Vector Calculus Questions and Answers

Which angles are vertical angles R 0 P H S U T Q ZQPS and ZTSP N ZQPS and OPN

Which angles are supplementary angles O N M H P R Q S ZPQS and ZMNQ ZMNL and ZONO ZONL and MNQ ROS d

A community college is planning to expand its library Forty students were asked how many times they visited the library during the previous semester Their responses are given below Construct a frequency distribution letting each class have a width of 1 OOT 0 0 1 22222 33333 4 5 6 7 9 5 6 8 9 5 6 8 9 10 10 4 4 578 1 2 3 4 6 7 9 123 4 0 Number of Visits 0 Number of Studen

Find WX in rectangle WXYZ N W 7p 35 6p 28

0 roots of the complex number below D 1729 cos 108 sin 108 A cos 4 76 sin 4 76 9 cos124 76 isin 124 76 9 cos 244 76 isim 244 767 B 243 cos4 76 isin 4 76 243 cos 124 76 isin 124 76 243 cos 244 76 in 244 7 243 cos 36 sin 36 243 cos 156 isin 156 243 cos 276 isin 276 9 cos 36 isin 36 9 cos 156 isin 156 9 cos 276 Isin 276 E 9 cos 72 isin 72 9 cos 192 isin 1929 9 cos 312 sin 312 C

Find the equation of the line in slope intercept form Describe or show your work No work No Credit 800 400 C 5000 10000 15000 20000 25000

Twenty members of a health club who jog were asked how many miles they jog per week The responses are to the right Construct a stem and leaf display For single digit data use a stem of 0 Complete the stem and leaf display Use ascending order 12 24 9 14 14 21 7222 6 tost 31 28 44 21 32

Integrate the given function over the given surface 2 G x y z z over the hemisphere x y z 16 z 20 The value of the surface integral is www

Suppose that you randomly selected 20 adults If 20 of the population are smokers what is the probability that a all 20 are not smokers Round this probability to four decimal places 0 0115 b exactly 6 smoke Round this probability to four decimal places 0 1090 X c exactly 3 smoke Round this probability to four decimal places 0 0521 X d at least 6 smoke Round this probability to four decimal places 0 6700 x e more than 6 smoke Round this probability to four decimal places 0 6339 X f How many of the 20 people would you expect to smoke Round to four decimal places

Find the measure of Ax 269 16 X 629

A plane travels N30 W at 440 mph and encounters a wind blowing due west at 35 mph Part 0 3 Part 1 of 3 a Express the velocity of the plane v relative to the air in terms of i and j Write yo

he given forces in units of pounds act on an object Round all intermediate calculations to 4 decimal places F3 15 lb Part 0 2 Part 1 of 2 40 48 F 7 lb F 10 lb 12 a Find the resultant force R Express your answer in terms of i and j Round your angu

Solve the triangle a 7 b 6 C 20 C 2 46 Round to two decimal places as needed 103 6 Round to one decimal place as needed 1 Round to one decimal place as needed A

Which of the following numbers could not be the probability of an event Select one TU 2 a Ob 3 TU OC 0 95 Od 3 C 3 0

Determine whether the series is convergent or divergent k 1 k K 4k 7 O convergent O divergent If it is convergent find its sum If the quantity diverges enter DIVERGES

Listen Determine the volume of a pyramid with height 4 and base an equilateral triangle with side a 4 16 3 16 3 3 10 16 3 5 3 3 2

The goal is to evaluate A VxF nds v where F 5yz 3xz 5xy and S is the surface of the upper half of the ellipsoid x y 5z 1 220 a Evaluate a surface integral over a more convenient surface to find the value of A b Evaluate A using a line integral a A

Evaluate the line integral S dr for the following function and oriented curve C a using a parametric description of C and evaluating the integral directly and b using the Funda Theorem for line integrals Q x y xy C r t sint cost for Osts Using either method C Type an exact answer dr T

Let F 2xy z x 2xz and let C be the circle r t 6 sin t 5 cost 2 sin t for 0 t 2 Evaluate F dr Simplify your answer C F dr using any method C

Use Green s Theorem to evaluate the line integral Assume the curve is oriented counterclockwise 7x 7x In 7y dy 5y arctan x dx where C is the boundary of the square with vertices 2 5 4 5 4 7 and 2 7 17 Type an exact answer 7x In 7y dy 5y arctan x dx

Draw Euler circles for the argument and determine whether the conclusion follows from the premises All skateboards roll All riding toys roll All skateboards are riding toys Is this conclusion valid or invalid Valid Invalid Choose the correct diagram roll 00 0 riding toys skateboards riding toys skateboards

Determine whether each of the following line integrals is indepen dent of path If it is find a function h such that dh P dx Qdy If it is not find a closed pathy around which the integral is not zero a x dx ydy b x dx y dy c y dx xdy d y dx x dy Solution We compute the partial derivatve because if h exist we have that dh Pdx Qdy where OP ay 0Q dx a b P r OP dy 0 Pdx 9 y h 2 y P x aP 0 y Q y 39 0 dr fQdy f x Q y aQ 0 da f Pdx 9 y Qdy f x 6 h 22 y 6

before starting the next problem al plan answer Then skip four blank lines 2 The value of a certain baseball card in dollars t years after 2000 varies according to the equation V t 15t 1000 0 t 12 Include a unit of measure in your answers a Find the average rate of change in the value of the card between 2005 and 2007 Show your work and steps and state the symbolic answer using function notation Then write a short word sentence stating the context meal plan answer Include the correct unit of measure in your word sentence answer Then skip two blank lines before starting the next part b Plot the graph on a graphing device no need to include the grap here and use it to approximate to the nearest dollar the highest value of the card between 2000 and 2012 Then write a short word sentence stating the context meal plan answer Include the correct unit of measure in your word sentence answer Then skip four blank lines before starting the next problem Note There are various free online graphing calculators Here is one www desmos com Zoom in for accuracy to determine the answer 3 Find and simplify the average rate of change of h x 5 2x on the interval from x a to angwer using function notation Then skip

The height of a radio tower is 500 feet and the ground on one side of the tower slopes upward at an angle of 10 a How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 170 feet from the base of the tower b How long should a second guy wire be if it is to connect to the middle of the tower and be secured at a point 170 feet from the base on the flat side a What is the length of the first guy wire feet Do not round until the final answer Then round one decimal place as needed 500 ft 170 ft

int is building a wooden swing set for his children Each supporting end of the swing set is to be an A frame constructed with two 7 foot long 4 by 4s joined at a 30 angle To prevent the swing set from ping over Clint wants to secure the base of each A frame to concrete footings How far apart should the footings for each A frame be he footings should be about feet apart Round to two decimal places as needed SLE

Use the change of base formula to approximate the y intercept Round your answer to four decimal places 10 y 10 5 5 C 5 10

4 20 points Consider the curve given by the equation y ln x y Find the equation of the tangent line at 1 0

Find a polar equation that has the same graph as the equation in x and y x y 25

Determine the value of c 3 1 24 a t 34 1

1 3 2 1 4 5 Determine the direction angles of the vector v 12 pts

For what numbers x 2x x 2 does the graph of y tan x have vertical asymptotes Refer to the graph which shows y tan x in blue and y cos x in red In the interval 2x x 2 what is the smallest value of x for which the graph of y tan x has a vertical asymptote 3 MA 111111 2 Type an exact answer using as needed Use integers or fractions for any numbers in the expression Simplify your answer Within the given interval what is the next x value for which y tan x has a vertical asymptote 7 Type an exact answer using as needed Use integers or fractions for any numbers in the expression Simplify your answer T

8 Solve 1 of 3 A landscape designer is designing a flower garden for a triangular area that is bounded on two sides by the client s house and driveway The length of the edges of the garden along the house and driveway are 18 ft and 8 ft respectively and the edges come together at an angle of 80 Draw a diagram and then find the area of the garden to the nearest square foot An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm Find the area of the triangle A park in the shape of a quadrilateral ABCD has ZC 90 AB 9 m BC 12 m CD 5 m and AD 8 m How much area does it occupy

5 Find the exact value no calculator HINT it is not on the unit circle so what is option B sec sin 2 5

Two sides and an angle are given below Determine whether the given information results in one triangle two triangles or no triangle at all Solve any triangle s that results a 3 b 2 A 80 C Select the correct choice below and if necessary fill in the answer boxes to complete your choice Type an integer or decimal rounded to two decimal places as needed OA A single triangle is produced where B C and c OB Two triangles are produced where the triangle with the smaller angle B has B OC No triangles are produced C and C and the triangle with the larger angle B has B and c

What is the derivative dy dx for a sinx 2 x b sinx 2 2 c sinx Vx d sinx 2 2 e sinx 2 x y xsin r dr

Find g 2 for the following functions Answer in new window f x x 1 and g x x 7

Use summation formulas to evaluate the sum Z k 20k 8 34 O K 20k 8 25313 k 1 O 34 O k 20k 8 1793 k 1 34 O K 20k 8 25577 k 1 34 k 20k 8 2057 34 k 1 k 1

At what value of x does the minimum or maximum occur for the function below O A O B O C O D minimum at x 7 maximum at x 3 minimum at x 3 maximum at x 7 f x 8 x 7 3

owing functions Step 4 of 4 Find Answer How to enter your answer opens in new window f 4 1 1 1 1 3 and g 0 2 1 1 4 2

onsider the following functions f x 2x and g x x tep 1 of 2 Find the formula for f g x and simplify your answer Then find the domain for f g x Round your answer to two decimal places if necessar swer f g x ITE Keyboard S

A rancher has 2 400 meters of fencing to be used to enclose a rectangular grazing area along an existing fence old fence grazing area What dimensions of the enclosure should be used so that the grazing area will be maximized 600 meters by 600 meters 600 meters by 1 200 meters 700 meters by 1 000 meters X 1 200 meters by 1 200 meters

lf life of an element is 79 7 yr and the initial quantity is 4 5 kg we can wit Agekt to model the quantity of the element left a function of the form A t after t years Find the values of Ao and k Round k to four decimal places Ao

Determine all the horizontal asymptotes of the graph of 15x x 2 f x 2x 13x 7 0 v 12 1 y 7 O y 7 1 O y 15 2 O y 15

Problem 6 10 points Related Rates Suppose you have an ice cream cone with radius 4 cm and height 12 cm with some melted boysenberry ice cream in it The ice cream leaks out the bottom of the cone at a rate of 8 cm min At what rate is the height of the ice cream changing when the height of the ice cream is 2 cm Hint The volume of a cone is given by V r h Jay

Find the exact area between the graphs of f x cosx and g x 2 cosx between x 0 and x 2 O4 units O2 units O 2 units 4 units

While jogging with her running club Carly s velocity varied as shown on the graph below Find Carly s total distance traveled on the interval 0 3 Velocity Miles Hour LA N 0 IN 14 G 7

Complete the sentence below Lett be a real number and let p a b be the point on the unit circle that corresponds to t Then sint C and cost Lett be a real number and let p a b be the point on the unit circle that corresponds to t Then sint and cost

Evaluate 1x 31 6 dx using the following graph 7 O S 3 6 dx 21 5 of 31 6 dx 42 5 0 S 1 1 31 3 6 dx 17 5 0 1 31

Use summation formulas to evaluate the sum 4k 19k 7 26 O 4K 19k 7 31480 k 1 O 26 O 4K 19k 7 18317 26 O 4K 19k 7 18142 k 1 4k 19k 7 31655 X 1

Apr 27 4 24 46 PM Unique ID 1347 Find all angles 0 x 360 that satisfy the equation below to the nearest 10th of a degree 9 tan x sin x tan x