Vector Calculus Questions and Answers

Graph the rational function f x 7 2 x 2 Start by drawing the vertical and horizontal asymptotes Then plot two points on each piece of the graph Finally click on the graph a function button 6 5 4 7 6 5 4 5 6 8 X 1 S

Find the least common multiple of these two expressions H 856 32 8v uy and 12u y

x t Find a plane containing the line y t 8x 7y 8z 2 1 3t 5 6t and orthogonal to the plane 7 5t

Consider the following function Answer 2 Points 8 Step 3 of 3 Identify the correct graph of this piecewise defined function 4 t x 811 Enable Zoom Pan 2 O 4 O Enable Zoom Pan if x 3 if x 3 8 Enable Zoom Pan 81 0 0 4 O C x Enable Zoom Pan K

Simplify the following assuming x 0 y 0 and z 0 80x y z 20x y z

Simplify completely assuming both x 0 and y 0 16x y6 Provide your answer below

How would you expand x 3y y 2x 10 4th term in expansion of 4y

11 2nd term in expansion of 3u 1

Find the distance between the points 4 9 and 8 1 Give an exact answer in simplest radical form Do not round

Graph the equation y 2x 5 by plotting points To plot points click on a point on the graph and drag it to the desired location Provide your answer below S 5

Replace the polar equation with an equivalent Cartesian equation 1 2 cos 0 3 sin e O 2y 3x 1 2x 3y 1 1 2x 3y 0 1 1

X 5 3 Step 2 of 2 Find the formula for g f x and simplify your answer Then find the domain for g f x Round your answer to two decimal places if necessary Answer f x x 2 and g x g f x Domain Keypad Keyboard Shortcuts

Answer Step 2 of 2 Find two points on the graph of this function other than the origin that fit within the given 10 10 by 10 10 grid Express each coordinate as an Integer or simplified fraction or round to four decimal places as necessary Enter the coordinates to plot points on the graph w x ACI 2x 10 5 Enable Zoom Pan 10 Ke Keyboard She

For what values of b are the given vectors orthogonal Enter your answers as a comma separated list 31 b 6 b b b b

Find the angle between the vectors First find an exact expression and then approximate to the nearest degree u 7 4 v 6 1 exact approximate 23 X

Convert the Cartesian coordinate 6 4 to polar coordinates 0 0 2 r 0 r 2 13 Enter exact value 0 188 80 Question Help Vides 1 F X retry this question below OF

a Find the average value of f x x 3 on the interval 2 5 b Find c such that f c fave

Find the minimal distance from the point P 4 1 0 to the surfac 2 1 2x 2y

25T b If s 4 and P s represent points on the unit circle find a real number t in the interval 0 2 such that P t P s Recall that P t

A construction crew is lengthening a road The road started with a length of 59 miles and the crew is adding 2 miles to the road each day Let L represent the total length of the road in miles and let D represent the number of days the crew has worked Write an equation relating L to D Then use this equation to find the total length of the road after the crew has worked 37 days Equation Total length of the road after 37 days miles 0 0 O 5

Give three different polar points that are at the 5TT same position as A 3 Point 1 8 You can use degrees or radians in the angle but remember to use the degree symbol if you give an angle in degrees

Enter exact Va des X y Question Help Worked Example 1 Message instructor Submit Question Question 7 0 1 pt 398 i Details Convert the point with Cartocian coordinatos

Consider vectors a 3 2 and b 4 7 find the vector a b and choose the correct answer below O 7 9 0 1 9 O 7 5 O The vector a b does not exist

Total score of 12 points Score for Question 1 of 2 points 1 The hypotenuse of a right triangle measures 2 15 centimeters and its shorter leg measures 2 6 centimeters What is the measure of the larger acute angle of the triangle Round your answer to the nearest tenth of a degree Answer

Given t 8 7 and u 11 4 what is t u O 116 O 60 O 12 O 116

36 One spring day Elroy noted the time of day and the temperature in degrees Fahrenheit His findings are stated below At 6 a m the temperature was 50 F For the next 4 hours the temperature rose 3 per hour The next 6 hours it rose 2 per hour The temperature then stayed steady until 6 p m For the next 2 hours the temperature dropped 1 per hour The temperature then dropped steadily until the temperature was 56 F at midnight On the set of axes below graph Elroy s data Temperature F 80 70 60 50 6 am 12 Noon 6 pm 12 Midnight State the entire time interval for which the temperature was increasing Determine the average rate of change in degrees per hour from 6 00 p m to midnight

ons Course Packet on break even points A manufacturer of We All Love Business Calculus tee shirts has a monthly fixed cost of 35 000 and a processing cost of 5 for each tee shirt produced The shirts sell for 10 each If the break even level for the production and sale of x tee shirts is defined to be where the total revenue is equal to the total cost find the break even value for x Break even value of x

Let f x 2x 3x 4 and g x 2x 1 Determine the rule for the composite functions fo g and go f fog x ons gof x

If f x 7 and g x 5x 4 compute the compositions fog 1 and gof 1 5x 2 fog 1 gof 1

3 Which image is a rotation about the point of the figure shown below 1 point 7 57V 4 When the flower below is rotated clockwise 90 where will the red petal be in the ima

Find the potential function f for the field F 8x i 3y j 5z k

Critical 9 Thinking The palm tree on the left is 10 years old The palm tree on the right is 8 years old The trees grow at the same rate a Estimate the height y in feet of each tree b Plot the two points x y where x is the age of each tree and y is the height of each tree d c What is the rate of growth of the trees Write an equation that represents the height of a palm tree in terms of its age

e the Alternating Series Estimation Theorem or Taylor s Inequality to estimate the range of values of x for which the given approximation is accurate to within the stated error Check your answer graphically Enter your answer using interval notation Round your answers to three decimal places sin x x Jerror 0 0001

B Use the graph of the rational function g x pictured below to answer the following questions a Complete the following statements As x o the graph of g x 2 As x 3 the graph of g x As x 17 the graph of g x b What factor is guaranteed to be in both the numerator and denominator of the equation of g x Justify your answer 0 c What factor is guaranteed to be in the denominator of g x but not in the numerator Justify your answer d If g 0 what factor is guaranteed to be in the numerator but not in the denominator Justify e Identify the horizontal asymptote and hence write the equation of g x

2 Create 2 points in R using 4 and 1 Write the vector and parametric equations for the line formed by these 2 points

14 D 1 point Choose EVERY true proportion AB AC BD CE AD DO AB BC DE AB BD BC DE AC BC AE DE m

A news item is heard on the late news by 4 of the 64 people in a small community By the end of the next day 16 people have heard the news Write an equation for the number of people y have heard the news in t days How many people have heard the news after 3 days Complete the equation below y 64 1 Do not round until the final answer Then round to three decimal places as needed

1 point A triangle has vertices of 0 3 5 3 1 5 0 1 5 If it is dilated with center at the origin and a scale factor of 2 what will be the coordinates of the image 0 7 6 3 0 3 0 4 6 0 0 6 0 4 6 0 0 3 0 1 3 2 0 0 3 2

1 point triangle has vertices of 0 3 5 3 1 5 0 1 5 If it is dilated with center at the origin and a scale factor of 2 what will be the coordinates of the image 0 7 6 3 0 3 0 4 6 0 0 6 0 4 6 0 0 3 0 1 3 2 0 0 3 2

BA Are the triangles similar Not similar Yes by the AA rule Yes by the SSS rule Yes by the SS rule B D

21 116 Find the volume of the figure shown A 60 cubic feet B 62 cubic feet C 64 cubic feet D 72 cubic feet E None of the above 12 ft 3 ft 4 ft Triangular prism

Match each method of proof the left column with its description the right column Direct proof Proof by contraposition Proof by contradiction Proof by counterexample A In order to prove that p q T we show that q p T B The method is used to prove that the original statement Vx P x Q x is false by showing that 3x P x AQ x T c Show that in the implication p q q can not be false if p T Show that the negation of the original theorom implies mont

It takes Fena Tailoring 3 hr of cutting and 6 hr of sewing to make a tiered silk organza bridal dress It takes 6 hr of cutting and 3 hr of sewing to make a lace sheath bridal dress The shop has at most 24 hr per week available for cutting and at most 21 hr per week for sewing The profit is 325 on an organza dress and 236 on a lace dress How many of each kind of bridal dress should be made each week in order to maximize profit What is the maximum profit The shop should make organza dresses and lace dresses to yield a maximum profit of

Which vector is represented by the orange vector 5 3 O 2 10 3 7 7 10 9 8 7 6 5 4 9 10 2 6 7 8 9 10

1 y csc x 3 y tan x A B C 2 y sec x 4 y cot x D UIU

Determine whether the vectors u and v are parallel orthogonal or neither u 6 2 v 8 24 O Parallel ONeither Orthogonal

City X is 55 miles due south of City Y and City Z is 40 miles due west of City X What is the bearing of City Z from City Y to the nearest tenth of a degree S 36 W

Give the exact value sin 60 03 O O 2 3 m

Evaluate the determinant x 0 2 2 3 x x 1 3 x x 0 2 3 x x 1 3 x

Students at a high school can participate in three sports softball basketball and soccer with separate teams for boys and girls The participation matrices for 2017 and 2018 are given below where the rows represent softball basketball and soccer respectively and the columns represent boys and girls respectively Complete parts a and b below P2017 124 111 152 135 120 161 P2018 120 117 160 138 117 165 Complete the statement below to explain what each entry in P represents Each entry in P represents the participation in each sport where the first column represents girls the first row represents softball the second row represents basketball and the third b Suppose P2019 0 92P 2018 Find P2019 and explain what it could represent Each entry in the matrix P total P2019 Type an integer or decimal for each matrix element Round to the nearest integer as needed What could the matrix P2019 represent have 2017 2019 2018 the second column represents Soccer could represent a n 0 decrease in boys and girls playing the sports in compared to