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gogolik [260]
4 years ago
10

How does the exponent of each power of ten correspond with placing a decimal

Mathematics
1 answer:
miv72 [106K]4 years ago
8 0
Each power of ten multiplies or divides the number by 10.
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Susan designed a circular pool with a diameter of 25 meters.What is the area of the bottom of the pool? Round to the nearest ten
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A circle's radius that has an initial radius of 0 cm is increasing at a constant rate of 5 cm per second.
djyliett [7]

Answer:

a) r(t)=5t

b) A=\pi\cdot r^2

c) A=\pi\cdot (5t)^2

d) A=25\pi  t^2

Step-by-step explanation:

We know that the circle is increasing its radio from an initial state of r=0 cm, at a rate of 5 cm/s.

This can be expressed as:

r(0)=0\\\\dr/dt=5\\\\r(t)=r(0)+dr/dt\cdot t=0+5t\\\\r(t)=5t

a) Radius of the circle, r (in cm), in terms of the number of seconds, t since the circle started growing:

r(t)=5t

b) Area of the circle, A (in square cm), in terms of the circle's radius, r (in cm):

A=\pi\cdot r^2

c) Circle's area, A (in square cm), in terms of the number of seconds, t, since the circle started growing:

A=\pi\cdot r^2\\\\A=\pi\cdot (5t)^2

d) Expanded form for the area A:

A=\pi\cdot (5t)^2=25\pi\cdot t^2

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