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kogti [31]
3 years ago
14

The Grand Canyon is approximately 2^9 kilometers long. Mariner valley is a canyon on mars that is approximately 2^12 kilometers

long. How many times longer is mariner valley than the Grand Canyon
Mathematics
1 answer:
gulaghasi [49]3 years ago
3 0
2^12 - 2^9 would equal 3,584 
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-0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.

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x= distance between the wall and ladder

Ф = angle between the ladder and ground

The rate of change is: dx/dt = 0.8 ft/s

We need to find dФ/dt when x = 8 ft/s

From the triangle in the figure we see that:

cos Ф = x/10

=> x = 10 cosФ

Now, the rate of change will be

d(x)/dt = d/dt (10cosФ)

dx/dt = -10 sin Ф dФ/dt

dx/dt = 0.8 (given)

to find dФ/dt

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100 = 64 +  (Perpendicular)^2

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Putting values in:

dx/dt = -10 sin Ф dФ/dt

0.8 = -10(3/5) dФ/dt

0.8 = -6 dФ/dt

=> dФ/dt = 0.8 / -6

dФ/dt = - 0.133 radians/s

So, -0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.

3 0
3 years ago
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