it takes for the ball to hit the ground is given as follows: 2.5 seconds.
b) The time it takes for the maximum height is of: 1 second.
c) The maximum height is of: 36 feet.
d) The equation would be of: h(t) = 30 + 32t - 16t².
How to obtain the features?The quadratic function for the ball's height is given as follows:
h(t) = 20 + 32t - 16t².
In which:
20 feet is the initial height.32 feet per second is the initial velocity.-16 ft/s² is the gravity.The coefficients are given as follows:
a = -16, b = 32, c = 20.
Then the discriminant is of:
D = b² - 4ac
D = 32² - 4 x (-16) x 20
D = 2304.
The positive root gives the time it takes for the ball to hit the ground, as follows:
t = (32 + sqrt(2304))/32
t = 2.5 seconds.
The time to reach the maximum height is the t-coordinate of the vertex, hence:
t = -b/2a
t = -32/-32
t = 1 second.
The maximum height is of:
h(1) = 20 + 32 - 16
h(1) = 36 feet.
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The height of a cylinder is decreasing at a constant rate of 4 feet per second, and the volume is increasing at a rate of 476 cubic feet per second. At the instant when the height of the cylinder is 8 feet and the volume is 583 cubic feet, what is the rate of change of the radius? The volume of a cylinder can be found with the equation V = Tr?h. Round your answer to three decimal places.
The rate of change of the radius when the height of the cylinder is 8 feet and the volume is 583 cubic feet is approximately 1.854 feet per second.
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as;
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
We are given that;
dh/dt = -4 ft/s and dV/dt = 476 ft^3/s. We need to find dr/dt when h = 8 ft and V = 583 ft^3.
Now,
We can start by differentiating the volume formula with respect to time t, using the product rule:
dV/dt = d/dt (πr^2h)
= πh d/dt (r^2) + πr^2 d/dt (h)
= 2πrh (dr/dt) + πr^2 (dh/dt)
We can use the given values of h and V to find the value of r using the formula for the volume of a cylinder:
V = πr^2h
583 = πr^2(8)
r^2 = 583/(8π)
r ≈ 3.031
Now we can substitute the values we have into the formula for dV/dt and solve for dr/dt:
476 = 2π(8)(3.031)(dr/dt) + π(3.031)^2(-4)
dr/dt = (476 + 36π(3.031)^2) / (16π(3.031))
dr/dt ≈ 1.854
Therefore, by the given volume the answer will be 1.854 feet per second.
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PLEASE HELP
Find the value of each trigonometric value.
The values of the trigonometric functions for angle C in the given right-angled triangle are
[tex]sin(C) = 0.6 \\ cos(C) = 0.8 \\ tan(C) = 0.75 \\ csc(C) = 1.7\\ sec(C) = 1.25 \\ cot(C) = 1.3[/tex]
What is Pythagoras theorem?
According to Pythagorean theorem to find the length of the other leg of the triangle,
[tex]a^2 + b^2 = c^2[/tex] where a and b are the legs of the triangle and c is the hypotenuse.
So, in this case,
[tex]a^2 + 30^2 = 50^2 \\ a^2 + 900 = 2500 \\ a^2 = 1600 \\ a = 40
[/tex]
Here given all three sides of the triangle.
We need to find the values of the trigonometric functions:
[tex]sin(C) = \frac{opposite \: leg}{hypotenuse }= \frac{30}{50} = 0.6 \\ cos(C) = \frac{adjacent}{hypotenuse} = \frac{40}{50} = 0.8 \\ tan(C) = \frac{opposite}{adjacent} =\frac{ 30}{40} = 0.75 \\ csc(C) =\frac{ hypotenuse}{opposite} = \frac{50}{30} = 1.666... \\ sec(C) = \frac{hypotenuse}{adjacent} = \frac{50}{40} = 1.25 \\ cot(C) = \frac{adjacent}{opposite} = \frac{40}{30} = 1.333...
[/tex]
Therefore, the values of the trigonometric functions for angle C in the given right-angled triangle are
[tex]sin(C) = 0.6 \\ cos(C) = 0.8 \\ tan(C) = 0.75 \\ csc(C) = 1.666... = 1.7\\ sec(C) = 1.25 \\ cot(C) = 1.333... = 1.3[/tex]
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(b^((3)/(2))*a^(4))^(-(1)/(4)) Vrite your answer without us ssume that all variables are
The answer is b^((-3)/(8))*a^(-1)
The expression (b^((3)/(2))*a^(4))^(-(1)/(4)) can be simplified by using the properties of exponents. First, we can distribute the exponent -(1/4) to each of the terms inside the parenthesis:
b^((3)/(2))^(-(1)/(4))*a^(4)^(-(1)/(4))
Next, we can simplify the exponents by multiplying them:
b^((-3)/(8))*a^((-4)/(4))
Finally, we can simplify the exponents further:
b^((-3)/(8))*a^(-1)
So, the final answer is b^((-3)/(8))*a^(-1). This is the simplified form of the expression without any assumptions about the values of the variables.
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A triangle has sides with lengths of 20 feet, 21 feet, and 29 feet. Is it a right triangle?
Answer:
Yes
Step-by-step explanation:
please solve this homework please
Answer:
Step-by-step explanation:
first you find the numbers that go with the numbers like base times height
times length then you add it all up read this two times to understand
What is the value of the first quartile?
3
6
8
11
The requried value of the first quartile is 4.5.
What is the Interquartile range?Interquartile range (IQR): The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.
To find the first quartile (Q1), we need to arrange the given values in ascending order and then find the median of the lower half of the values.
The given values arranged in ascending order are:
3, 6, 8, 11
The lower half of the values are:
3, 6
The median of the lower half is:
(Q1) = (3 + 6)/2 = 4.5
Therefore, the value of the first quartile is 4.5.
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in the diagram below FG is parallel to CD. if FG is 1 less than CF, FE=5 and CD=8, find the length of CF
Accοrding tο similarity οf triangles, the length οf CF is 8/3.
What is similarity οf triangles?Similarity οf triangles is a cοncept in geοmetry that describes the relatiοnship between twο triangles that have the same shape but may be different in size. Twο triangles are cοnsidered similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal.
Since FG is parallel tο CD, we can use similar triangles tο find the length οf CF. Let's call the length οf CF x. Then we have:
FE/FG = CD/CF
Substituting the given values, we have:
5/(x-1) = 8/x
Crοss-multiplying, we get:
5x = 8(x-1)
Expanding the brackets, we get:
5x = 8x - 8
Subtracting 5x frοm bοth sides, we get:
3x = 8
Dividing bοth sides by 3, we get:
x = 8/3
Therefοre, the length οf CF is 8/3.
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Complete question:
What is (44x600)+56-67+99+3x6=?
Answer:
Than thats great
Bus #7 left River Street School partially filled with students and then stopped to pick up 15 more students at the Park School. it continued its route as follows:
At the next 4 stops it dropped off two students at each stop.
Three students got off at the following stop.
The next six stops let off one student at each stop.
Ten students then got off at the Centerville after-school-program, where five kindergarten students boarded the bus.
The bus then dropped off seven kids at its last stop, leaving only the driver aboard.
How many students were on the bus when it left the River Street School? Show your work and explain your reasoning.
14 students were on the bus when it left River Street School.
To find out how many students were on the bus when it left River Street School, we need to work backwards from the end of the route and account for all the students that were picked up and dropped off along the way.
At the last stop, seven students were dropped off, leaving only the driver aboard. This means that there were 7 students on the bus before the last stop.
Before that, five kindergarten students boarded the bus at the Centerville after-school-program, which means that there were 7 - 5 = 2 students on the bus before the kindergarten students boarded.
Before that, ten students got off at the Centerville after-school-program, which means that there were 2 + 10 = 12 students on the bus before they got off.
Before that, the bus made six stops and let off one student at each stop, which means that there were 12 + 6 = 18 students on the bus before those stops.
Before that, three students got off at one stop, which means that there were 18 + 3 = 21 students on the bus before that stop.
Before that, the bus made four stops and dropped off two students at each stop, which means that there were 21 + (4 x 2) = 29 students on the bus before those stops.
Finally, before that, the bus picked up 15 students at the Park School, which means that there were 29 - 15 = 14 students on the bus when it left River Street School.
14 students were on the bus when it left River Street School.
Starting from the end of the route and working backwards, we accounted for all the students that were picked up and dropped off along the way. By subtracting the number of students that were picked up from the number of students that were on the bus at each stop, we were able to find out how many students were on the bus when it left River Street School.
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