Vector Calculus Questions and Answers

31 3 17 y 4y 3y e t 3u t y 0 0 y 0 0 I 5e 0 t 3

X 16 Solve the following system of equations 3x 5y Sz 21 4x 5z 17 2x Sy 6 16 3 52 19 51 4X 8 X 2 17 Find the value of xif A 11 A IAE 4x 3 141 4x 3 11 4x 3 y 52417 0 23 a 5 7 52 21 152 51 201 202 48 68 4 8 352 263 99 3 0 3 72 93 32 0 8 2x 53462 16 2 52 77 65 62 16 Sa h 105 kre 32 1 724155 15 72 109 5 108 15 45 3 69 5 3 63 15 93 18 Does the matrix A 33 IA 24 1 24 48 0 A have a verse because 14170 9 What is the geometric effect of the following transformations on a figure 33 b x 1 44 758 115 2 3 3 have an inverse Use mathematical language to explain your answer 1 3 3 32 51 0 37 5 33 3x4 q 83 2 30 9 15 21 15 ing 3x4 20 5 20 3x 1 2 2

Determine the Cartesian equation of the plane 0 0 3 1 1 5 1 5 t 1 4 3

3 Find the inverse function of 4 2 x f x

Determine the angle between the following lines F 1 2 3 0 1 3 R F 5 2 0 5 1 1 4 SER

In ASTU s 50 inches t 58 inches and u 27 inches Find the measure of ZS to the nearest 10th of a degree

La ecuaci n de la par bola con foco 3 2 y v rtice 3 0 es O a x 3 8 y 2 Ob x 3 8y Oc x 3 Od x 3 8 y 2

8 Determine the value of X and Y U 45 45 40 O Y X Y 40 cos 20 cos 45 sin 20 45 Y 40 sin 20 cos 45 D X 2 40 cos 20 sin 45 A B C E X 40 cos 20 sin 45 X 40 sin 20 sin 45 F Y 40 G none of these

How many parallel sides can a triangle have

Question 28 1 point Convert the angle to decimal degrees and round to the nearest hundre

x 3 y y 9 Drag and drop an answer to each box to correctly complete the equation ConvertX r CO to polar form C

Pretend it s 1980 and you want to secretly test how much a sprinter s race time improves by using steroids Which type of test would you use Assume every sprinter in your sample is given steroids and you record their before and after race times O Independent 2 Sample T Test O Matched Pairs T Test

Divide 12 2cis 7 3 3cis 6 Drag a value into each box to correctly express the quotient in polar form 12 2cis 7 3 3cis 7 6 cis

b 1 3 and C 11 2 isc What is inc in component form Enter your answer by filling in the boxes 2 6 0 6 7 8 9 10

PROBLEM 8 24 pts Construct the angle bisector t of a Poincar angle ZBAB in the Poincar disk model where A o hint there are two ways to do this one of which involves picking B and B so that AB AB in the Poincar disk

Given AABC with A 116 b 7 and c 10 find a Round your answer to the nearest tenth

For the hyperbola The directrix is horizontal vertical The center is at y 2 8 The vertices are at The foci are at x 10 3 1

Suppose a parabola section has focus 3 2 and directrix y 5 The a intercept s are commas The y intercept s are commas Enter the coordinates as ordered pairs separated by Enter the coordinates as ordered pairs separated by C

The graph of 16x 192x 9y 72y 576 is a ellipse O parabola Ohyperbola which has undergone the translations left 6 units then up 4 units right 6 units then down 4 units left 6 units then down 4 units right 6 units then up 4 units

If the Ratio Test yields a value of 1 then it is uncertain whether the series converges or diverges True O False

The Taylor series centered at 0 aka MacLaurin Series for f x x sin x has only ever powers of x O True False 4

Vector a is expressed in magnitude and direction form as 33 130 What is the component form Enter your answer rounded to the nearest hundredth by filling in the boxes 0 A 1 2 3 4 5 6 N

If is an angle in standard position with terminus in the fourth quadrant and cos 0 tan 0 1 3 10

t is 1 6 ll ll What is the value of Enter your answer as a simplified radical in the box The initial point of llall and its terminal point is 3 2 To C 10 11 12

sin arctan cos arctan 13 19 13 19 0 564684 0 825307

Divide 6 3cis 7 3 5cis 5 3 Drag a value into each box to correctly express the quotient in polar form 6 3cis 7 3 5cis 5 6 5T 6 15 3 7T 6 2 15 6 T 6 cis 2 15 LO 5

What is the vector shown in component form T 6 A T 2 7 N Enter your answer by filling in the boxes

a 3 5 and 6 Represent a b using the head to tail method Use the Vector tool to draw the vectors complete the subtraction by the head to tail method and draw To use the Vector tool select the initial point and then the terminal point Move Vector 10 9 8 7 6 5 4 10 9 8 7 6 5 3 2 1 2 3 3 2 19 1 4 1 4 y 5 Undo N 2 3 4 Redo 5 6 7 x Reset 8 9 10 b

The graph shown is a horizontal translation of the graph of y sin x 2 5 3 4 3 2 3 T 3 1 2 J3 2 3 T 4 35 3 2 The equation of the graph shown is y The graph could also be a horizontal translation of the graph of y In that case the equation of the graph would be y function COS Enter a sine function Enter a cosine

2 7 sin 0 cos 0 Enter your answer in slope intercept form by filling in the boxes Enter values so that fractions are simplified Convert y 8 x to rectangular form

j 1 a j 1 d 2a n 1 d Hint First write down what P 1 says and then prove it Then write down what P k 1 says and prove that using the fact that P k is true P 1 says a 1 d j 1 a k 1 P k 1 says a j 1 d j 1 sequences Write your proof on paper and upload a photo of it Choose File No file chosen

Find a geometric power series for the function centered at 0 by the following methods 2 f x 5 x a by the technique shown in Examples 1 and 2 n 0 b by long division Give the first three terms f x

D A C B 1 List the pairs of adjacent angles 2 List the pairs of vertical opposite angles 3 Angle Z and Angle X on intersecting lines are vertical angles If Angle Z is 63 what is Angle X 4 Angle K and Angle J on intersecting lines are adjacent angles If Angle K is 105 what is angle J

3 In the triangle shown we can find the angle 0 as follows a sin b 8 cos c tan 10 8 6 4 To find sin cos we let cos A and complete the right triangle at the top of the next column We find that sin cos

The price p t of a product is assumed to satisfy the differential equation A Show that p t 4 Ce 0 3t Substituting p 4 Ce 0 3t and is the general solution of this differential equation and evaluate p lim p t 1 dp dt dp 1 2 0 3p Complete parts A through C below dt into the differential equation gives on the left side of the equation and 1 2 Simplifying the left side gives and simplifying the right side gives on the right side of the equation This shows that p t 4 Ce is a solution to the differential equation 0 3t

A rocket is launched upward with a velocity of 128 feet per second from the top of a 45 foot stage What is the maximum height attained by the rocket height function

Consider the following piecewise defined function f x Answer Step 1 of 3 Evaluate this function at x 6 Express your answer as an integer or simplified fraction If the function is undefined at the given value indicate Undefined 3x x 3 ifx 1 if x 2 SO Keyboard Selecting a radio button will replace the entered answer value s with the radio button value If the radio button is not selected the entered answer is used

Evaluate the determinant of the matrix A 26 48 13 24

Determine the cofactor of a13 in the matrix 8 18 2 1 A 0 7 7

Determine the cofactor of a32 in the matrix A 1 3 5 1 4 2 2 2 8

Given the following matrices if possible determine 3B 3A If not state Not Possible Answer 9 2 3 8 A 7 B 7 4 0 10 1 8 Selecting a checkbox will replace the entered answer value s with the checkbox value If the checkbox is not selected the entered answer is used Keybo

Let D be an ellipse rotated counterclockwise by radius was 6 and vertical radius was 3 76 4321 1 2 Convert radians as pictured below Before rotation the horizontal Q 4x 2y dA into an integral over a polar integral over a unit circle type theta for 0 dr de

A volleyball was hit into the air at a speed of 21 miles per hour at an angle of 40 from the horizontal Express this velocity in vector form Round your answer to four decimals Answer 2 Points Keyp Kouboard St

Consider the following matrix 26 7 13 17 6 49 35 45 5 4 Step 3 of 3 Determine the value of ay if possible If the element indicated is not in the matrix state None Answer Let A Keybo Selecting a radio button will replace the entered answer value s with the radio button value If the radio button is not selected the entered answer is used

Find the sum of the first 47 terms of the arithmetic sequence 0 7 14 21 847

Simplify the following expression 5 3 27

Use any convenient method to solve the following system of equations If the system is dependent express the solution set in terms of one of the variables Leave all fractional answers in fraction form Answer 3x 4y 22 28 x 5y 42 6 4r y 62 22 Selecting an option will display any text boxes needed to complete your answer O Only One Solution Inconsistent System Dependent System Keypad Keyboard Shortcuts

A tank holds 2 000 gallons of water which drains from the bottom of the tank in half an hour The values in the table show th remaining in the tank in gallons after t minutes t min V gal a If P is the point 15 520 on the graph of V find the slopes of the secant lines PQ when Q is the point on the graph with t 5 10 20 25 and 30 b Estimate the slope of the tangent line at P by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to P Step 1 msec 5 msec 10 1 376 890 a If P is the point 15 520 on the graph of V find the slopes of the secant lines PQ when Q is the point on the graph with t 5 10 20 25 and 30 Slopes of secant lines passing through P 15 520 and Q t V t can be calculated using the following V t 520 t 15 15 20 25 30 520 520 212 56 0 We begin by calculating the slope when t 5 In the last step round your answer to one decimal place V 5 520 5 15 Updates Available Do you want to inst

30 On a different level the new function h t 3t 12t 36 is used to model the height of the bird If the bird misses the target and hits the ground for how long was it in the air

III Find the length of side AC C A 118 24 22 B