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Rashid [163]
3 years ago
8

Math short answer question! Please help!

Mathematics
1 answer:
IRISSAK [1]3 years ago
7 0
Part 1:

The circumference of the smaller circle is...
C = 2*pi*r
C = 2*pi*2
C = 4*pi


The circumference of the larger circle is...
C = 2*pi*r
C = 2*pi*8
C = 16*pi


The ratio of the two circumferences is
16*pi:4*pi = 4:1
which means that for every single full rotation of the larger gear, the smaller gear will complete four rotations

If we flip things around, we will have the ratio 4:1 turn into 1:0.25 (divide both parts by 4). Now this says that for every single rotation of the smaller gear, the larger gear rotates 1/4 or 25% of the larger circle circumference. 

1/4 of 360 degrees is 90 degrees

So the larger gear will rotate 90 degrees when the small gear completes a full revolution. 

Answer: 90 degrees

=====================================================

Part 2:

This was pretty much answered in part 1 above. The answer here is 4. The circumference of the larger gear is 4 times larger (since the radius is 4 times larger), so the gear ratio here is 4:1.

Answer: 4

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Answer:

<em>The surface area of the sphere is 314 mi².</em>

Step-by-step explanation:

According to the given diagram, the diameter of the sphere is 10 mi.

If the radius is r, then diameter =2r

So....

2r=10\\ \\ r=\frac{10}{2}= 5

<u>Formula for the surface area of a sphere</u>:  A_{S}= 4\pi r^2

Plugging the value of r into this formula, we will get...

A_{S}=4\pi(5)^2\\ \\ A_{S}=4\pi(25)\\ \\ A_{S}=4(3.14)(25)\ \ [Using\ \pi=3.14]\\ \\ A_{S}=314

So, the surface area of the sphere is 314 mi².

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What is the volume of the sphere?
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Answer: 113.1

Step-by-step explanation:

The formula is \frac{4}{3}\pir^{3}

The radius is 3, and 3 cubed is 27.

Then, 27 x \pi is about 84.82

Finally, 84.82 x \frac{4}{3} is about 113.1

Hope this helps. Please mark as brainliest, thanks!

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Suppose quantity s is a length and quantity t is a time. Suppose the quantities v and a are defined by v = ds/dt and a = dv/dt.
finlep [7]

Answer:

a) v = \frac{[L]}{[T]} = LT^{-1}

b) a = \frac{[L}{T}^{-1}]}{{T}}= L T^{-1} T^{-1}= L T^{-2}

c) \int v dt = s(t) = [L]=L

d) \int a dt = v(t) = [L][T]^{-1}=LT^{-1}

e) \frac{da}{dt}= \frac{[L][T]^{-2}}{T} = [L][T]^{-2} [T]^{-1} = LT^{-3}

Step-by-step explanation:

Let define some notation:

[L]= represent longitude , [T] =represent time

And we have defined:

s(t) a position function

v = \frac{ds}{dt}

a= \frac{dv}{dt}

Part a

If we do the dimensional analysis for v we got:

v = \frac{[L]}{[T]} = LT^{-1}

Part b

For the acceleration we can use the result obtained from part a and we got:

a = \frac{[L}{T}^{-1}]}{{T}}= L T^{-1} T^{-1}= L T^{-2}

Part c

From definition if we do the integral of the velocity respect to t we got the position:

\int v dt = s(t)

And the dimensional analysis for the position is:

\int v dt = s(t) = [L]=L

Part d

The integral for the acceleration respect to the time is the velocity:

\int a dt = v(t)

And the dimensional analysis for the position is:

\int a dt = v(t) = [L][T]^{-1}=LT^{-1}

Part e

If we take the derivate respect to the acceleration and we want to find the dimensional analysis for this case we got:

\frac{da}{dt}= \frac{[L][T]^{-2}}{T} = [L][T]^{-2} [T]^{-1} = LT^{-3}

7 0
3 years ago
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