Vector Calculus Questions and Answers

2 The point P quadrant a y lies on the unit circle What is the value of the y in simplest form if the point is in the 2nd d 3 2 2 415 b 19 5 C 14 5

50 Use a geometric series to find the rational number represented by the decimal 81 r A 01 B 1 C 81 I

3x y 3 41 Use this system to find the value of the y x 2y 8 A 3 B 2 C 3 D 2

9 What are the roots of f x 16 A 2 2 21 2i B 2 2 21 2i C 2 2 2 2 D 21 21 21 21

23 Given logb2 4 logb3 5 logb5 6 Use properties of logarithms to find the following value log 75 A 86 B 1 7 C 41

11 Write f x 16 in factored form f x A x 2 x 2 x 2 x 21 B x 2 x 2 C x 2 x 2 D x 2 x 2

19 Let z 1 3i and z 4 5i Find Z 1 A 4 5i B 4 5 C 4 5i D V41

B 2x 3x 1 11 sdi to musc 2x 3 x 1

3 Geometry Find the perimeter of the rectangle below 3y 5 2 y

39 Dimensions of Carpets Two square carpets are used in the reception area of a hotel The sum of the areas of the carpets is 865 square feet The difference of the areas of the carpets is 703 square feet Find the dimensions of each carpet

A jet leaves a runway whose bearing is N 36 E from the control tower After flying 5 miles the jet turns 90 and flies on a bearing of S 54 E for 6 miles At that time what is the bearing of the jet from the control tower The jet s bearing from the control tower is Round to the nearest degree as needed N

You leave your house and run 6 miles due west followed by 4 5 miles due north At that time what is your bearing from your house The bearing from your house to you is Round to the nearest degree as neede

Save Next question A piano tuner uses a tuning fork If the F one octave below middle C has a frequency of 176 vibrations per second write an equation in the form d sin oot for the simple harmonic motion CARR d 0 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression

A sheet bounded by y 4 x and y 1 has density proportional to the distance from the origin Find the center of mass of the sheet 0 u 1 and 0 U T

Calculate the upward flux of the vector field F x y z through the part of the paraboloi z 25 2 y that s above the zy plane

Find the range of the given function 5 f x 2x2 8x 4 A 4 B 4 C 2 D 2

69 Find the equation of variation given r varies inversely as u and r 3 when u 11

Verify the identity 1 cos a sin a 1 cos a 1 cos a 1 cos a sin a 1 cos a sin a 1 cos a sin a 1 2 cos a sin a 1 cos a sin a X sin a 1 cos a sin a 1 cos a

Find the reference number for each value of t a t 2 7 b t 7n 9 c 2 9 d 65 41 t 2 5T 7 t 5 73 52 PREVIOUS AN

Having given segments a b and c construct segment x ab c

1 point Find the mass of the solid bounded by the xy plane yz plane 2 plane and the plane x 2 y 2 z 4 1 if the density of the solid is given by 8 x y z x 2y mass

Evaluate the line integral OF dr by evaluating the surface integral in Stokes Theorem with an appropriate choice of S Assume that C has a counterclockwise orientation when viewed from above C F x y 2 x y z C is the boundary of the square x 16 ly 16 in the plane z 0 F dr Type an exact answer

Use the Divergence Theorem to compute the net outward flux of the vector field F across the boundary of the region D F 7z 4x 6x 5y y 3z D is the region between the spheres of radius 2 and 3 centered at the origin The net outward flux is Type an exact answer using as needed

20 Find the exact solution of the exponential equation in terms of logarithms Use a calculator to find an approximation to the solution rounded to 2 decimal places 300 1 025 2 1000 2 5 3 100 10 6 1 710 100 10 6x 1 100 10 61 1 90 1996 1 109

Evaluate the surface integral f x y z ds using a parametric description of the surface S f x y z 2x 2y where S is the hemisphere x y z 4 for z 0 The value of the surface integral is Type an exact answers using as needed

A new car is purchased for 19000 dollars The value of the car depreciates at 11 25 per year What will the value of the car be to the nearest cent after 14 years

Give a parametric description for a right circular cylinder with radius a height h and axis along the z axis including the intervals for the parameters r u v 0 0sus osvs

Compute the curl of the following vector field F 4x 5y 4xy 3z The curl of F is i j k

Prove that in any metric space finite intersection of open sets is open re the following sets open or closed in a b for any fe C a b xe a b 2 f x 3 xe a b 3 f x or f x 1

Find the eigenvalues A A2 and associated unit eigenvectors 2 of the symmetric matrix A 1 10 16 15 The smaller eigenvalue X The larger eigenvalue has associated unit eigenvector has associated unit eigenvector 2 C C

45 Use the Binomial Theorem to find the term containing x42 x 3 6 A 2160x42 B 1620x42 C 1080x42 O D 540x42

Write the first trigonometric function in terms of the second for in the given quadrant cos 8 sin 0 0 in Quadrant IV cos 0 cos 2T 0 sin 2 0 x

Find the indicated vector difference 2A 8 Choose the correct answer below OA OC A AID B O B OD

Use the Laws of Logarithms to expand the expression 3x9 log3 y

We can combine 8 log x log y log z to get

Let f xz yz V 4zi 2yj x z k W y 2i y 2 x 2 j 2z 2k Find i V V f ii V 2 xzf iii V V x W

Express the equation in exponential form a In x 7 3 b In x 5 7

Which expression is equivalent to O a be O a b 2 O 1 a b a29 b ab a 5b Assume a 0 b 0

Which expression is equivalent to 04 23 O 25 O 4 O 45 12 334 2

Recursive formulas and spreadsheets can be used to make predictions about lots of important issues outside of the world of finance One such issue is our global population 1 Visit the U S Census Bureau s Global Population Clock Website a What is the current global population 7 938 113 527 b How does the global population seem to be changing It s increasing quicky by each second c How long do you think it might take until there are 1 billion more people on earth than there are today lo years 2 Current estimates are that the global birth rate is about 1 8 per year and the global death rate is about 0 7 per year Use these statistics along with your response from Question la to answer the following questions a What will be the global population 1 year from now 2 years from now LEB 1 year 2 years b Write a recursive NOW NEXT rule that describes how the global population is changing from year to year

A car travels east in a straight path at a speed of 60 miles per hour for 2 hours and then turns around and travels west in a straight path at a speed of 30 miles per hour for 6 hours. Taking direction into account, how many miles is the car from its starting position? 400 miles 180 miles 120 miles -60 miles

Convert the angle 4π/3 from radians to degrees.

For each of the following angles, find the radian measure of the angle with the given degree measure (you can enter as 'pi' in your answers): -350° -400° 10° -350° 80°

In a circle of radius 2 miles, the length of the arc that subtends a central angle of 3 radians is __ miles.

For the line L: r= (1, -5) + s(3, 5), s e R, determine the following: a. an equation for the line perpendicular to L, passing through P(2, 0) b. the point at which the line in part a. intersects the y-axis

A point on the terminal side of angle is given. Find the exact value of the indicated trigonometric function. (5,7); Find tanθ. A. 7/5 B. 5/7 C. /9 D. 7/9

If the equation of a line is r = s(3, 4), SER, name the coordinates of three points on this line. Write a vector equation, different from the one given, in part a., that also passes through the origin. Describe how the line with equation 7 = (9, 12) + t(3, 4), tER relates to the line given in part a.

Complete the following question on your own paper. Answers without work will not receive credit. There is no need to type anything in the box on this question. Complete parts (a) and (b) with f(x, y) = x²y² + xy³. (a) Find Vf. (b) Find the directional derivative of f at the point (-2, 1) in the direction of u = (-2, 3). Leave your answer in exact form (do not give a rounded answer from a calculator).

Solve the equation in the complex number system. x²2 - 12x+37=0 The solution set is . (Use a comma to separate answers as needed.)

Which of the following are a gradient vector field? Select all options that are a gradient vector field. F = F = (10x + 4y)i + (4x - 5y)j (3x + 2y)i + (5x – 2y)j ✓ F = y cos(xy)i + x cos(xy)j ✓ F = yi+xj OF ✓ F = yeyi+ xeyj = i+ -J Y