What's the missing side

A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon

zmey [24]

Using implicit differentiation, it is found that the radius is increasing at a rate of 0.0081 cm per minute.

<h3>What is the volume of a sphere?</h3>

The volume of a sphere of radius r is given by:

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

Applying implicit differentiation, the rate of change is given by:

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

In this problem, we have that:

$\frac{dV}{dt} = 500, r = 70$

Hence the rate of change of the radius is given as follows:

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

$19600\pi\frac{dr}{dt} = 500$

$\frac{dr}{dt} = \frac{500}{19600\pi}$

$\frac{dr}{dt} = 0.0081$

The radius is increasing at a rate of 0.0081 cm per minute.

More can be learned about implicit differentiation at brainly.com/question/25608353

#SPJ1

4 0

2 years ago

Help with this please.

Ivanshal [37]

Answer:

True
True

Step-by-step explanation:

This question asks you to compare the coordinates of the vertex of each function.

__

The vertex of the function is its minimum, the point where the graph stops decreasing and starts increasing. It is the lowest point on the graph.

The vertex is (-4, -1). The minimum is -1, located at x = -4.

The vertex is (1, -25). The minimum is -25, located at x = 1. We know this is the minimum because there are no g(x) values that are lower (more negative).

<h3>comparison</h3>

The minimum of f(x), -1, is greater than the minimum of g(x), -25. TRUE

The x-value of f(x) at its minimum, -4, is less than the x-value of g(x) at its minimum, 1. TRUE

8 0

2 years ago

Verify the identitiy:

Advocard [28]

Answer:

$\frac{sinx}{1-cos x}$ = $cosecx$ + $cot x$

Step-by-step explanation:

To verify the identity:

sinx/1-cosx = cscx + cotx

we will follow the steps below;

We will take just the left-hand side and work it out to see if it is equal to the right-hand side

sinx/1-cosx

Multiply the numerator and denominator by 1 + cosx

That is;

$\frac{sinx}{1-cos x}$ = $\frac{sinx(1+cosx)}{(1-cosx)(1+cosx)}$

open the parenthesis on the right-hand side of the equation at the numerator and the denominator

sinx(1+cosx) = sinx + sinx cosx

(1-cosx)(1+cosx) = 1 - cos²x

Hence

$\frac{sinx(1+cosx)}{(1-cosx)(1+cosx)}$ = $\frac{sinx + sinx cosx}{1-cos^{2}x }$

But 1- cos²x = sin²x

Hence we will replace 1- cos²x by sin²x

$\frac{sinx}{1-cos x}$ = $\frac{sinx(1+cosx)}{(1-cosx)(1+cosx)}$ = $\frac{sinx + sinx cosx}{1-cos^{2}x }$ = $\frac{sinx+sinxcosx}{sin^{2}x }$

= $\frac{sinx}{sin^{2}x }$ + $\frac{sinxcosx}{sin^{2}x }$

= $\frac{1}{sinx}$ + $\frac{cosx}{sinx}$

= $cosecx$ + $cot x$

$\frac{sinx}{1-cos x}$ = $cosecx$ + $cot x$

Note that;

$\frac{1}{sinx}$ = $cosecx$

$\frac{cosx}{sinx}$ = $cot x$

6 0

3 years ago

A train is traveling at a constant speed of 105 miles per hour. How many feet does it travel in 3 seconds? Remember that 1

ipn [44]

Answer:

in 3 seconds the train should travel 462 feet

Step-by-step explanation:

So, first, we convert the miles into feet.

105 x 5280 = 554400

This means the train travels 554400 feet per hour.

then, we convert the hour, into second.

Since an hour has 60 minutes, and a minute has 60 seconds, we simply multiply:

1(hour) x 60(minutes) x 60(seconds) = 3600

So the train moves 554400 feet every 3600 seconds.

To get how many feet it travels in one second, we divide this by 3600.

3600/3600 and 554400/3600

1 and 154.

For every second the train travels 154 feet.

Then we simply multiply them by 3.

3x1 and 3x154, which equals:

3 and 462.

So the train travels 462 feet every 3 seconds.

I tried to explain this as simply as I can.

I hope its all correct.

6 0

3 years ago

10th grade Geo | What does JK equal?

ladessa [460]

Answer:

16

Step-by-step explanation:

6x-7=2x+3 Cause point M is the midpoint, so JM and MK have to be equal.

4x=10

x=2.5

JM=15-7=8 and MK=5+3=8

8+8=16

4 0

3 years ago