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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Which represents the volume of the cylinder, in cubic

11Alexandr11 [23.1K]

Answer: 300π

Step-by-step explanation: Volume=(pi)(radius^2)(height)

Volume=(pi)(5^2)(12)

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3 years ago

Rebecca and dan are biking in a national park for three days they rode 5 3/4 hours the first day and 6 4/5 hours the second day

AfilCa [17]

Answer:

Rebecca and Dan need to ride $7\frac{9}{20}\ hrs.$ on the third day in order to achieve goal of biking.

Step-by-step explanation:

Given:

Goal of Total number of hours of biking in park =20 hours.

Number of hours rode on first day = $5\frac34 \ hrs.$

So we will convert mixed fraction into Improper fraction.

Now we can say that;

To Convert mixed fraction into Improper fraction multiply the whole number part by the fraction's denominator and then add that to the numerator,then write the result on top of the denominator.

$5\frac34 \ hrs.$ can be Rewritten as $\frac{23}{4}\ hrs$

Number of hours rode on first day = $\frac{23}{4}\ hrs$

Also Given:

Number of hours rode on second day = $6\frac45 \ hrs$

$6\frac45 \ hrs$ can be Rewritten as $\frac{34}{5}\ hrs.$

Number of hours rode on second day = $\frac{34}{5}\ hrs.$

We need to find Number of hours she need to ride on third day in order to achieve the goal.

Solution:

Now we can say that;

Number of hours she need to ride on third day can be calculated by subtracting Number of hours rode on first day and Number of hours rode on second day from the Goal of Total number of hours of biking in park.

framing in equation form we get;

Number of hours she need to ride on third day = $20-\frac{23}{4}-\frac{34}{5}$

Now we will use LCM to make the denominators common we get;

Number of hours she need to ride on third day = $\frac{20\times20}{20}-\frac{23\times5}{4\times5}-\frac{34\times4}{5\times4}= \frac{400}{20}-\frac{115}{20}-\frac{136}{20}$