Pls help quickly maath

If the radius of a sphere is increasing at the constant rate of 3 centimeters per second, how fast is the volume changing when t

kotykmax [81]

How fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.

To solve the question, we need to know the volume of a sphere

<h3>Volume of a sphere</h3>

The volume of a sphere V = 4πr³/3 where r = radius of sphere.

<h3>How fast the volume of the sphere is changing</h3>

To find the how fast the volume of the sphere is changing, we find rate of change of volume of the sphere. Thus, we differentiate its volume with respect to time.

So, dV/dt = d(4πr³/3)/dt

= d(4πr³/3)/dr × dr/dt

= 4πr²dr/dt where

dr/dt = rate of change of radius of sphere and
4πr² = surface area of sphere

Given that

dr/dt = + 3 cm/s (positive since it is increasing) and
4πr² = surface area of sphere = 10 cm²,

Substituting the values of the variables into the equation, we have

dV/dt = 4πr²dr/dt

dV/dt = 10 cm² × 3 cm/s

dV/dt = 30 cm³/s

So, how fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.

Learn more about how fast volume of sphere is changing here:

brainly.com/question/25814490

7 0

2 years ago

The price elasticity of demand for good X is half the price elasticity of Good Y. A 20% rise in the price of good X results in a

Keith_Richards [23]

The answer is

60% rise in quantity demanded of good x.

Explanation:

Percentage change in quantity demanded for good Y:

= (Change in Quantity ÷ Initial Quantity) × 100

= (60 units ÷ 400 units) × 100

= 15%

Percentage change in price of good Y = 10% Rise

Therefore, the price elasticity of demand for Good Y is as follows:

= Percentage change in Quantity demanded ÷ Percentage change in price

= 15 ÷ 10

= 1.5

Hence,

Price elasticity of demand of good x:

= 2 × price elasticity of demand of good y

= 2 × 1.5

= 3

Percentage change in price of good x:

= (Change in price ÷ Initial price) × 100

= (2 ÷ 10) × 100

= 20%

Therefore,

Price elasticity of demand for Good x = Percentage change in Quantity demanded ÷ Percentage change in price

3 = Percentage change in Quantity demanded ÷ 20

3 × 20 = Percentage change in Quantity demanded

60% = Percentage change in Quantity demanded for good x

Hence, 60% rise in quantity demanded of good x.

7 0

3 years ago

What is 1/4 divided by 1/2, and create and solve a real-world word problem that uses the above division expression.

Gnoma [55]

Answer:

1/4 divided by 1/2 equals 1/2

Real-world problem:

A constructor official knows that he needs 1/2 sack of cement to produce 10 blocks of concrete for a wall. The official only has 1/4 of the sack left and want to know how many blocks he can produce with this material.

Step-by-step explanation:

Since you know that 1/2 of the sack is needed to make 10 blocks, you can use this information to find the number of blocks that 1/4 of a sack can make. The question you want to answer is:

if $\frac{1}{2}$ of a sack produces 10 blocks, how may blocks $\frac{1}{4}$ of a sack can produce?

Using the Rule of Three you can solve

$\frac{\frac{1}{4} }{\frac{1}{2}} =\frac{2}{4}=\frac{1}{2}$

Now you know that 1/4 of a sack can produce 1/2 the number of blocks that 1/2 of the sack can produces, this means that you can produce 5 blocks of concrete.

8 0

3 years ago

26 Can anyone help!!!

lbvjy [14]

Ok, first let's find how much a nickle is worth, a nickle is worth $0.05.

0.05 x 27 = $1.35

0.05 x 32 = $1.60

0.05 x 39 = $1.95

0.05 x 47 ≠ $2.45 (It's equal to $2.35)

I hope this helps!

5 0

3 years ago

What is x-4/3=3x+4/7 what is x expain how you got the answer

Nookie1986 [14]

X-4/3 = 3x-4/7
First add 4/3 to each side -->x = 3x + 16/21
Then Subract 3x from each side -->-2x = 16/21
Then divide each side by -2 --->x = -3.81

8 0

3 years ago

Read 2 more answers