Mathematics, 14.04.2020 21:11 mariahmimibrooks

A spherical balloon is inflating with helium at a rate of 6464piπ StartFraction ft cubed Over min EndFraction ft3 min. How fast is the balloon's radius increasing at the instant the radius is 22 ft? How fast is the surface area increasing?

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Answer from: macycj8

the surface area will increase 16 feet per minute

Step-by-step explanation:

Allow me to revise your question for a better understanding.

A spherical balloon is inflating with helium at a rate of 64π Start Fraction ft cubed Over min End Fraction ft3 min. How fast is the balloon's radius increasing at the instant the radius is 2 ft? How fast is the surface area increasing?

Given that:

$\dfrac{dV}{dt} = 64\pi \dfrac{\text{ ft}^3}{\text{min}}$ (1)

As we know that, the volume of a spherical balloon can be calculated by using the following formula:

$V = \dfrac{4}{3}\pi r^3$ where r is the radius

Substitute V into (1), we have:

$\dfrac{dV}{dt} = \dfrac{d}{dt}(\dfrac{4}{3}\pi r^3)\\\\\dfrac{dV}{dt} =4\pi r^2\dfrac{dr}{dt}$

In this situation, the instant radius is: 2f

So we have:

$64\pi = 4\pi (2)^2\dfrac{dr}{dt}\\\\\Rightarrow \dfrac{dr}{dt} = 4$

The radius of the balloon is increasing at a rate of 4 feet per minute

The the surface area has the formula as:

SA1 = 4π $r^{2}$

If the radius of the balloon is increasing at a rate of 4 feet per minute, so the

the surface area will increase 16 feet per minute because:

SA2 : 4π $(4r)^{2}$ = 16 (4π $r^{2}$ ) = 16 SA1

Hope it will find you well.

Answer from: Quest

c. x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

$\frac{little}{big} =\frac{side mn}{side ab}=\frac{side on}{side cb}$ .

$\frac{0.96}{1.2}=\frac{x}{3}$

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

$0.96(3)=1.2(x)\\2.88=1.2x\\\frac{2.88}{1.2}=\frac{1.2x}{1.2} \\2.4=x$

Answer from: Quest

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.

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