# Vector Calculus Questions and Answers

Calculus
Vector Calculus
Use the formula for the general term the nth term of a geometric sequence to find ag with the given first term a 6 and common ratio r 2 OA 1 536 OB 1 532 OC 22 OD 3 072
Calculus
Vector Calculus
Approximate the number using a calculator Round your answer to three decimal places 2 6 OA 6 000 OB 5 462 OC 4 899 OD 32 000
Calculus
Vector Calculus
Find the zero of the function shown below f x 2 2x 3x 4 8 x 4 O A OB 12 5 5 C 4 OD 4
Calculus
Vector Calculus
5 The surface area of a cube is equal to the sum of the areas of each of its six square faces The formula to find the surface area of a cube is A 6x where x is the side length of one of the square faces Jack has two cubes that he needs to paint One of them has a side length of 2 inches and one has a side length of 1 5 inches How many square inches does he need to paint
Calculus
Vector Calculus
Find the value of the summation 3 2k
Calculus
Vector Calculus
Find the period in degrees Then sketch the graph using degrees 54 y tan 0 55 y sin 0 60 120 180 240 300 360 90
Calculus
Vector Calculus
For the rectangular coordinates 2 2 2 2 a plot the point and b give two pairs of polar coordinates for the point where 0 0 360 K a Choose the correct plot of 2 2 2 2 below OA Ay B Ay COL O C b Give two pairs of polar coordinates for the point where 0 0 360 Type an ordered pair Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in degrees Do not include the degree sym Use a comma to separate answers as needed
Calculus
Vector Calculus
For the point a Choose the graph that represents the point 1 1 37 OA x 2 in polar coordinates a plot the point b give two other pairs of polar coordinates for the point and c give the rectangular coordinates of the point 4 3x 2 Q B x 2 3x 2 0 Q Q OC x 2 3x 2 0 Q b What are the coordinates of the point for which r 0 and 2x 0 4x 11x 4 Type an ordered pair Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression What are the coordinates of the point for which r 0 and 0 0 2x Type an ordered pair Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression OD R 2 3x 2 Q
Calculus
Vector Calculus
5 Determine the value of x such that the points A 3 5 B x 7 C 8 10 and D 0 2 form the parallelogram ABCD Hint The order of the letters matters
Calculus
Vector Calculus
Watch the video that describes plotting points with polar coordinates Click here to watch the video Plot the point 3 240 Then find the rectangular coordinates of the given point In rectangular coordinates 3 240 is Type an ordered pair Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Choose the graph OA 180 180 90 270 90 270 0 Q Q OB below 180 180 90 270 90 270 0
Calculus
Vector Calculus
4 Given u and 7 draw the following vectors a u b 20 V V c u v d u v V
Calculus
Vector Calculus
calculator a Choose the graph that represents the point A polar coo1 hates plot the point Give two other pairs of polar coordinates for the point Do not use a R 2 3x 2 2 3x 2 0 OC x 2 3x 2 b What are the coordinates of the point for which r 0 and 2 0 4x O D x 2 3x 2 Type an ordered pair Simplify your answer Type an exact answer using it as needed Use integers or fractions for any numbers in the expression
Calculus
Vector Calculus
For the point 1 and c give the rectangular coordinates of the point 3x 4 x 2 3x a Choose the graph that represents the point 1 4 OA 3x 2 in polar coordinates a plot the point b give two other pairs of polar coordinates for the po B x 2 3x 2 Q O C x 2 3x 2 Q G O D x 2 3x 2 Q L b What are the coordinates of the point for which r 0 and 2n 0 4x Type an ordered pair Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression
Calculus
Vector Calculus
11 In the following diagram OA a OB b and OC c Points P Q R and S are the mid points o OA AB BC and CO respectively Determine the following vectors in terms of a b and c a P A S b B R a PQ b QR
Calculus
Vector Calculus
7 Given a 6cm b 3cm and the angle between these vectors when arranged tail to tail is 35 determine 2a b geometrically as well as the angle formed between 2a b and vector a
Calculus
Vector Calculus
3 cos vcos 3v sin vsin 3v
Calculus
Vector Calculus
7 cos 3vcos 5v sin 3vsin 5v
Calculus
Vector Calculus
8 sin 3vcos v cos 3vsin v
Calculus
Vector Calculus
4 cos 6xcos 2x sin 6xsin 2x
Calculus
Vector Calculus
6 cos 50cos 20 sin 50sin 20
Calculus
Vector Calculus
24 4x 20x 5 x 5
Calculus
Vector Calculus
Given u and 7 draw the following vectors 4 a u b 20 V V c u v 15 v d u v V v
Calculus
Vector Calculus
2 For the vectors 3 12 0 and b 5 5 7 determine the vector 2a 5b 3 For the point P 2 4 5 plot this point in R and list the coordinates of the points that form a rectangular prism with this point and the origin Y 2
Calculus
Vector Calculus
12 Vector a joins the x and y intercepts tail at the x intercept and head at the y intercept of the line 2x 3y 6 Determine a as a quadrant bearing
Calculus
Vector Calculus
Application 3 An airplane is on a heading of 030 at an airspeed of 800 km h There is a wind of 75 km h from 315 Using trigonometry find the resultant velocity as a true bearing of the airplane Include a diagram
Calculus
Vector Calculus
1 cOSX 1 COSX fadesi a a dakilerden hangisine e equal
Calculus
Vector Calculus
3 cos2x 2sin x 1 ifadesinin de eri ka t r
Calculus
Vector Calculus
I 1 sin cos 1 ifadesinin sonucu ka t r
Calculus
Vector Calculus
The tables to the right give price demand and price supply data for the sale of soybeans at a grain market where x is the number of bushels of soybeans in thousands of bushels and p is the price per bushel in dollars Use quadratic regression to model the price demand data and linear regression to model the price supply data Complete parts A and B below A Find the equilibrium quantity and equilibrium price The equilibrium quantity is thousand bushels Round to three decimal places as needed GIIB Price Demand X 0 10 20 30 40 Price Supply p S x 6 33 6 39 p D x X 6 60 0 6 51 10 6 45 20 6 43 30 6 40 40 6 44 6 51 6 54
Calculus
Vector Calculus
Write the first five terms of the geometric sequence an 4an a 2 OA 8 32 128 512 2 048 OB 4 8 32 128 512 O C OD 2 2 6 10 14 2 8 32 128 512
Calculus
Vector Calculus
Write the first five terms of the arithmetic sequence a 2 d 2 A 2 4 6 8 10 4 6 8 10 12 0 2 4 6 8 OD 2 3 4 5 6 OB O C
Calculus
Vector Calculus
5 Solve the equation Do not use a calculator Give an exact value 5 points 1 4 ln 2z 1 5
Calculus
Vector Calculus
7 Find the Cartesian coordinates of the polar point 2 3
Calculus
Vector Calculus
dy Is there a value of n which makes y x a solution to the equation 3x y If so what is the exact value dx Enter NA if there is no value for n n
Calculus
Vector Calculus
Use the definition of continuity to determine the value of the constant c for which the function fis continuous on where f y cy 8 if y 5 c y 8 if y 5
Calculus
Vector Calculus
A factory selling cell phones has a marginal cost function C x 0 01x 3x 229 where a represents the number of cell phones and a marginal revenue function given by R x 429 2x Find the area between the graphs of these curves and x 0 What does this area represent O total revenue for 200 cell phones sold O total profit for more than 200 cell phones sold total profit for 200 cell phones sold O total cost for 200 cell phones sold
Calculus
Vector Calculus
Graph the curves r 2 4 cos 0 and r 2 4 sin 0 Identify the correct sketch of r 2 4 cos 0 O A 8 8 OA 8 Identify the correct sketch of r 2 4 sin 0 8 Q 8 U ON OB B 8 8 A 001 Q ON AST OC O C 84 18 T Di Q Q This test 25 point s possible This question 4 point s possib OD OD B C 8 Q
Calculus
Vector Calculus
a the z axis at 1 2 3 b the x axis at 2 6 1 c the y axis at 2 4 4 a Choose the correct equation of a plane perpendicular to the z axis the plane perpendicular to each of the following axes at the given points with a single equation or a pair of O A x 1 B y 2 C Z 3 b Choose the correct equation of a plane perpendicular to the x axis A Z 1 B x 2 O c y 6 c Choose the correct equation of a plane perpendicular to the y axis A y 4 B x 2 www
Calculus
Vector Calculus
20 points We are given a vector field F x y z axy z Bx y where a are some nknown constants It is known that H identically and that 3 2k 2x x ind a and 3
Calculus
Vector Calculus
Prof Rudy Meangru Solve the following equ 1 sin 1 2
Calculus
Vector Calculus
press 1 234234234234 as a ratio of intege
Calculus
Vector Calculus
Find the volume V of the described solid S The base of S is the region enclosed by the parabola y 2 3x2 and the x axis Cross sections perpendicular to the y axis are squares V
Calculus
Vector Calculus
Solve for 0 0 0 2x 2 sin 0 sin 6 31 21 5x 0 2 5 10
Calculus
Vector Calculus
Given side a 24 side b 28 and side c 30 find the area of triangle AABC 0316 336 909 285
Calculus
Vector Calculus
TABLE OF INDEFINITE INTEGRALS fcf x dx cff x dx fkdx kx C X 1 f xndx C n 1 dx In x C n 1 fe dx e C sin x dx cos x C sec x dx tan x C sec x tan x dx sec x tan x dx sec x C 1 x 1 sinh x dx cosh x C f x g x dx f f x dx g x dx dx tan x C ax a dx in a cos x dx sin x C fcsc x dx cot x C CSC x cot x dx csc C CSC X C 1 1 x S cosh x dx sinh x C enc dx sin x C 14 csc t 2e dt tai
Calculus
Vector Calculus
Consider a 400 N weight suspended by two wires as shown in the figure Find the magnitudes and components of the force vectors F and F2 F N Round to one decimal place as needed F N Round to one decimal place as needed F Round to one decimal place as needed F F14 25 50 400 N
Calculus
Vector Calculus
Find the volume of a parallelepiped with one of its eight vertices at A 0 0 0 and three adjacent vertices at B 2 1 0 C 0 5 1 and D 4 6 8 The volume of the parallelepiped is Simplify your answer
Calculus
Vector Calculus
Suppose that a box is being towed up an inclined plane as shown in the figure Find the force w needed to make the component of the force parallel to the inclined plane equal to 2 2 lb The force w is about lb Round to the nearest hundredth as needed COO
Calculus
Vector Calculus
Find the area of the parallelogram whose vertices are given below A 2 3 B 2 0 C 8 3 D 4 6 The area of parallelogram ABCD is square units