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AveGali [126]
3 years ago
13

Plz help!!!

Mathematics
1 answer:
kvv77 [185]3 years ago
6 0

Answer:

Step-by-step explanation:

Here, y = 10 million = 10000000

10000000 = \frac{1}{2}*(1.21)^x

Simplifying and taking natural log on both sides:

ln(20000000) = x*ln(1.21)

x = 88.19 years

The number of snowboarders will be 10 million for the first time in year 2076.

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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!!!

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