Question

Calculus area between curves question. Diagram and question included below.

Answer 1

Question #4 only.

Answer 2

You must find the point of intersection. What is your plan for that?

Answer 3

Well, I set the two functions equal to one another and tried solving for x. But after using the quadratic formula both my answers were negative and the graph shows we're in Quadrant I

Answer 4

Well, then something went horribly wrong. Let's try it together.

\(1000 - 0.4x^{2} = 42x\)

What shall we do, first?

Answer 5

Hence why I came here haha. If you move the squared term & the constant to the right we get 0 = 0.4x^2 +42x - 1000

Answer 6

Okay. That looks good. Now what? Personally, I would multiply by 10.

Answer 7

Oh wait! I found the mistake. I said c was +1,000 instead of negative.

Answer 8

After correcting that I found x to equal -125 or 20. We reject the negative answer because the graph is in Q1. So x=20?

Answer 9

There you go. This is why we WRITE DOWN our work. We may need to review it. Excellent work.

Answer 10

It is written down just on a separate sheet of paper haha. Okay so I'm unsure of where to go from here.

Answer 11

Now, we just need the integration. How do you find the area between two curves? Your limits are [0,20]

Answer 12

Top minus bottom or right minus left

Answer 13

for q1. you have to rouphly draw the curves other than finding the point of intersection.

Answer 14

I solved Q1-3, thanks though :)

Answer 15

tkhunny: Thank you for all of your help with this! I figured out the integration and got the correct answer.