12. [1'2 Puintsl I DETAILS I LARCALCH 3.1'D11. Find the length and width of a rectangle that has the given perimeter and a maximum area. Pen'meter: 212 meters :m :m Need Help? 13. [42 Paints} DETAlLS LARCALCH 3.1013. Find the length and width {in feet]: of a rectangle that has the given area and a minimum perimeter. Area: 25 Square feet Need Help? ft [smaller 1value] ft (larger value} A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (1, 2) (see figure below). (a) Write the length _ of the hypotenuse as a function of x. ,x>1 (b) Use a graphing utility to approximate x graphically such that the length of the hypotenuse is a minimum. 6 8 10 -2 -8 -B O -10- O -10 10 10 2 O Find the value of x that produces the minimum value L. (Round your answer to three decimal places.) X = (c) Find the vertices of the triangle such that its area is a minimum. (Order your answers from smallest to largest x, then from smallest to largest y.) ( x, y) = CL (x, ) ) = ( (x, y ) = (- mem W Use differentials and the graph of fto approximate the following. {Round your answers to two decimal places.) 24. [-1'2 Points] DETAILS LARCALC1 1 3.9.0315\". MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The total stopping distance Tof a vehicle is shown below, where Tis in feet and x is the speed in miles per hour. T = 2.5x + 0.5x2 Approximate the change and percent change in total stopping distance as speed changes from x = 20 to x = 21 miles per hour. {Round your answers to one decimal place.) 25. [-32 Points] DETAILS LARCALC11 3.9.939. MY NOTES ASK YOU R TEACHER PRACTICE ANOTHER The period of a pendulum is given by the equation shown below, where .L is the length of me pendulum in feet. g is the acceleration due to gravity, and Tis the me in seconds. T=21Ir i Q We pendulum has been subjected to an increase in temperature such ihat the length has increased by 1% (3) Find the approximate percent change in the period. :92. (b) Using the result in part (a), nd the approximate error in this pendulum clock in 1 day. S min Need Help? lim 9 cos 1 X - 00 4x Need Help? Read It /2 Points] DETAILS LARCALC11 3.7.005. Find two positive numbers that satisfy the given requirements. The sum is S and the product is a maximum. (smaller value) ( larger value) Need Help? Read It Watch It [-/2 Points] DETAILS LARCALC11 3.7.007. Find two positive numbers satisfying the given requirements. The product is 768 and the sum of the first plus three times the second is a minimum. (first number) (second number) Need Help? Read It Watch It [-/2 Points] DETAILS LARCALC11 3.7.009. Find two positive numbers satisfying the given requirements. The sum of the first and twice the second is 320 and the product is a maximum. (first number) (second number) Need Help? Read It Watch It