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
Answer:
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Answer:
4x - 5y - 9 = 0
Step-by-step explanation:
The equation of a straight line passing through the points (-4,-5) and (1,-1) is given by 
⇒ 
⇒ 5y + 25 = 4x + 16
⇒ 4x - 5y - 9 = 0 ....(1) (Answer)
Now, this above equation can be represented as
Therefore, the x-intercept is (Answer)
And the y-intercept is . (Answer)
Let's solve your equation step by step.
5(k - 2) - 8k= -34
Step 1: Simplify both sides of the equation.
5(k - 2) - 8k= -34
(5)(k) = (5)(-2) + - 8k= -34 (Distribute)
5k + -10 + -8k = -34
(5k + -8k) + (-10) = -34 (Combine Like Terms)
-3k + -10 = -34
-3k - 10 = -34
Step 2: Add 10 to both sides.
-3k - 10 + 10 = -34 + 10
-3k = -24
Step 3: Divide both sides by -3.
-3k\3 =-24\-3
K= 8
Answer:
K=8
Hope this helps
Answer: 21
Step-by-step explanation:
