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dexar
2 months ago
5

If a car goes around a turn too quickly, it can leave tracks that form an arc of a circle. By finding the radius of the circle,

accident investigators can estimate the speed of the car. To find the radius, accident investigators choose points A and B on the tire marks. Then, the investigators find the midpoint C of AB¯¯¯¯¯¯¯¯. Use the diagram to find the radius r of the circle. Round your answer to the nearest tenth.

Mathematics
2 answers:
Zina [12.3K]2 months ago
8 0
Given:
Segment AC = 130 feet
Segment CD = 70 feet

To find r, the radius, I'll use the Pythagorean theorem since r is the hypotenuse.

Segment CE = r - 70 feet

Applying the Pythagorean theorem:
r² = 130² + (r - 70)²
r² = 16,900 + (r - 70)(r - 70)
r² = 16,900 + r² - 140r + 4,900
r² - r² + 140r = 16,900 + 4,900
140r = 21,800
r = 21,800 / 140
r = 155.71 feet

Therefore, the circle's radius measures 155.71 feet.
PIT_PIT [12.4K]2 months ago
3 0

Answer: 155.7

Detailed solution:

Start with the given information.

Length of segment AC is 130 feet.

Length of segment CD is 70 feet.

Apply the Pythagorean Theorem here, where r^{2} equals a^{2} plus b^{2}.

To determine segment CE, calculate r minus 70.

Thus, r^{2} equals 130^{2} plus (r-70)^{2}.

Expression: r^{2} equals 16,900 plus r^{2} minus 140r plus 4,900.

Move -140r to the left side, eliminate the two r^{2}, then combine 16,900 and 4,900.

This results in 140r equals 21,800.

Divide both sides by 140.

The radius r calculates to 155.7 when rounded to one decimal place.

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Find the measure of x. Line PU has points R and S between points P and U, lines QR and ST are parallel, line QR intersects line
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  • Solution for x is 1

Detailed explanation:

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1 month ago
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Choose Yes or No to tell if the digit in the ones place is 1/10 the value of the digit in the tens place.
babunello [11817]

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5 0
1 month ago
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A photocopy machine can reduce copies to 80% of their original size. By copying an already reduced copy, further reductions can
PIT_PIT [12445]

Part a) When a page is scaled down to 80%, how much enlargement is necessary to bring it back to its original size?

Let

x---------> the percent enlargement

Given the original size is 100%

This means:

x*80%=100%

x=(100%/80%)

x=1.25--------> 1.25=(125/100)=125%

Thus,

The answer to Part a) is

The percent enlargement required is 125%

Part b) Estimate how many successive copies of a page are needed to make the final copy less than 15% of its original size.

Since the photocopy machine reduces sizes to 80% of the original

Therefore:

Copy N 1

0.80*100%=80%

Copy N 2

0.80*80%=64%

Copy N 3

0.80*64%=51.2%

Copy N 4

0.80*51.2%=40.96%

Copy N 5

0.80*40.96%=32.77%

Copy N 6

0.80*32.77%=26.21%

Copy N 7

0.80*26.21%=20.97%

Copy N 8

0.80*20.97%=16.78%

Copy N 9

0.80*16.78%=13.42%-------------> 13.42% < 15%

Therefore,

The answer to Part b) is

The necessary number of copies to achieve this is 9


6 0
1 month ago
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