Vector Calculus Questions and Answers

Solve exactly 9 HU 27 5x 1 Entry tin If you include logar

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Find the solution of the The exact solution in t The approximate solut Question Help Vide Calculator

Find the centroid of the region bounded by y x 338 and x 338 assuming the density 6 x y 1 Use symbolic notation and fractions where needed Give your answer as point coordinates in the form x y 70304 3

16 15 14 13 18 11 10 9 8 0 L O f x A D C 3 2 2 3 6 8 9 10 11 12 4 The curve above is the graph of a sinusoidal function It goes through the points 12 0 and 2 0 Find a sinusoidal function that matches the given graph If needed you can enter T 3 1416 as pi in your answer otherwise use at least 3 decimal digits

Simplify and write the trigonometric expression in terms of sine and cosine 1 f x tan a csc x f x

If sect tan t f t 1 f t tant then

CHO Simplify and write the trigonometric expression in terms of sine and cosine 1 cos y 1 secy

Given the following vector field and oriented curve C evaluate F x y on the parabola r t 4t 3t for 0 t 1 The value of the line integral of F over C is Type an exact answer using radicals as needed fF Tds C

The amount of garbage G produced by a city with population p is given by G f p G is measured in tons per week and p is measured in thousands of people The town of Tola has a population of 35 000 and produces 13 tons of garbage each week Express this information in terms of the function f Of 13 35 O f 35 13 Of 13 35

x 4x x 6 and H x 4 x 2 The graphs of the functions h x intersect at P 1 4 and Q a b where a b E Z Determine the values of a and b writing your answer in the form a b

The cost of erecting the ground floor of a building is 35 000 The cost of adding an extra floor increases by 5 for each extra floor Find the total cost of erecting 5 floors

Bonus Madison wants to swim across a lake from point A to point B but wants to know the distance she will have to swim The figure shows the distance from a point C to each end of the lake The measure of the angle at point C is 32 How far will she need to swim 10 pts Hwy 20 4 2 miles Lake William 32 CR 3 3 5 miles A

Determine the bearings for each of the following 3 pts each b a W S N 0 160 E W N E 8 55

Az 10 5 3 5 7 5 25 9 A parallelogram with sides 7 and 15 has a shorter diagonal of 10 Find the length of the longer diagonal 15 15 7 15 10 2 15 XU COSA SA 7

Find the inverse of the given nonsingular matrix 98 33 The inverse of the matrix 98 33 is Type an integer or simplified fraction for each matrix element

Solve for y from the given equations using determinants 4x y z 5 2x 2y 3z 10 5x 2y 6z 1

Compute the given product 101 251 531 1 2 1 3 5 1 101 12 251 13 531 5 1

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Re arrange the follwing equation in order to solve for x x y 5 For the toolbar press ALT 510 PC or ALTHEN F10 Mac

A rectangular metal tank with an open top is to hold 62 5 cubic feet of liquid What are the dimensions of the tank that require the least material to build The tank that requires the least amount of material to build has length Simplify your answers ft width ft and height ft

U V 10 10 V u v u 10 5 10 10 5 5 10 10 u X 10 X 10 10 10 5 5 10 u v 5 10 10 5 5 10 u v 5 5 u u

C 3u 5v 3u 5v 40 3u 5v 3 u 4 40 20 20 20 40 3u 5v y 20 40 y 40 20 20 40 3 u 20 40 40 X X 40 40 20 3u 5v 20 40 R 3u 5v 20 40 y 40 20 40 3 u 20 3 u 20

Convert the equation f t 37 Give answers accurate to three

Find u v u v and 3u 5v Then sketch each resultant vector u 5 7 v 8 0 a u v u v 15 10 5 8 6 4 2 5 5 5 5 V 10 10 u v U V x 15 X 15 15 10 5 5 5 V 10

Solve for w in the equa 2 log4 1 256 W

Consider a circle with radius 20 that is centered at the origin Find the exact x and y coordinates of 11T the point on this circle corresponding to an angle x y Remember to give exact answers using square roots if necessary

11T Without using a calculator compute the sine and cosine of 6 What is the reference angle In what quadrant is this angle sin 11 COS Type sqrt 2 for 2 and sqrt 3 for 3 by using the reference angle radians answer 1 2 3 or 4

A legislative committee consists of 9 Dem

Current Attempt in Progress Manufacturing overhead data for the production of Product H by Shakira Company assuming the company uses a standard cost system are as follows Overhead incurred for 45 400 actual direct labor hours worked Overhead rate variable 8 fixed 1 at normal capacity of 54 000 direct labor hours Standard hours allowed for work done Compute the total overhead variance Total overhead variance S 411 660 9 45 340

Consider the function F x y e e x 14 14 and the point P 2 2 a Find the unit vectors that give the direction of steepest ascent and steepest descent at P b Find a vector that points in a direction of no change in the function at P a The direction of steepest ascent is

1 Sketch the curve by elimination the parameter and indicate the direction of increasing t a x 3t 4 y 6t 2 b x 2cos t y 5sin t 0 t 2 c x 2sin t y 3cos t 0 t

Solve the following system of equations using matrices row x y z 2x 3y 2z x 3y 2z 6 2 11

J x 2 sin x 6 cos r on 7 7 Enter DNE if an answer does not exist a Give the domain of f in interval notation intervals b Determine the intervals on which f is concave up down f is concave up on f is concave down on Based on your answers in a and b determine the inflection points of f help numbers Each answer should be entered as an ordered pair x y Separate multiple answers with commas d Find the critical numbers of f and use the Second Derivative Test when possible to determine the relative extrema Relative maxima occur at x with commas Relative minima occur at x commas help Separate multiple answers Separate multiple answers with e Find the x values where f x has a relative maximum or minimum f has relative maxima at x with commas f has relative minima at x with commas Separate multiple answers Separate multiple answers

VEIVI LIJE INGALIudici In the following questions consider the function Enter DNE if an answer does not exist a Give the domain of f in interval notation infinity infinity b Determine the intervals on which f is concave up down f is concave up on 3 2 infinity f is concave down on infinity 3 2 f x x help Based on your answers in a and b determine the inflection points of f 3 2 535 4 help numbers Each answer should be entered as an ordered pair x y Separate multiple answers e Find the x values where f x has a relative maximum or minimum d Find the critical numbers of f and use the Second Derivative Test when possible to Relative maxima occur at x 4 199 Separate multiple answers with c Relative minima occur at x 7 466 5 Separate multiple answers with co

Consider the function f x x 4 5x Its derivative is f x 3x 2 9x 12 Its second derivative is f x 6x 9 A 12x1 The graph that correctly displays f x in black and f x in orange is OA B YOU 10 D help formulas f is concave down on 2 infinty Using the graphs of f and f indicate where fis concave up and concave down Enter E f is concave up on 5 2 help intervals

y MuetsUGNAREmpt 1 of 3 10 11 00 12 13 the murder of Alexander Litvinenko a Russian dissident was though The half life of 210 Po is 138 4 yr If 0 8 mg of 210Po is present in a sam the function for the given values of I and interpret the meaning in co 38 4 76 8

Answer the following True or False If f x is continuous at x 3 and f 3 True False 2 then lim f x 2 x 3

P x 5 2 1 a Use transformations of the graph of y 5 to graph the given function b Write the domain and range in interval notation c Write an equation of the asymptote Part 0 3 Part 1 of 3 a Use transformations of the graph of y 5 to graph the given function 183 A P 5

Graph the feasible region for the system 5x 7y 35 3x 5y 15 0sy 2 x 0 Use the graphing tool to graph the syster Click to

Graph the feasible region for the following s bounded or unbounded

Determine the area of the region bound by the following curves Leave your answer in exact form no decimals Hint Sketch the region a f x 2 z and g x 2 8 b y 8x y and 21 y x

46 Describe the graph of the equation r 6 sin 8 A a circle of radius 3 with center at the point 3 90 B a circle of radius 6 with center at the point 6 90 C D a circle of radius 3 with center at the point 3 0 a circle of radius 6 with center at the point 6 0

0 Change the point 4 300 from polar to rectangular coordinates A 2 3 2 B 2 2 3 C 2 2 3 D 2 3 2

31 Multiply and express your result in algebraic form a bi 4 cos 85 i sin 85 x 5 cos 50 i sin 50 A 10 2 10 2 B 20 2 201 2 C 20 2 201 2 D 10 2 10i 2

14 A bowl contains 5 apples 3 oranges and 6 bananas Without looking Carl chose one piece of fruit for 8 himself What is the probability that he chose an apple or an orange 15 Bob wants to create

2 Heidi bought a used Jeep for 13 500 She put down 2 000 and paid 220 monthly for 60 months What is the amount of finance charge Joyce will pay 02 26 50 Amount of finance charge

The table below shows the cost of different numbers of goldfish at a pet store COST OF GOLDFISH Number of Goldfish 5 10 15 20 Cost 1 50 3 00 4 50 6 00 The cost is a linear function of the number of goldfish Which statement describes the rate change of this action The cost increases 1 50 each time 1 goldfish is added The cost increases 0 30 each time 1 goldfish is added The cost increases 3 00 each time 5 goldfish are added The cost increases 6 00 each time 5 goldfish are added

Determine a the area and b the perimeter of the

Suppose that the marginal propensity to save is ds dy 0 1 in billions of dollars 7y 8 and that consumption is 7 billion when disposable income is 0 Find the national consumption function Round the constar integration to the nearest hundredth C y