Vector Calculus Questions and Answers

1 Draw the level sets 2 1 0 1 2 of the following scalar functions be detailed with the proce please a b r x y 2x 3y h x y x yl

Two children are throwing a ball back and forth straight across the back seat of a car The ball is being thrown 9 mph relative to the car and the car is travelling 35 mph down the road If one child doesn t catch the ball and it flies out the window in what direction does the ball fly ignoring wind resistance direction degrees measured relative to the car s forward

Graph the solution set of the inequality where x is a X

K Graph the equation using th 5x 6y 30

Solve the following triangle C A 44 B 34 a 102 meters Simplify your answer b meters Round to the nearest tenth as needed C meters Round to the nearest tenth as needed

K Graph the equation using the x an x 2y 4

Solve the right triangle angle C is the right angle Round to the nearest tenth where necessary a 3 4 B 32 9 OA A 57 1 b 4 4 c 4 OB A 57 1 b 4 4 c 5 6 OC A 57 1 b 2 2 c 4 O D A 57 1 b 1 1 c 3 6

Solve the triangle A a 10 b 6 c 8 Round to one decimal place as pooded

A parallelogram has adjacent sides 7 cm and 15 cm If the shorter diagonal is 10 cm long find the length of the longer diagonal The longer diagonal is approximately cm long Round the final answer to one decimal place as needed Round all intermediate values to two decimal places as needed

Find the area K of the triangle specified below a 10 b 13 c 19 The area K is square units Do not round until the final answer Then round to two decimal places as needed

Find the domain of the following vector valued function 9 r t cos 2ti e j k Select the correct choice below and fill in any answer box es to complete your choice OA tt or t OB t ts or ta OC t t OD t t OE t t OF t ts OG tsts sts OH t t

Graph the curve described by the following function indicating the direction of positive orientation r t costi 3 sin tj for 0 st 2x Choose the correct graph below OA Q G OB 5 OC Q Q O D

Find a function r t for the line passing through the points P 0 0 0 and Q 7 5 1 Express your answer in terms of i j and k r t 7ti k for

K Name two pairs of congruent angles in the fi

QUESTION 13 Simplify 2 7 7 4 3

2 a 8 Pts Parameterize the infinite 2D straight line that is parallel to the vector 3 4 that goes thru the point P 2 5 at time t 0 After you find a parameterization modify it to be an arc length parameterization X 3 2 032 3 Y t 4 5 a txt bo tyt at t o S 3 2 0 31 ve 0 5444 4 5 0 4 155 5 4

A hyperbola is given by the equation y2 16 x2 9 1 The graph of the given equation opens up and dow Select one True False

K Graph the equation by plottin y x 4

Draw a Venn diagram to illustrate the statement Captains of all teams in a certain school are ser

Suppose a product s revenue function is given by R q 8q 2 800q where R q is in dollars and q is units sold Also it s cost function is given by C q 125g 10000 where C q is in dollars and q is units produced Find a simplified expression for the item s Marginal Profit function MP q and record your answer in the box Be sure to use the correct variable Use the Preview button to check your syntax before submitting your final result DO

A circle has the equation 4 x 3 2 4y2 16 Find the center hk and radius r and graph the circle Find the intercepts if any of the graph Use the graphing tool to graph the circle Click to

Q1 x3y x2y y2 2x4 if f x x2 is a given solution Q2 dy 2 y y2 dx knowing that f x 2 is a particular solution

foci at 0 2 and 0 2 and asymptotes at y x and y x

Find the length of the following two dimensional curve L T TU r t 7 cos t 7 sin t for Osts 4 root power using radicals as needed

Find the unit tangent vector T and the curvature K for the following parameterized curve r t 13 sint 6 sin t 7 cost

50 A wire from the top of a TV tower to the ground makes an angle of 52 with the ground and touches the ground 180 feet from the base of the tower Approximately how high is the tower A 290 feet B 230 feet O C 110 feet OD 140 feet

39 Evaluate tan 60 sin 45 without using trigonometric tables or your calculator A 5 B O C 73 3 12 OD D 7

38 Evaluate sin 45 cos 30 without using trigonometric tables or your sec 45 calculator O A B C 4 N o Al D 3

30 tan 30 cot 68 0 O A 20 OB 10 O C 60 D 30

10 2x 9x k 0 11 3x 10x k 0 solve for k given that one root is twice the other solve for k given that one root is two more than the other

Find and sketch the domain of the function Do this on paper Your instructor may ask you to turn in this work f x y y x ln y x y V V 0

Question 6 5 1 17 the future value of this loan 16 397 at 8 for 11 months Future value of the loan is nd to the nearest cent as needed

O Points 0 of 1 ro coupon bond with a face value of 8000 and a 2 5 interest rate compounded s s What is a fair price to pay for the zero coupon bond today r price to buy the bond at would be not round until the final answer Then round to the nearest cent as needed

Points 0 of 1 bond with a face value of 1000 and a 6 3 interest rate compounded serniannually a fair price to pay for the bond today fair price to buy the bond at would be o not round until the final answer Then round to the nearest cent as needed

3 3 Marks Find the general solution of the equation y 9y 2x 5 Y is a function of X 4 3 Marks Find the solution of the differential equation y 7y 12y 8sinx e x y is a function of x

The IVP y 12xy 2x y 0 7 has solution y x

Consider r t costi sintj t 8 k Determine all points on the graph of the function for which the tangent vector is orthogonal to the position vector cos 2 sin 2 2 8 cos 2 sin 2 0

12 Find all points at which the curve r t 2ti tj t k intersects the hyperbolic paraboloid z y 9

5 Find the arc length of the curve r t 3ti k over the interval 0 t 3

4 Consider the vector valued function r t t i 1 t 1 Find parametric equations of the tangent line to the graph r t at the point P 4 1 0 j 4 1 k

A linear function is given f x 5x 6 a Sketch the graph No Solution Help 10 9 8 7 6 5 4 b Find the slope of the graph 3 2 1 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Fill WebAssign Graphing Tool Graph Layers After you add an ob can use Graph Laye properties

Write two equivalent expressions for the opposite of the polynomial 10c 3 13c 2 2c 7

The following are ages of 16 of the signers of the Declaration of Independence 69 45 46 42 34 42 42 32 46 39 70 47 27 60 34 34 Send data to calculator Send data to Excel Find 20th and 75th percentiles for these ages If necessary consult a list of formulas a The 20th percentile 0

7 16 Values of Trigonometric Functions Find the value of the trigonometric function If possible give the exact value other wise use a calculator to find an approximate value rounded to five decimal places 7 a sin 3 T awdd y 37 b cos 4

1 The point P x y is on the unit circle in Quadrant IV If x VII 6 find y 2 The point P in the figure at the left has y coordinate Find a sin t b cos t c tant d sec t 3 Find the exact value 7 6 a sin c tan 5T STF 3 13TT 4 b cos d csc 3 T 2 4 Express tant in terms of sin t if the terminal point determined by t is in Quadrant II 5 If cos t and if the terminal point determined by t is in Quadrant III find tant cott csc t 6 7 A trigonometric function is given a Find the amplitude period phase and horizontal shift of the function dat b Sketch the graph of one complete period 6 y 5 cos 4x 1 7 y 2 sinx

u 1 S q Match the vectors p q 7 5 and with one of the combinations of the and vectors from the graph Vector Vector Combination TOO 2 r HQ P a 3u b 3u v c V d u v e v 2u Question Help Video

11 22 Inverse Trigonometric Functions with a Calculator U a calculator to find an approximate value of each expression co rect to five decimal places if it is defined 11 sin 13 cos 15 cos 0 92761 17 tan 10 19 tan 1 23456 nige ande 21 sin 0 25713 12 sin 14 cos 16 sin 0 13844 18 tan 26 20 cos 1 23456 OLE 2 3 22 tan 0 25713

Question 10 A vector with magnitude 5 points in a direction 115 degrees counterclockwise from the positive x axis Write the vector in component form Vector Give each value accurate to at least 1 decimal place Question Help Video Submit Question

Question 11 Two children are throwing a ball back and forth straight across the back seat of a car The ball is being thrown 7 mph relative to the car and the car is travelling 25 mph down the road If one child doesn t catch the ball and it flies out the window in what direction does the ball fly ignoring wind resistance Question Help Video Submit Question degrees measured relative to the car s forward direction

Diana has available 160 yards of fencing and wishes to enclose a rectangular area a Express the area A of the rectangle as a function of the width W of the rectangle b For what value of W is the area largest c What is the maximum area a a A W