Calculus word problems

Question

Hi, I really need help with these two word problems

1. The upper right hand corner of a piece of paper, 15 in. by 10 in., as in the figure, is folded over to the bottom edge. How would you fold it so as to minimize the length of the fold? In other words, how would you choose x to minimize y?

2. Two sides of a triangle have lengths 9 m and 17 m. The angle between them is increasing at a rate of 2/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60? (Round the answer to three decimal places.)

Thanks!

Answer 1

Hi Regina, I will get you started on question 2. No diagram for question. although my guess is you are folding that corner to touch the bottom of the page somewhere along its edge.

 

2. The length of the 3rd side depends on the size of the included angle. The formula for that relationship is the Law of Cosines. Does that sound familiar. For example a² = 9² + 17² - 2(9)(17) cos A.

 

Use implicit differentiation with respect to t. The idea is to solve for da/dt given that dA/dt = 2/m/min. You will also have to find the value of a when A = 60. Remember that the derivative of the constants in that formula is 0.

 

Hopefully that is enough to get you started.