Vector Calculus Questions and Answers

Consider a 400 N weight suspended by two wires as shown in the figure Find the magnitudes and components of the force vectors F and F2 F N Round to one decimal place as needed F ON Round to one decimal place as needed F 00 Round to one decimal place as needed F1 25 50 400 N

Find the following for the vectors v 101 9k and u i k a v u v ul b the cosine of the angle between v and u c the scalar component of u in the direction of v d the vector proj u a v u Type an exact answer using radicals as needed v Type an exact answer using radicals as needed u Type an exact answer using radicals as needed b The cosine of the angle between v and u is Type an exact answer using radicals as needed c The scalar component of u in the direction of v is Type an exact answer using radicals as needed d proj u Type your answer in terms of i j and k Type an exact answer using radicals as ne

Write inequalities to describe the following sets a The interior of the sphere of radius 4 centered at the point 3 6 2 b The exterior of the sphere of radius 4 centered at the point 3 6 2 a Choose the correct inequality OA x 3 y 6 z 2 s1 OB x 3 y 6 z 2 16 OC x 3 y 6 z 2 16 OD x 3 y 6 z 2 10 16 b Choose the correct inequality OA x 3 y 6 z 2 16 OB x 3 y 6 2 2 16 OC x 3 y 6 z 2 16 16 OD x 3 y 6 z 2 1 2

Use substitution to evaluate the indefinite integral Provide your answer below f In 2x dx 5x In 2x 5x dx

Find the equivalent expression 1 sin x 1 sin x 1 sin x 1 sin x O 4 tan x sec x O 4 cot x csc x O4 tan x sec x O 4 cot x csc x O 4 cot x sec x

Evaluate the indefinite integral given below Provide your answer below 20 5 dx 2e 6 x4 X5 31 dx

The measure of the angle 330 in standard position is given Find two positive angles and two negative angles that are coterminal with the given angle 670 1 060 70 345 690 1 050 30 390 O 710 1 020 50 360 426 786 294 654

Find the missing side lengths Leave your answers as radicals in simplest form 25 26 30 7 3 A x 7 3 y 14 B x 14 y 7 C x 7 2 y 7 D x 7 2 y 7 3 A 60 5 3 y A x 10 y 5 B x 10 3 y 5 5 3 C x 10 3 y 3 5 3 D x 10 y 3

Find the value of each trigonometric ratio 29 tan X 20 30 50 40 355554 Z 30 tan C B 12 U 35 20 37

12 g x 2 x 25 A 8 x 5 B g x 2x 3 25 2 C g x D g x 6 4x 3 2 13 g x 4 3x 2 A g x 12 x 4 B g x 2x 4 3 C g x 25 2x 5 D g x 2 2

Solve the equations below exactly Give your answers in radians and find all possible values for t in the interval 0 t 2 If there is more than one answer enter your solutions in a comma separated list a sin t when t b cos t c tan t 3 2 1 3 when t when t A 94

Use a calculator to approximate the value of the expression if possible Round your answer to the nearest cos 0 58

x y 2 2 4x 2y 2z 5 r x 2 2 y 1 2 z Center 1 Answer 1 x 2 2 y 1 2 z 1 2 1 Answer 2 1 K

6 6 6 Evaluate log10 log100 log1000 log10000 in two different ways Explain your methods

The federal tax rate for single filers is given as a percentage of taxable income in the graph below Find a C lim r x b lim r x x 9525 d x 9525 lim r x X 9525 lim r x x 50 000 Tax rate percentage 30 20 10 y r x 9 525 38 700 82 500 Taxable income in dollars 11

1 point Show that A APBP 16 53 14 3 13 31 are similar matrices by finding an invertible matrix P satisfyin and B

Sketch the graph of the function by making a table of values Use a calculator if necessary Simplify your answers completely Round your answers to four decimal places h x 1 1 5 1 0 5 10 h x 1 1 15 10 y 15 10 5 5 10 15 10 15 X 15 10 15 10 y 5 5 10 15 5 10 15 X

Sketch the graph of the function by making a table of values Use a calculator if necessary Simplify your answers completely Round your answers to four decimal places h x 1 1 x O 5 1 0 5 10 h x 1 1 15 10 15 10 5 y 15 10 5 S 10 15 y 15 10 5 10 15 10 10 15 15 X O 15 10 15 10 7 15 10 S 7 y 10 15 15 10 5 10 15 S 10 10 15 15 X

Match the exponential function with one of the graphs labeled I or II Rx 5x 1 I 5 3 3 2 1 O The graph of f x 5 1 is graph I O The graph of f x 5x 1 is graph II 1 2 3 X II 3 2 1 2 1 2 3 X

Determine the missing coordinates of the points on the graph of the function X X 3 x 2 X2 Y2 1 X3 Y3 ym 7 1 X1 y1 y R 22 7 45 y cos x X3 Y3 3 x

Fill in the blank to complete the trigonometric identity Simplify your answer completely

Solve the exponential equation 3 81

Find all solutions of the equation in the interval 0 2m algebraically Use the table feature of a graphing utility to check your answers numerically 7 sec x 7 tan x 7

Factor the expression and use the fundamental identities to simplify Use a graphing utility to check your result graphically 2 sec x 2 sec x 2 sec x 2

Complete the table of values rounded to two decimal places f x 5e x 3 X 3 2 1 0 1 2 3 Sketch a graph of the function 3 2 1 3 O 2 1 y 15 10 5 10 15 y 15 10 5 10 15 1 2 1 2 3 3 2 1 3 2 1 y 15 10 10 15 y 15 10 S 10 15 1 2 1 2

Use a calculator to evaluate the function at the indicated values Round your answers to three dec h x e h 1 h h 5 h 5 h 1 h h 5 h 5 W

Tue or False 12 x Let x x 1 2x 4 a The graph of r has a vertical asymptote x 1 O True O False b The graph of r has a vertical asymptote x 2 O True O False c The graph of r has a horizontal asymptote y 1 O True O False d The graph of r has a horizontal asymptote y O True O False

Find all horizontal and vertical asymptotes if any If an answer does not exist enter DNE Enter your answers as a comma separated list of equations r x 3 X 9 vertical asymptote s horizontal asymptote 10

2 Refer to the given vectors for the problems that follow 5 points each a Find v 3u u i 2j v i

A tree casts a shadow 6 feet long At the same time a person who is 4 feet tall casts a shadow that is 2 feet long How tall is the tree 19 feet 17 feet 15 feet 12 feet

X Given f x x 3x 2x 1 What is the degree of the function As x approaches negative infinity f x is approaching

Find where x 2x 0 Write your answer in interval notation Round to one decimal place as needed Try again Left Interval 0 00 Right Interval undefined Edit my response

Use a graphing utility to approximate the real solutions Round to two decimal places x 3x 6x 1 0 Solution 1 Solution 2

www Find the solution to the equation given below Exact values only e 5

Solve the equation 3x 1 10 Show your work Round to one decimal place as needed Solution 1 Solution 2

Use the properties of logarithms to condense the expression Assume z 6 5 In z In z 5 2 In z 6

A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building Round your answer to two decimal places Enter an integer or decimal number more Question Help Message instructor

14 sin A B 7 A 24 25 C

13 sin A B 9 A 40 41

12 sin X X 50 48 Z 14 Y

Find the value of each trigonometric ratic 11 cos X Y 27 36 45 X

Question 4 Find the domain of function r z 22 7x 3 Write your answer using interval notation in the box below Enter your values as integers or reduced fractions Domain of r z 21 72 3 Question Help Video Morrago instructor

angle between u 4 5 and v 1 2 to the nearest tenth of a degree The angle between u and v is Round to the nearest tenth O

u 41 v 21 8 a 4u Type your answer in terms of I and J 5u

Use Lagrange multipliers to find the maximum and minimum values of f x y x 4xy subject to the constraint x y 106 if such values exist Enter the exact answer If there is no global maximum or global minimum enter N Optimal f xv

The figure below shows level curves for production f x y as a function of the quantities x and y of two raw materials utilized The cost of the materials is 15x 20y thousand dollars What is the maximum production possible with a budget of 300 thousand dollars How much of each raw material should be purchased to achieve this maximum 20 15 10 5 Y 2000 CT 5 10000 20000 10 15 20 25 Enter the answers to the nearest integer The maximum production possible is i of x and J dollars of y should be purchased

Evaluate sin 9x lim 20 e 1 Question Help Video Written Example M

If csc 0 1 and 0 0 2 then evaluate the following 10 1 sec 0 2 sin 0 3 cos 0 4 tan 0 5 cot 0 JI CI

Solve the problem 30 A wheel with radius 3 m rolls at 17 rad s How fast is a point on the rim of the wheel rising when the point is 7 3 radians above the horizontal and rising Round your answer to one decimal place A 12 8 m s D 25 5 m s B 102 0 m s C 51 0 m s 30

Evaluate the following Give your answer as a fraction NO DECIMAL numbers If sin 0 0 0 2 then cos 0 equals tan 0 equals sec 0 equals