Please help quickly pls D:

Preview Activity 3.5.1. A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. How fast is the

ArbitrLikvidat [17]

Answer:

The radius is increasing at a rate of approximately 0.044 in/s when the diameter is 12 inches.

Because $\frac{dr}{dt}=\frac{5}{36\pi }>\frac{dr}{dt}=\frac{5}{64\pi }$ the radius is changing more rapidly when the diameter is 12 inches.

Step-by-step explanation:

Let $r$ be the radius, $d$ the diameter, and $V$ the volume of the spherical balloon.

We know $\frac{dV}{dt}=20 \:{in^3/s}$ and we want to find $\frac{dr}{dt}$

The volume of a spherical balloon is given by

$V=\frac{4}{3} \pi r^3$

Taking the derivative with respect of time of both sides gives

$\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

We now substitute the values we know and we solve for $\frac{dr}{dt}$ :

$d=2r\\\\r=\frac{d}{2}$

$r=\frac{12}{2}=6$

$\frac{dV}{dt}=4\pi r^2\frac{dr}{dt}\\\\\frac{dr}{dt}=\frac{\frac{dV}{dt}}{4\pi r^2} \\\\\frac{dr}{dt}=\frac{20}{4\pi(6)^2 } =\frac{5}{36\pi }\approx 0.044$

The radius is increasing at a rate of approximately 0.044 in/s when the diameter is 12 inches.

When d = 16, r = 8 and $\frac{dr}{dt}$ is:

$\frac{dr}{dt}=\frac{20}{4\pi(8)^2}=\frac{5}{64\pi }\approx 0.025$

The radius is increasing at a rate of approximately 0.025 in/s when the diameter is 16 inches.

Because $\frac{dr}{dt}=\frac{5}{36\pi }>\frac{dr}{dt}=\frac{5}{64\pi }$ the radius is changing more rapidly when the diameter is 12 inches.

8 0

3 years ago

A triangle has one leg of 24 inches and one leg of 10 inches. For the triangle to be a right triangle, what must be the length o

meriva

Answer: 26 inches

Step-by-step explanation:

The hypoteneuse is the longest side in a triangle. From the question, we are already informed that a triangle has one leg of 24 inches and one leg of 10 inches.

To calculate the hypotenuse, we add the square of both legs together which are the opposite and adjacent and then find the square root. This will be

hypotenuse² = 24² + 10²

hypotenuse² = 576 + 100

hypotenuse² = 676

hypotenuse = ✓676

hypotenuse = 26

The hypothenuse is 26 inches

7 0

3 years ago

Jill is a pitcher for her softball team. She had 4 strikeouts in her first game, and 10 strikeouts in her second game. What is t

pogonyaev

Answer:

150% increase

Step-by-step explanation:

Since it went up, we know it is an increase

Take the new amount and subtract the original amount

10-4 = 6

Divide this by the original amount

6/4 = 1.5

Multiply by 100% to change to percent form

150%

8 0

4 years ago

Read 2 more answers

PLZ HELP WILL GIVE CROWN

tigry1 [53]

Step-by-step explanation:

the answer of x is different you can see in the picture

5 0

3 years ago

What is the vertex of the quadratic function f(x) = (x-6)(x+2)

lisov135 [29]

For this case we have the following function:

We rewrite the function making distributive property.
We have then:

To find the vertex of the function, we derive:

We equal zero and clear the value of x:

We evaluate the function for the value of x obtained:

Then, the vertice of the parabola is:

Answer:
the vertex of the quadratic function f(x)=(x-6)(x+2) is:

Read more on Brainly.com - brainly.com/question/2073813#readmore

3 0

3 years ago