Vector Calculus Questions and Answers

If y= +2, what is the value of y when x = 3i? 21/5 + 128 % 25 25 0-25 + 2i 2²/5 + 1/8 O-1-18i 25 O- +18 i 25

Round to 2 significant figures. 5,239 Step 2: Now we need to round up or down. What is the answer rounded to two significant figures?

Let f(x) = sin(x) and g(x) = sin(x). Which of the following statements are correct? Select all that apply. g(f(2x)) = 2n of g(f(x)) is defined for all real numbers x f(g(0)) = 0 f(g(x)) is defined for all real numbers.x g(f(x)) = x for all real numbers.x f(g(x)) = = x for all real numbers x

Find an equation of the line that contains the given pair of points. (24, 26), (7, 9) D

You need to arrange four of your favorite books along a small shelf. How many different ways can you arrange the books, assuming that the order of the books makes a difference to you? ways ……

In how many ways can the expression a4 b5c³ be rewritten as a product without exponents? The number of ways a4 b5c3 can be written without exponents is A

A roller coaster travels 350 feet horizontally and then travels 130 feet at an angle of 60° from the ground. What is the direction of the resultant vector? [?]°

A mouse is trapped in a maze. To find his way out, he walks 15 m east, makes a 90° left turn, walks 8 m, makes another 90° left turn, and walks 10 m. What is the direction of the resultant vector?

Let y=2(x-5)2-6. Part A: Is the given relation a function? Is it one-to-one? Explain completely. If it is not one-to-one, determine a possible restriction on the domain such that the relation is one-to-one. Part B: Determine y¹. Show all necessary calculations. (5 points) Part C: Prove algebraically that y and y¹ are inverse functions. (5 points)

Period = Phase Shift = Terminal point Graph lies above y Sketch the graph of the basic cycle of y = 3 csc (2x + π/8) Asym: are x = Select the basic graph A = below y = = X y

A club with eleven members is to choose three officers: president, vice-president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled? ways COS

If the odds in favor of E occurring are 27, then find P(E) and P(E'). P(E)= (Type an integer or a simplified fraction.) P(E)= (Type an integer or a simplified fraction.)

A car travels 10 km southeast and then 15 km in a direction 60° north of east. Find the magnitude of the car's resultant vector. [?] km

A pedestrian walks at a rate of 6 km per hour east. The wind pushes him northwest at a rate of 13 km per hour. Find the direction of the resultant vector. [?]°

Find all points with coordinates of the form (a, a) that are a distance 7 from P(-3, 4). (x, y) = (-3,-3) (smaller x-value) (x, y) = (4,4) X X ) (larger x-value)

Find the field in which the parametric equations are used. O Linear Motion O Projectile Motion O Curve Sketching O All of the choices

Identify the correct option regarding the compositions of two functions f(x) and g(x). (fog)(x) = g(f(x)) (fog)(x) = f(g(x)) (fog)(x) = f(x)g(x) (fog)(x) = (f/g)(x-¹)

Which of the following represent vector quantities? 1. Displacement II. Area III. Volume

Represent the complex number 1 + √3 in polar form. O2(cos 30° + isin 30°) O2(cos 60° + isin 60°) O2(cos 120° + isin 120°) 2(cos 90° + isin 90°)

Find an equation of the tangent plane at the given point: 1 F(r, s) = 27³52, (1, 1) 30.5 2 = Note: Your answer should be a function of r and s.

Find a formula for a function f that satisfies the following conditions. lim f(x) = 0, lim f(x) = -00, f(7) = 0, X418 X-0 lim f(x) = 00, X-8 lim f(x) = -00, X-8+

Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) a = 3i - 8j + k, b = 9i - k

Solve cos(x) = 0.42 on 0 < x < 2π There are two solutions, A and B, with A B A = B = Give your answers accurate to 3 decimal places

Find the lengths of the sides of the triangle PQR. |PQ| = |QR| = |RP| 11 P(4, -2, -1), Q(8, 0, 3), R(10, -4, -1) Is it a right triangle? Yes No Is it an isosceles triangle? Yes No

Find the value of -3(- i | + 2 j - 4 k ). 7 +23-4k)! 3 i-6j+ 12 k 0-371-67-127 Ⓒ 37+-65-12 k Q-3 i k - 6 + 12 k

At what point on the curve y = x4 does the normal have a slope of 16?

The symbol "||" is used to denote the O Magnitude O square O square root O subtraction of a vector

Let u = [2, 2, 1] and √ = [-4, 3, -8]. Find the scalar projection of u on 40 897 10 V89 30 89 › 10 25 17 (0,25) 89 89 89 -10 √ 89 80 89 on :

23. Given = [1, 7, 9] and, a) Find the angle between = [-2, 5, -3] and w = [4, -6, 8]. and w. 13 Marks] b) Are the vectors and and w coplanar? Show your answer algebraically. [3 Marks]

Find an equation of the sphere with center (3, -11, 6) and radius 10. Use an equation to describe its intersection with each of the coordinate planes. (If the sphere does not intersect with the plane, enter DNE.) intersection with xy-plane intersection with xz-plane intersection with yz-plane 70

Find the distance from (4, -9, 7) to, each of the following. (a) the xy-plane (b) the yz-plane (c) the xz-plane. (d) the x-axis (e) the y-axis (f) the z-axis

Which of the following matrices A can be multiplied with the vector B <2, 1, 3> to give the product AB? A2×3 matrix A3 x 2 matrix A2 x 2 matrix A 2x1 matrix

23. Given = [1, 7, 9] and, a) Find the angle between and w. 13 Marks] -[-2, 5, -3] and w=[4, -6, 8]. b) Are the vectors i and i and w coplanar? Show your answer algebraically. [3 Marks]

Vector component of Vand W are as follows. Find the direction of the resultant vector. V= (13.5, -21.07) W = (-0.9, -14.6) W= [?] Round to the nearest hundredth.

A bicyclist rides 11.2 kilometers east and then 5.3 kilometers south. What is the magnitude of the bicyclist's resultant vector? Hint: Draw a vector diagram. [?] kilometers Round your answer to the nearest tenth.

Find an equation of the tangent y = 2x² - 10x + 1, line to the curve at the given point. (6,13)

A car travels 87 miles north and then 114 miles west. What is the angle of the car's resultant vector? Hint: Draw a vector diagram. [?]°

Find the six trigonometric functions of the angle. (If an answer is undefined, enter UNDEFINED.) 117 6 sin(-11) - cos(-11) - 6 tan(-11) - csc(-11) - sec(-11) - cot(-11) - H

A person swims 6.4 meters per second north while being pushed by a current moving west at 2.1 meters per second. What is the magnitude of the swimmer's resultant vector? Hint: Draw a vector diagram. [?] m/s Round your answer to the nearest tenth.

Simplify cos(tan-¹()). |x| OA. √x² +1 √x²-1 OB. OC. √√1-x² 1 VI- -x² OD. X √√x²-1 OE √√x².

Find the horizontal and vertical components of this vector. ([?],[]) |f|=17

A vector has a magnitude of 8 in the 95° direction. What are the horizontal and vertical components? ([? ], [ ]) Round to the nearest tenth.

Problem 14. (-1, -1/3) be the point on the unit circle that corresponds to t. Find the values of cost and tan t, and then evaluate 2 cost + tan²t. b) Find the exact value of sin-¹ ( ¹ (sin (57)). a) Lett be a real number and let P

Use the following graph of a function f to determine y to the nearest integer for y = f(-2). Af(x)

Let F= cos(5t)i + tj + 5t'k and G = t cos(5t) i + t'j+5e¹k Find the cross product FXG=

Describe the toolkit function and it's transformation. The function is f(x) = log(-x-2)-5 Multiple answers: Multiple answers are accepted for this question Select one or more answers and submit. For keyboard navigation... SHOW MORE a Reflection about the x-axis b Vertical Stretch n d f g h Vertical Shrink Reflection about the y-axis Horizontal Stretch Horizontal Shrink Horizontal Shift Left Horizontal Shift Right

Finance. A person wishes to have $27,500 cash for a new car 3 years from now. How much should be placed in an account now, if the account pays 5.3% annual interest rate, compounded weekly?

Solve for x. Write your answers, separated by a comma. (a) x - 11 = 13 x = -2,24 (b) 11- x - 2| = - 8 x= -17,21 (c) | 3 - 2 = 6 x = -42,78 = 10

Sketch the trace (in the plane z = 2) of the function f(x, y) = 1/2.

(a) Find expressions for each side of the right triangle that uses x, 8, or both given that 0 = tan-¹(). A = B = C = 6 C A B