Application of derivatives Questions and Answers

Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c guaranteed by the theorem f x x 6x 1 0 9 f c 28 C

Find the distance from the point to the plane 2 3 1 x 2y 3z 17 The distance is Type an exact answer using radicals as needed

The vector v ai bj is perpendicular to the line ax by c Use this fact to find an equation of the line through P perpendicular to v Then draw a sketch of the line including v as a vector starting at the origin P 1 8 v 4i j

Let u 2 3 and v 2 3 Find the component form and magnitude length of the vector 5u 3v The component form is 5u 3v Simplify your answers

9 2 What Did One Dog Say To The Other Dog Write the letter of each answer in the box containing the exercise number Find the hypotenuse c of the right triangle with the given side lengths a and b 1 a 15 b 20 3 a 13 b 84 5 a 6 b 17 5 Find the side length b of the right triangle with the given hypotenuse c and side length a 7 c 61 a 11 8 c 82 a 80 9 c 34 a 16 10 c 65 a 63 12 c 10 a 5 13 An access ramp to a building is 3 7 meters long The distance from the beginning of the ramp to the base of the building is 3 5 meters How tall is the ramp 11 c 13 a 6 6 14 A rectangular garden is 14 feet wide and 48 feet long If you stand in one corner of the garden how many feet away is the corner diagonally across from you 10 6 2 a 5 b 12 4 a 65 b 72 6 a 6 b 7 2 13 14 4 12 1 8 3 7 Answers T 93 3 P 1 2 9 E 18 5 D 18 N 25 U 9 0 97 H 50 N 60 G 30 O 13 M 11 2 1 85 S 16 11 5

1 Let z e y sin x y e cos x y Show that it satisfies the equation xz Y y 0 Answer

1 Let z e sin x y e cos x y Show that it satisfies the equation x2 y y 0

2 Integrate f x y z x 3y z z over the line segment C joinin the origin to the point 1 1 1

ind all solutions of the following system of linear equations 4x2 8x3 x2 3x3 202 5 02 x1 371 12 1 6

Deductible 2000 00 Event 1 Description Tree damage Foundation repairs Repair cost 2 500 00 25 000 00 If no insurance claim is submitted for Event 2 what is the owner s out of pocket cost for the repair A 500 B 2 000 C 25 000 Event 2 D 2 500

A lamp has the shape of a parabola when viewed from the side The lamp is 32 centimeters wide and 32 centimeters deep How far is the light source from the bottom of the lamp if the light source is placed at the focus 32 cm 32 cm cm Light source 32 cm 16 32 32 cm 0 0 cm 16 32 E

Find the period phase shift and amplitude of the function y 2 cos TX 2 Give the exact values not decimal approximations Period Phase shift 8 X B

A parabola is shown below Its vertex and another point on the parabola are labeled Write an equation of the parabola 0 3 4 142 9 010 0 0

Find an equation of the parabola with vertex 3 3 and focus 3 9 1 X 3 0 0 5

Question You are told that h is a one to one function with values h 2 9 and h 4 10 Which of the following must be true Select all correct answers Select all that apply h 2 9 h 9 2 h 10 2 h 9 10 h 10 4 h 4 10 m

How many functions are there from a set with 4 elements to a set with 6 elements