Vector Calculus Questions and Answers

Graph the function h x 5 sin x y N O

What is the approximate value of log 25 O 0 233 O 0 557 O 0 620 1 796

What is the solution of log2 3x 7 3 1 3 O 4 O 5 O O 16 3

Find the exact value of cos 45 in simplest form with a rational denominator

2 In the diagram ACE is an equilateral triangle Vertices B D and F are the midpoints of AC CE and EA and AB and AF v 6 marks Write the following in terms of u and a AC b AD 1 C CE d EB Give an example of a vector that is equal to e 2 v f u v A F U B E D C

7 Find the number of cm3 in 2 0 2 54 cm 1 00 in 11

8 How many minutes in 3 5 years 9 How many decades are there in 9 centuries There are 10 years in a decade 10 In the fictitious country of Ayarceeville 1 00 chemzels equals 0 50 U S dollars What is the cost of 6 onions in Ayarceeville if 3 onions weigh 1 5 lb and the price one pound of onions is 35 cents in the US 11 What is the cost to drive from Sacramento to San Francisco 90 miles if the cost of gasoline is 3 98 gal and the automobile gets 18 mi gal of gasoline 12 How many cars are there in a long freight train if it takes the entire train 2 00 min to pass a station as it travels 40 0 miles per hour Each car is 50 0 feet long There are 5280 feet in a mile 13 How many oranges are in a crate if the price of a crate is 1 60 and the price of oranges is 0 20 lb On the average there are three oranges per pound 14 The price of a ream of paper is 4 00 There are 500 sheets of paper in a ream If a sheet of paper weighs 0 500 oz what is the price per pound of paper There are 16 oz in a pound

Describe how the graph of g x x 1 graphs Then graph the function Select the correct choice below and fil OA Start with the graph of y

A cup of coffee ha F t 75 110 Use a central diffe

The point P is on the unit circle Find P x y from the given information The x coordinate of P is 2 and the y coordinate is negative 25 P x y

For the vectors u 4 2 and v 5 4 calculate proj u and scal u proj u 140 112 41 41 scal u Type an exact answer using radicals as needed

53 62 Writing One Trigonometric Expression in Terms of Another Write the first expression in terms of the second if the terminal point determined by t is in the given quadrant 53 sin t cos t Quadrant II 54 cos t sin t Quadrant IV

41 54 Terminal Points and Reference Numbers Find a the reference number for each value of t and b the terminal point determined by t 41 t 11T 6 42 t 2TT 3

lad Attempt 1 on 1 0 5 points sten he flying horizontally at an altitude of one mile tly over a radar station Determine the rate at v e station is increasing when it is two miles awa pprox 670 mph

mpt 1 5 points 0 es down a vertical wall at a rate of 0 1 m e ladder is 3 m from the wall it slides aw hearest meter how long is the ladder

ar positive integers Evaluate T T cos nx cos nxdx Find Aria of shaded Reyich in terws of R r

Compute the dot product of the vectors u and v and find the angle between the vectors u 14 0 6 and v 1 3 4 v 0 U V

y f x is translated left 8 units and up 9 units then stretched horizontally by a factor of 5

In parts a and b use the given figure a Solve the equation f x g x b Solve the inequality g x f x h x y h x 6 2 f x 0 6 2 6 0 2 yog x Q Q

x x 2 3 x 1 5 Which expression is equivalent to log121 4 O 4log 2x 109 2 2 510g 2 x 1 4log12x log 2 5log 2x log 21 O log124x 10912 x 2 510g 2 x 1 4log12x 10g 2 x 2 5log 2 x 1

TOUTUDE asis

Cost Function The simplest cost function is the fixed cost of operating a business and the slope manufacturer has daily fixed costs of 1700 and

23 Find the value of a such that the lines z x 3 at y 1 4t 2 1 2t intersect Ans 1 t y 2 t z 1 t and 10

by plotting both lines and the point of in selow y 4x 12 y 3x 8

An education researcher claims that 56 of college students work year round In a random sample of 600 college students 336 say they work year round At a 0 01 is there enough evidence to reject the researcher s claim Complete parts a through e below a Identify the claim and state Ho and H Identify the claim in this scenario Select the correct choice below and fill in the answer box to complete your choice Type an integer or a decimal Do not round OA At most of college students work year round OB The percentage of college students who work year round is not OC of college students work year round OD At least of college students work year round OD Ho P H p Let p be the population proportion of successes where a success is a college student who works year round State Ho and H Select the correct choice below and fill in the answer boxes to complete your choice Round to two decimal places as needed OA Ho PS H p OB Ho P H ps OE Ho P H P OC Ho P H p OF H P H p

A ball of radius 13 with a cylindrical hole of radius 4 drilled through its center has volume volume

Solve the equation 2x 4 4 1 19

Find the real solutions of the ec 3x 3 8

24 a Find the distance from the plane 2z 3y a to the plane 52 15y 15 10z b Find the equation of a sphere that is tangent to these planes c Find the equa tion of the plane that contains the center of the sphere THOMAS

am store sells 24 flavors of ice cream Determine the number of possible 6 dip su y 6 dip sundaes are possible if order is to be considered and no flavor can be repea y 6 dip sundaes are possible if order is not considered and no flavor is repeated

8 Divergence theorem With F being a closed surface enclosing some simply connected volume V and for a vector field B x y z 2y 3x z use the divergence theorem Satz von Gau to calculate f x B d

Find all solutions to the following equation on the interval 2 12sin 4w 4 2

et 2 6 1 and 3 0 1 Find two unit vectors that are orthogonal to both 7 and J Are there any other unit vectors that are orthogonal to 7 and w Why or why not

Consider the points A parallelogram formed by 2 3 4 B 0 1 2 D 1 2 0 Find the area of the A B D and the point C such that AB and AD are adjacent

3 1 1 and w 2 4 3 Represent 7 as 7 1 72 where is parallel to w U2 is orthogonal to w

8 Find an equation for the plane which contains the point P 2 0 1 and also the line of intersection between the planes 2x 3y z 0 and x 4y 2z 5 1

Give parametric equations for the line passing through the points P 7 2 6 Q 3 0 6

Determine whether the line given by x 5 y 4 t z 2t intersects the pla 2xy z 5 If it does find the point of intersection

Find the resultant of the two complex numbers Draw the result on the complex number plane Z 3cis 30 Z 4cis 120

and the sot value of the expresif pestra f not possible enter POSSIB infectan

Use the given value and the trigonometric identities to find the remaining trigonometric functions of the angle sec 0 cot 9 0 sin 8 cos 9 tan 8 csc 0 cot 0

and 18 b Use the vectors to draw the following Make sure to draw the resulting vector a 3 points b b 3 points

The graph below is the function f x 5 4 3 2 1 0 3 L Find the following lim f x lim f x I 1 P lim f x I 1 f 1 3 4 5 a If a limit does not exist enter DNE

4 x 3 24 34 A 3 72 N to 7 M 2 3 T

Use the graph of y f x to answer the following V O 3 T 4 3 y f x 2 4 1 1 y 2 3 4 2 3 x

Find the area of the parallelogram that has adjacent sides u i 3j 3k and v 3j k The area of the parallelogram is Type an exact answer using radicals as needed

Find the center and radius of the circle x y 7 center x y radius 0 0 5 7 Sketch the graph of the circle y 5 5 X 10 5 X 5 5 5 y

Is the vector a a where a is a nonzero real number a unit vector Justify your answer

1 Given the vectors a 2 4 5 and b 4i 5j Bk calculate a a b b axb c The angle between the two vectors rounded to the nearest degree d The direction angle rounded to the nearest degree that b makes with the positi y axis e The area of the parallelogram formed by the two vectors

R is the region bounded by the functions f x 1 x and g x 1 and the lines x 1 and 2 4 Represent the volume when R is rotated around the y axis 4 S Use pi for and sqrt x for Volume dx