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lesya [120]
3 years ago
7

The radius of a sphere is increasing at a rate of 3 mm/s. how fast is the volume of the sphere increasing when the diameter is 1

0 mm?
Mathematics
1 answer:
vredina [299]3 years ago
5 0

We will find the rate of change of volume with respect to the change of radius.


Volume, V(r) = (4/3) π r^3


Find rate of change of volume with respect to change of radius by differentiation


V'(r)=dV/dr = d[(4/3) π r^3]/dr = (4/3) π d[r^3]/dr =(4/3) π 3r^2


Therefore when diameter=10mm, r=5mm


V'(r)=V'(5)=(4/3) π (3(5^2))=(4/3) π 75 = 100 π mm^3/mm

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4 0
2 years ago
You are trying to decide whether to use Uber or Lyft during a vacation. Uber charges $3 to pick up plus an additional $0.25 for
zubka84 [21]

Answer:

6 Miles and the cost is $4.50

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3+0.25=0.75x

3+0.50x

6=x

0.75x+?

0.75 x 6= 4.50

7 0
3 years ago
A triangle has side lengths of 15 millimeters, 10 millimeters, and 13 millimeters. What kind of triangle is it?
Akimi4 [234]

Answer:The triangle is acute

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Help! This is due today!
bulgar [2K]

Answer:

27π

Step-by-step explanation:

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= π × 6^2

= 36π

36/4

= 9

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4 0
2 years ago
Which statements about the graph of the function f(x) = –x2 – 4x + 2 are true? Check all that apply. The domain is {x|x ≤ –2}. T
Leto [7]
The graph of the function f(x) =-x^2-4x + 2 is parabola with branches going down in the negative direction of y-axis. 
The vertex of parabola has coordinates:

x_v=\dfrac{-(-4)}{2\cdot(-1)}=-2, \\ y_v=-(-2)^2-4\cdot (-2)+2=-4+8+2=6

Then you can conclude that all x are possible, that means that the dimain is x\in (-\infty,\infty) and the maximum value of y is at the vertex, then the range is (-\infty,6].The function is increasing for x<-2 and decreasing for x>-2 (since vertex is the maximum point).
When x=0, y=2. 
Hence,
<span>The domain is {x|x ≤ –2} - false.
</span>
<span>The range is {y|y ≤ 6} - true.
</span>
<span>The function is increasing over the interval (–∞ , –2) - true.
</span>
<span>The function is decreasing over the interval (−4, ∞) - false.
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8 0
3 years ago
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