Vector Calculus Questions and Answers

Construct a power series for 1 x 1 x 1 x 1 Determine the interval of convergence

Match the equation with its graph x y 2 3 Submit Answer DO

Find the angle between the vectors u i 2j v 6i 2j 4k The angle between the vectors is 0 2 46 radian s Round to the nearest hundredth as needed

A 420 unit hotel is trying to determine their daily rates From experience the hotel manager knows that all rooms are typically occupied when the daily room rate is 86 Market research indicates that for every increase of dollars in the daily room rate there will be a rooms vacant Each occupied room costs 22 per day to service and maintain What should the hotel charge per day in order to maximize profit

Determine whether each labeled point is an absolute maximum or minimum a relative maximum or minimum or ne ABCDEFG Select Select Select Select Select Select Select B E C AN F D A G

1 Let A 12 3 4 and f x x 2x 1 Compute f A

3 Find the outward flux for the field F xy i y j across the curve C given below W x y 1

Solve the following linear programming problem graphically Maximize p 4x 5y subject to x y 3 2x y 4 x y 0 Caution Any method other than the

Consider a triangle ABC like the one below Suppose that a 20 b 24 and 4 30 The figure is not drawn to scale Solve the triangle Carry your intermediate computations to at least four decimal places and round your answers to the nearest tenth If no such triangle exists enter No solution If there is more than one solution use the button labeled or B C 0 c 0 D No solution

Hooke s Law In Exercises 5 10 use Hooke s Law to determine the variable force in the spring problem 5 force of 5 pounds compresses a 15 inch spring a total of 3 inches How much work is done in compressing the spring 7 inches 6 A force of 250 newtons stretches a spring 30 centimeters How much work is done in stretching the spring from 20 centimeters to 50 centimeters

Find T N and x for the plane curve r t 8t i 8 In cos t j T Type exact answers using radicals as needed KIN 2 t KIN

Let n be the largest integer such that n 2017 and the sum of its digits equals the product of its digits Find the sum of the digits of n

Find the sum and product of the root for the quadratic equatior x 2 3x 12 0

Find the x and y values at the minimum of f x 2x xy 2y 4y 7

Given f x y 3x 6zy5 6y2 find fxx x y

Find the perimeter of the triangle whose vertices are 10 4 2 4 and 2 1 Write the exact answer Do not round

Sketch a graph of f x 2 x 2 4 5 4 5 4 3 2 1 Clear All Draw 3 2 1 1 2 3 4 5 1 2 3 er 4 5

Can anything be said about the speed of a particle whose acceleration is always orthogonal to its velocity Give reasons for your answer Fill in the blanks Since all of the particle s acceleration is in the direction none of its acceleration is in the direction Therefore the particle s speed is

Let F x f ec2 dt Find an equation of the tangent line to the curve y F x at the point with x coordinate 3

Find the perimeter of the triangle whose vertices are 3 4 3 1 and 4 3 Write the exact answer Do not round

Evaluate the definite integral 1 3x 3x 3x dx

Overview Did you watch the How to Derive the Quadratic Formula If not I highly encourage you do so The second to last line shows the fractions separated before being combined into one like so b 2a b 4ac 2a Directions Think about this formula and answer the following questions Be sure to be thorough and respond to two of your classmates 1 This formula allows us to find the roots zeros of a quadratic function Explain how you know the roots are always symmetric around the x coordinate of the vertex 2 Using this last idea if a function has the roots of x 4 and x 12 what is the x coordinate of it s vertex 3 How does the discriminant relate to this idea post 4 Lastly though it is not relevant to graphing prove that the two roots x x x b It might be best if you work this out on paper and attach a picture of this part to your a

Find the x intercept s of the following function f x 2x 4x 6 Give your answer as ordered pairs separated by commas if necessary For example if you found that the solutions were 1 2 and 3 4 you would enter 1 2 3 4

r t 3t cos t i 3t sin t j 2tk Choose the correct graph below OA O C the position of a particle in space at time t Determine the graph of the position function Spe OB O D

The equation r t t 7 i 31 j 21 k is the position of a particle in space at time t Find the angle between the velocity and acceleration vectors at time t 0 The angle is radians Type an exact answer using x as needed

Determine the equation of the parabola graphed below Provide your answer below 5 4 3 2 0 2 3 4 5 16

atch the equation with its graph Need Help 1 20 no noz

Match the equation with its graph x y 2 7 O DO DO DO

Match the equation with its graph x y 2 7 Submit Appun DO DO DO DO

A jet ski company charges a flat fee of 31 00 plus 1 75 per hour to rent a jet ski Another company charges a fee of 25 75 plus 3 50 per hour to rent the same jet ski

The graph of a function f is given below 0 a State the value of f 1 f 1 X b Estimate the value of f 2 f 2 X

5 and sec y 2 If sin x an T where x and y lie between 0 and 2 evaluate sin x y

and B 8 6 be points in the plane a Find the slope of the line that contains A and B b Find an equation of the line that passes through A and B What are the intercepts x y x intercept y intercept x y c Find the midpoint of the segment AB x y d Find the length of the segment AB e Find an equation of the perpendicular bisector of AB 2

How is the graph of the function obtained from the graph of f y f x O reflected about the x axis O reflected about the y axis O stretched horizontally by a factor of 1 O shifted 1 unit downwards O shifted 1 unit downwards and reflected about the x axis If you have had difficulty with these problems you should look at Sections 1 1 1 3 of your te

10 The population y in the year x of the counties listed is approximated by the given equations where x 10 corresponds to 2010 and y is thousands Solve this system of equations and interpret the answer County A x 20y 67 County B x 10y 27 County C y 4 Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA The system has exactly one solution The solution is Type integers or fractions OB The system has infinitely many solutions of the form Type Integers or fractions OC The system has no solution What does the answer represent Select the correct choice below and if necessary fill in the answer boxes to complete your choice y where y is any real number OA All three counties had the same population of OB Two counties had the same population of in the year OC There will be infinitely many times when the three counties will have the same population OD There will never be a time when all three counties have the same population in the year

Rationalize the numerator and simplify 36 h 6 h If you have had difficulty with this problem you may wish to cor

3x 11x 20 If you have had difficulty with this problem you may wish

4x y z 4 Choose the correct graph of the equation OA X OB X www S O C X

Find the angle between the planes 8x 7y 10 and 4x 3y 10z 6 The radian measure of the acute angle is 0 Round to the nearest thousandth

Question After 2 minutes a submarine had descended to 160 feet After 4 minutes the submarine had descended to 280 feet Assuming a linear function write an equation in the form d t mt b that shows the depth d t after t minutes Be sure o include d t in your answer

Find the 6th term of the expansion 2x 1 a 448x6 b 448x5 OA OB OC OD 84x5 C d 84x

You may remember that the area of a triangle is A B H where B is the base of the triangle and H is the height Suppose that the area of a triangle is 288 square feet and the base is 4 times the height Find the base of the triangle in feet Provide your answer below

Recall that the area of a triangle is A B H where B is the base and H is the height The base of a triangle is 4 times the height If the area is 392 square feet then what is the height of the triangle in fee Sorry that s incorrect Try again

Given the following function which table shows correct values of f x f x 7 10x Select the correct answer below O X 0 1 2 f x 7 3 15 X 0 1 2 f x 7 3 15 X f x 0 10 X f x 7 3 0 1 2 3 20 1 2 3 3 4 11 3 21 X 01 2 f x 7 0 12 3 13 23 3 20

Solve the following pay off matrix 30 0 90 40 80 15 20 20 50

Find the derivative y x 8x 3 x O A y O B y O c y 2x 8 2x3 2 2x 8 X 3x 8x 3 2x3 2 3x 8x 3 OD y X

Decide whether the limit exists If it exists find its value lim f x 1 2 1 f x PAY N OA 0 B 2 O C 1 OD Does

Find the equation of the line which has slope 10 and y intercept 5 Give your answer in the form y mx b uronewer below

Imagine x varying from x 2 to x 2 7 When x changes from x 2 to x 2 7 Ax 7 For this change in x the change in y is A y 42 The value of y when x 2 7 2 7 is Yf y the change in y Yf y Ay Yf Yf

Aces Incorporated a manufacturer of tennis rackets began operations this year The company produced 6 000 rackets and sold 4 900 Each racket was sold at a price of 90 Fixed overhead costs are 78 000 per year and fixed selling anc administrative costs are 65 200 per year The company also reports the following per unit variable costs for the year Direct materials Direct labor Variable overhead Variable selling and administrative expenses Prepare an Income statement under variable costing ACES INCORPORATED Income Statement Variable Costing 12 8