Vector Calculus Questions and Answers

Give the exact values of the sine and cosine of the special angles listed below sin 6 5 cos 6 sin 0 cos 0 11 cos IM sin 7 7 6 11 11

Find exact function values No decimals If undefined answer DNE a 117 6 sin 77 4 COS tan 57 4

use matrix inversion to solve the given linear system x y 2 z 2 x 3 y 2 z 0 21 4x 5y 5z 3 22 2x 6y 5z 4 2x 3y 62 9 x 4y 4z 1

1 074 Points MY NOTES DETA ASK YO Marginal Cost The following function C x 20

Obtain an equivalent system by performing the stated elementary operation on the system Multiply the first equal by 4x 8y 7x 8x 4x 8y 7x 8x 3z 8 14y 14z 14 11y 15z 40 11 3z 8 14z 14 14y 11y 15z 40 Type integers or simplified fractions y Save C

A tank contains 80 kg of salt mized in 1000 L of water A solution of concentration tank at a rate of 10 L min 0 04 kg of salt enters the The solution is mixed and drains out of the tank at the same rate Find the concentration of salt in the tank in Kg L as time approaches infinity

A quadratic function has its vertex at 9 9 When written in vertex for h k II 111

Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always four times its height Suppose the height of the pile increases at a rate of 3 cm s when the pile is 15 cm high At what rate is the sand leaving the bin at that instant Let V and h be the volume and height of the cone respectively Write an equation that relates V and h and does not include the radius of the cone Type an exact answer using it as needed Differentiate both sides of the equation with respect to t dV dt Type an exact answer using as needed The sand is leaving the bin at a rate of Type an exact answer using I as needed

Model the curve with a sine function Note that the graph may or may not be drawn with the same scale on the two axes f x ANA 13 5 9 4 5 4 5 2 13 5 G

35 What is the answer a no solution b 38 41 c 53 8 d 36 52

21 What are the answers 5TT 3 b a Tar and C F3 F F F d TT TT and and and 11TT 6 5TT 6 211

To answer questions 22 23 find the solution set of 2 cos2x in the interval 0 x 2T 2 or when a table or calculator is used in the interval 0 x 360 22 What is the second from the last step a cos x 1 2 b cos x 1 1 C cos x 2 d cos x 1

The owner of a van installs a rear window lens that has a focal length of 0 310 m When the owner looks out through the lens at an object located directly behind the van the object appears to be 0 260 m from the back of the van and appears to be 0 320 m tall a How far from the van is the object actually located and b how tall is the object Rear window lens a Number i 1 225 Person Units m Image of person O

The function f is given by the

Find the size of the matrix Identify a square column or row matrix Give the additive in 6 86 2 42 The size of the matrix is 2 x 3 The matrix is of no special type The additive inverse of the matrix is

Conclusion A Normal plane is a palne containing the normal vector of surface at a particular point A Inclined plane is a plane inclined at an angle to the horizontal A Oblique plane is a plane surface is inclined to one of the principal plane and a side or a diogonal or diameter of a plane surface is parallel to that principal plane and inclined to other plane surface will be calkled oblique plane Do upvote and comment for more clarification