Substitution method y= 3x-2 and 2x-3y=16<br><br>solution (__), (_

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

The equation and graph of a polynomial are shown below. The graph reachesits minimum when the value ofx is 4. What is the y valu

olga_2 [115]

The y-value of this minimum is 4 .

6 0

3 years ago

McKenzie sells textbooks. She receives 7% on her first $1,000 in sales and 15% on the balance of her sales. How much would she e

Alisiya [41]

The commission would be $2095.

Step-by-step explanation:

Given,

Commission on first $1000 = 7%

Amount of commission = 0.07*1000 = $70

Worth of sold items = $14,500

We will subtract $1000 from it.

Balance = 14500-1000 = $13500

Commission on balance = 15% = 0.15

Amount of commission = 0.15*13500

Amount of commission = $2025

Total commission = 70+2025 = $2095

The commission would be $2095.

Keywords: percentage, subtraction

Learn more about subtraction at:

#LearnwithBrainly

3 0

3 years ago

Compound inequality that represents all the numbers between -4 and 6

KatRina [158]

You can write it as:
-4≥x≤6

*The '≥' and '≤' just means that it is greater than or less than but it can still be equal to the number you are comparing it to.

Hope this helps! :)

6 0

3 years ago

Skyler goes to a school which has 1000 students in it.

Dmitry [639]

Answer:

it's estimated that 750 students in the whole school dislike the 8:30am start time.

Step-by-step explanation:

Since 30 of the 40 students said "no", it means 30/40, or 3/4 of the random sample disliked the 8:30am start time. Multiply this by the whole population: 1,000 × (3/4) = 750.

Another way to check this is using 10/40 = .25 and doing 1000x.25 = 250 (the amount of students who liked it). Then subtract from whole population and it's 750.

5 0

2 years ago

Substitution method y= 3x-2 and 2x-3y=16solution (__), (__)thanks

Substitution method y= 3x-2 and 2x-3y=16solution (), ()thanks