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3 years ago

8

Kurt is running for student senate. He designed the t-shirt logo for his campaign. The logo is made up of a square with 14 cm si

des and four half circles. Use 3.14 for pi to approximate the area of the logo.

1 answer:

Ket [755]3 years ago

6 0

Answer:

......

Step-by-step explanation:

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The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6

Arlecino [84]

Answer:

$\approx \bold{6544\ in^3/sec}$

Step-by-step explanation:

Given:

Rate of change of radius of cylinder:

$\dfrac{dr}{dt} = +7\ in/sec$

(This is increasing rate so positive)

Rate of change of height of cylinder:

$\dfrac{dh}{dt} = -6\ in/sec$

(This is decreasing rate so negative)

To find:

Rate of change of volume when r = 20 inches and h = 16 inches.

Solution:

First of all, let us have a look at the formula for Volume:

$V = \pi r^2h$

Differentiating it w.r.to 't':

$\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)$

Let us have a look at the formula:

$1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))$

$3.\ \dfrac{dx^n}{dx} = nx^{n-1}$

Applying the two formula for the above differentiation:

$\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}$

Now, putting the values:

$\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}$

So, the answer is: $\approx \bold{6544\ in^3/sec}$

3 0

3 years ago

Here's the problem:

steposvetlana [31]

The three integers can be anything that leads down to the product of negative 4 or -4 is negative -2 x -1 x -2 i think this is it since i am also learning about this in 7th grade k12

5 0

3 years ago

Twice the difference of a number and 9 is equal to three times the sum of the number and 6. Find the number

bezimeni [28]

After modelling the mathematical statement and solving its equivalent mathematical relation, we get x = -36.

<h3>What is Equation Modelling?</h3>

Equation modelling is the process of writing a given mathematical statement in the form of a numeric mathematical expression taking into considerations the operations, constants and other variables.

Given in the question is a number such that twice the difference of a number and 9 is equal to three times the sum of the number and 6.

Assume that the number is x. Now, we will model the equation and solve for x. According to the question, the following mathematical relation represents the statement-

2(x - 9) = 3(x + 6)

2x - 18 = 3x + 18

x = - 36

Therefore, the number is -36.

To solve more questions on Equation modelling, visit the link below-

brainly.com/question/13536824

#SPJ1

8 0

1 year ago

Help quickly not much time

LenKa [72]

Answer:

The answer is x=2/3

6 0

3 years ago

Read 2 more answers

What property is illustrated by the statement 2/3 x 3/2 =1

Mariulka [41]

Answer:

Multiplicative inverse or reciprocal.

Step-by-step explanation:

Multiplicative inverse or reciprocal.

6 0

2 years ago

Read 2 more answers