plz explane how to answer it The graph below represents the velocity of a bicycl

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plz explane how to answer it

The graph below represents the velocity of a bicyclist. X is given in hours and Y is given in miles per hour. Suppose she started riding from her house. How far from her house was she after three hours. Find the total distance she made in three hours. Find the farthest she was from her house. Give an interval where her acceleration was negative but her velocity was positive. For the function f(x) = In(2x + 3): Find the linearization for f at x= -1. Use the linearization to approximate In(1.25). Is the approximation in part b) an overestimate or an underestimate? Explain why. A stone is thrown straight up from the edge of a roof, 650 feet above the ground, at an initial speed of 12 feet per second. The acceleration due to gravity is -32 feet per second. Find the formula for v(t), the velocity of the stone t seconds after its release. Find the formula for h(t), the height of the stone above the ground t seconds after its release. What is the highest height can the stone reach? At what time does the stone hit the ground? How fast is it going when it hits the ground? Given the function f(x) = ax3 - x4 where constant a is a positive parameter. Find the x-intercept and y-intercept , State x and y coordinates. Your answer may contain the parameter a. Find the critical point(s) of f(x). State x and y coordinates. Your answer may contain the parameter a. Check if these critical points are local max or min. Find the inflection point(s) of f(x). State x and y coordinates. Your answer may contain the parameter a. Sketch a representative graph of f(x) labeling the points found in (a) and (c).

Explanation / Answer

This is number seven. Y is miles per hour. If Y is greater than zero, she is moving away from home. At hour 2.5 the speed is zero. Then mores than 2.5 hours, she is headed towards home. The funny thing about this graph is that it takes her an hour (the first hour) to accelerate from zero to ten miles per hour.

Let's solve these in logical order.

(c) after 2.5 hours, she is going 0 mph and she hasn't started heading back yet. Here average speed in the first hour was 5 mph, so she travelled 5 miles (distance = rate times time), her average speed for the next hour was 10mph, so she went 10 miles. Here average spped for the next half hour was 5 mph so she went (1/2)*5 = 2.5 miles. Adding up these three distance, we have (5 + 10 +2.5)miles, or 17.5 miles

(c) 17.5 miles

(a) After three hours she is closer to home. The last 0.5 hours she heads back at an average speed of 5 mph. This is 2.5 miles

So the total is (5 + 10 + 2.5 - 2.5)miles or 15 miles. We could also just say 2.5 miles closer than our answer to (c) and that is also 15 miles from home

(a) 15 miles

(b) the total distance doesn't care what direction was, so she went 17.5 miles and then another 2.5 miles for a total of 20 miles

(b) 20 miles

(d) between 2 and 2.5 hours she was still going away from home, but at a smaller and smaller speed. So any time between 2 and 2.5 her acceleration was negative, but velocity was positive.

5. Stone (a) v(t) = Vo - g t

(b) h(t) = ho + Vo t - (1/2) g t ^2

(c) if the velocity is zero, the stone will be at its highest point in the trajectory.

v(t) = 0 = Vo - gt

Vo = gt

Vo/g = t

12ft/s/32ft/s^2 = 0.375 s

Use this time in second EQN

h(t) = 650ft + 12ft/s(0.375s) - (1/2)32ft/s^2(0.375s^2) = 652.25ft

let's check this. The average speed going up is half the starting speed, or 6 ft/s and it is going up for 0.375 s this product is 2.25ft and we add it to 650 ft and get the same answer - always check your work

(d) Stone hits the ground when h(t) = 0

0 = ho + Vo t - (1/2) g t ^2

we could use the quadratic formula

-16 t^2 + 12 t + 650 = 0

divide by two

-8t^2 + 6t + 325 = 0

{-6 +- SQRT(36 - - 4*8*325)}/2*(-8) = -6.01s or 6.76s

The one that makes sense is 6.76 seconds

(e) use this time in the first EQN

v(t) = 12ft/s - 32ft/s^2*6.76s = -204.313 ft/s

or 200 ft/s in downward direction

I would like to see if others have answered before I continue, so all for now.

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