## anonymous one year ago fan medal and testimonial what is the average rate of change of y with respect to x over the interval { 1,5} for the function y=4x+2? choices: 8 1/4( wrong) 2 4

1. Haseeb96

differentiate both sides of this function with respect to x |dw:1436163187408:dw|

2. Haseeb96

now dy/dx is showing speed

3. anonymous

oh that makes more sense I see what id id wrong lol

4. Haseeb96

in order to find average rate of change during the interval { 1,5} we use this formula

5. Haseeb96

|dw:1436163315029:dw|

6. anonymous

can you help me with two more uestions I have tried answering them and keep getting them wrong.

7. Haseeb96

okay tag me there

8. Haseeb96

if you like my explanation click at best response

9. anonymous

the height ,s , of a ball thrown straight down with initial speed 64ft/ sec froma cliff 80 ft. high is s(t)=-16t^2-64t+80, where t is the time elapsed that the ball is in the air. what is the instantaneous velocity of the ball when it hits the ground? 256 -96 0 112

10. anonymous

evaluate lim x->2 f(x) for f(x)= |dw:1436163800477:dw|

11. myininaya

average rate of change of y respect to x over the interval [1,5] is $\frac{f(5)-f(1)}{5-1} \text{ where} f(x)=4x+2$ or since f(x)=4x+2 is just a line you could use the slope of this line to determine the average rate of change over any given interval

12. myininaya

to find velocity just differentiate the position function

13. myininaya

but you will have to find when s=0 first

14. myininaya

since it wants to know the velocity when it hits the ground (means height is 0 there so that is why we set s=0)

15. myininaya

for the last one you will need to consider the left and right limits

16. Haseeb96

|dw:1436164260135:dw|

17. anonymous

what bout 2 and 3?

18. myininaya

well have you solved s=0 yet?

19. myininaya

and then differentiated s to find v

20. anonymous

I got 80

21. myininaya

how did you 80 from solving the equation s=0

22. myininaya

$-16t^2-64t+80=0 \\ \text{ you could divide both sides by -16 } \\ t^2+4t+5=0$ can you see if you can solve that?

23. myininaya

now this will tell us the value t such that s=0

24. myininaya

s=0 means the height=0 we want to find t such that when this happens so we can find the velocity when the ball hits the ground

25. anonymous

oh ok

26. myininaya

oops t^2+4t-5=0

27. Haseeb96

is it -196 ?>

28. myininaya

have you solved for t yet?

29. anonymous

not one of my choices for number 2

30. myininaya

I don't know if you still need help or not...

31. anonymous

I don't have an answer for number 2 or 3 lol I have tried everythig

32. myininaya

have you actually tried solving the equation I have asked you to yet/

33. myininaya

and then differentiating the position function to find the velocity function and then entering the number you found from solving s=0 into velocity function to find the velocity when the ball hits the ground

34. anonymous

yes and I am getting big numbers im terrible at it. this is hwat I got- -96 is that right?