Vector Calculus Questions and Answers

Example Find the function r t that satisfies the given conditions r t t cos nt 4 r 1 2 3 4

6 6 Graphing Li For what value of b P 4b 3 4 G

Factor the given trinomial comp x2 5x 24

A certain electronics manufacturer is making GPUs for gaming laptops GPU stands for graphics processing unit The manufacture found that the marginal cost C to produce x GPUs can be found using the equation C 0 03x 4x 900 If the marginal cost were 816 how many GPUs were produced Select an answer C

below Provide a sketch screenshot of the shape of the lamina The region bounded above by f x x 2 2 4 and below by g x x 2 The region bounded above by f x x 2 4 and below by g x x 2 between 0 4

ist K Points A B and C are three vertices of a re A 4 7 B 8 7 C 4 1 Choose the graph with the given points cor OB

Graph the equation using the slope and y in y x 4 Use the graphing tool to graph the line Use drawing the line

K Graph the solution set of the inequality 2 x 1 5

Find a vector orthogonal to 0 1 2 and 3 2 0

Although 240 is a special angle on the unit circle Aiden wanted to determine its coordinates using the sum and difference formulas Part A Determine cos 240 using the cosine sum identity Be sure to include all necessary work 5 points

Consider the points P 2 4 3 and Q 8 6 9 a Find PQ and state your answer in two forms a b c and ai bj ck b Find the magnitude of PQ c Find two unit vectors parallel to PQ

Estimate the limit numerically if it exists If an answer does not exist enter DNE X 6 lim X 0 X 1

8 Are the following vector functions a r t 4 sin 4t 4 cos 4t t b r t 4 sin 4 cos i 4 arc length parametrizations of the circle of radius 4 centered at 0 0 Justify answers

Given an acceleration vector initial velocity uo vo wo and initial position xo YoZo find the velocity and position vectors for t 0 a t 5t e 11 uo vo wo 0 0 1 xo Yozo 6 0 0 What is the velocity vector v t GUTEN M

Section 6 10 Homewor whether the graph is a function If it

Determine whether the graph is a function If it does represent range Using the vertical line test is this the graph of a function No

Find a formula for this function 05 0 1 y co COS 2 T 1 3 x D L

Find the indicated angle 0 Use either the Law of Sines or the Law of Cosines as appropriate Assume a 120 and c 135 Round your answer to two decimal places 0 O A C a 38 B

Find the indicated angle 8 Use either the Law of Sines or the Law of Cosines as appropriate Assume a 125 and c 141 Round your answer to two decimal places 8 0 A C C 0 a 380 B

For the function f y 48 28y find a f 3 b f 4 c f 3

liggs 2 Use proof by induction to show n 2n 3 for integer values n 3 2

K Benjamin s Backpacks can sell backpacks for 32 per backpack T a Write the cost and revenue equations b Graph both equations for 0 to 50 backpacks on the same axes c Use the graph to estimate the number of backpacks Benjamin s d Write the profit formula e Use the profit formula to determine whether Benjamin s Backpa f How many backpacks must Benjamin s Backpacks sell to realize

Graph the equation by plotting points y 2x 3

Find f g f g fg Find f g x 2x 11 f x 2 x g x x 9 X Find the domain of f g x Enter your answer using interval notation 0 00 Find f g x 7 and f g and their domains X Find the domain of f g x Enter your answer using interval notation 0 00 Find fg x Find Find the domain of fg x Enter your answer using interval notation 0 00

22 If 5 24 then 3 Estimate your answer to two decimal places 30

Fill in the blank To find the y intercept of the graph of a lin

Express x and y in terms of trigonometric ratios of 0 Express your answer in terms of 0 only X y 11 0 16 y

What are the chances that a person who is murdered actually knew the murderer The a his question explains why a lot of police detective work begins with relatives and frienc victim About 64 or people who are murdered actually knew the person who commi murder Source Chances Risk and Odds in Everyday Life by James Burke Suppose ective in New Orleans has 63 current unsolved murders ind the mean and the standard deviation for the approximating normal distribution Find the probability that i at least 35 of the victims knew their murderers ii at most 48 of the victims knew their murderers

14 If u x 3x 8 and X u x V x 15 IF f x x and g x 3 3

Find dy If cx y U 3 and U 3x dy dx

20 The expression e 10 f x can be written as ef where f x is a function of x Find f x

Stacey is building up frequent flier miles on her credit card so she can go on a trip during the summer As a result she is making all of her purchases on her credit card and paying the balance off in full before the bill is due If Stacey has an average daily balance of 301 71 during last month s billing cycle and her APR is 20 5 how much does she owe for finance charges

If A is 5 times as large as B then B is how many times as large as A Write your answer as a fraction in its lowest terms

S z x 4y 1 2 Suppose you are walking on S directly above the curve C given by C x t cos t quad y t sin t quad 0 leq t leq 2 pi Find the values of t for which you are walking uphill increasing 2

Find an angle between 0 and 27 that is coterminal with the given ang 5A 3

Problem 8 A teacher gives a 20 point test to 6 students The scores are shown here 16 20 9 10 18 14 910 14 18 20 a Find the percentile rank of a score of 16 Summarize the results 1633 133 5 b Find the percentile rank of a score of 10 Summarize the results 10 03 00 83 33 c Find the value corresponding to the 45th percentile Summarize the results

My friend has 448 to spend on a fence for her rectangular garden She wants to use cedar fencing which costs 12 meter on one side and cheaper metal fencing which costs 4 meter for the other three sides What are the dimensions of the garden with the largest area she can enclose length for cedar side width for other side meter meter What is the largest area that can be enclosed area meter squared If necessary round your answers accurate to two

The length of a rectangular garden is 7 feet longer than its width If the garden s perimeter is 194 feet what is the area of the garden in square feet

You can retry this question below B K G If all the graphs above R have equations with form y ab Which graph has the largest value for b orange 0 Which graph Which

sin ab COS tan What is n al T 0 1 2 3 4 Input Output 2 4 8 16 n 64 4 5 0 5 1 2 6 3 ans

The demand equation for a certain product is given by p 132 0 06x where p is the unit price in dollars of the product and x is the number of units produced The total revenue obtained by producing and selling a units is given by R xp Determine prices p that would yield a revenue of 5540 dollars Lowest such price Highest such price

The width of a rectangle is 1 less than twice its length If the area of the rectangle is 51 cm what is the length of the diagonal The length of the diagonal is Give your answer to 2 decimal places cm Note Since you are looking for the diagonal you will want to use the pythagorean theorem a b c

w sin z 5 cos y dy dz 25 y cos x dz dr 14xyz dx dy dw zp v fip v xp

Determine whether the given ordereu 5x 4y 8 10x 3y 15

Coffee is draining from a conical filter into a cylindrical pot at a rate of 4 cubic inches per minute The cylindrical pot has a diameter of 6 inches and a height of 6 inches The height and diameter of the cone filter are both 6 inches 6 in 6 in 6 in How fast is this water level h dropping How fast is this coffee level H rising Questions to Answer 1 How quickly does the height h of the water level in the cone filter fall if the water level h in the filter cone is 4 inches How does this answer change if the water level h in the filter cone is 2 inches 2 How fast is the coffee level H in the pot rising when the water level h in the filter cone is 4 inches How fast is the coffee level H in the pot rising when the water level h in the filter cone is 2 inches 3 TRUE or FALSE A The water level h in the cone filter is dropping at a constant rate B The coffee level H in the pot is increasing at a constant rate

1 2 3 Graph the function by applying an appropriat g x x Ty 8 6 NJE MANIFURKANZEL 4

13 csc x cot x CSC x sec x

f x y e cos 9y ind and classify all critical points of the function If there are more blanks han critical points leave the remaining entries blank C Y 1 IX r xy YY 9 10

2 Prove by mathematical induction that for nezt 1 5 9 4n 3 2n n

What s the relationship between systems and matrices How do you a matrix to solve system of equations