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Anarel [89]
2 years ago
13

What number has an absolute value of 17?

Mathematics
1 answer:
WINSTONCH [101]2 years ago
6 0
17 and -17

absolute value is just the distance the number is from zero
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George and Paula are running around a circular track. George starts at the westernmost point of the track, and Paula starts at t
arsen [322]

Answer:

George is 43.20 ft East of his starting point.

Step-by-step explanation:

Let Paula's speed be x ft/s

George's speed = 9 ft/s

Note that speed = (distance)/(time)

Distance = (speed) × (time)

George takes 50 s to run a lap of the track at a speed of y ft/s

Meaning that the length of the circular track = y × 50 = 50y ft

George and Paula meet 14 seconds after the start of the run.

Distance covered by George in 14 seconds = 9 × 14 = 126 ft

Distance covered by Paula in 14 seconds = y × 14 = 14y ft

But the sum of the distance covered by both runners in the 14 s before they first meet each other is equal to the length of the circular track

That is,

126 + 14y = 50y

50y - 14y = 126

36y = 126

y = (126/36) = 3.5 ft/s.

Hence, Paula's speed = 3.5 ft/s

Length of the circular track = 50y = 50 × 3.5 = 175 ft

So, in 4 minutes (240 s), with George running at 9 ft/s, he would have ran a total distance of

9 × 240 = 2160 ft.

2160 ft around a circular track of length 175 ft, means that George would have ran a total number of laps (2160/175) = 12.343 laps.

Breaking this into 12 laps and 0.343 of a lap from the starting point. 0.343 of a lap = 0.343 × 175 = 60 ft

So, 60 ft along a circular track subtends an angle θ at the centre of the circle.

Length of an arc = (θ/360°) × 2πr

2πr = total length of the circular track = 175

r = (175/2π) = 27.85 ft

Length of an arc = (θ/360) × 2πr

60 = (θ/360°) × 175

(θ/360°) = (60/175) = 0.343

θ = 0.343 × 360° = 123.45°

The image of this incomplete lap is shown in the attached image,

The distance of George from his starting point along the centre of the circular track = (r + a)

But, a can be obtained using trigonometric relations.

Cos 56.55° = (a/r) = (a/27.85)

a = 27.85 cos 56.55° = 15.35 ft

r + a = 27.85 + 15.35 = 43.20 ft.

Hence, George is 43.20 ft East of his starting point.

Hope this Helps!!!

6 0
3 years ago
How do I solve this question?
Montano1993 [528]

Answer:

p = \frac{3}{2} , q = 9

Step-by-step explanation:

4x² + 12x ( factor out 4 from each term )

= 4(x² + 3x)

Using the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² + 3x

= 4(x² + 2(\frac{3}{2} )x + \frac{9}{4} - \frac{9}{4} )

= 4(x + \frac{3}{2} )² - 4 × \frac{9}{4}

= 4(x + \frac{3}{2} )² - 9

4 0
2 years ago
What is the volume of the prism?<br> 3 m<br> mº<br> 13 m<br> 13 m
NARA [144]
13 m is the volume of the prism
6 0
3 years ago
How many is 3 1/2 pounds written as a combination of whole pounds and whole ounces
dusya [7]
3.5 pound = 3 5/10 pounds = 3 1/2 pounds 
Now, 1 pound = 16 ounces, so 1/2 pound = 16*1/2 = 8 oz

<span>So the answer is 3 pounds and 8 oz.</span>
5 0
3 years ago
Read 2 more answers
FIRST PERSON TO ANSWER WILL BE MARKED BRAINLEST
nirvana33 [79]

Answer:

thez nuts its A

Step-by-step explanation:

3 0
3 years ago
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