Vector Calculus Questions and Answers
Calculus
Vector CalculusIf y= +2, what is the value of y when x = 3i?
21/5 + 128
%
25
25
025 + 2i
2²/5 + 1/8
O118i
25
O +18 i
25
Calculus
Vector CalculusRound 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?
Calculus
Vector CalculusLet 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
Calculus
Vector CalculusFind an equation of the line that contains the given pair of points.
(24, 26), (7, 9)
D
Calculus
Vector CalculusYou 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
……
Calculus
Vector CalculusIn 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
Calculus
Vector CalculusA 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?
[?]°
Calculus
Vector CalculusA 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?
Calculus
Vector CalculusLet y=2(x5)26.
Part A: Is the given relation a function? Is it onetoone? Explain completely. If it is not onetoone, determine a possible restriction on the domain such that the relation is onetoone.
Part B: Determine y¹. Show all necessary calculations. (5 points)
Part C: Prove algebraically that y and y¹ are inverse functions. (5 points)
Calculus
Vector CalculusPeriod =
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
Calculus
Vector CalculusA club with eleven members is to choose three officers: president, vicepresident, and secretarytreasurer. 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
Calculus
Vector CalculusIf 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.)
Calculus
Vector CalculusA 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
Calculus
Vector CalculusA 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.
[?]°
Calculus
Vector CalculusFind all points with coordinates of the form (a, a) that are a distance 7 from P(3, 4).
(x, y) = (3,3)
(smaller xvalue)
(x, y) = (4,4)
X
X
) (larger xvalue)
Calculus
Vector CalculusFind the field in which the parametric equations are used.
O Linear Motion
O Projectile Motion
O Curve Sketching
O All of the choices
Calculus
Vector CalculusIdentify 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)(x¹)
Calculus
Vector CalculusWhich of the following represent vector quantities?
1. Displacement
II. Area
III. Volume
Calculus
Vector CalculusRepresent 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°)
Calculus
Vector CalculusFind 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.
Calculus
Vector CalculusFind a formula for a function f that satisfies the following conditions.
lim f(x) = 0,
lim f(x) = 00,
f(7) = 0,
X418
X0
lim f(x) = 00,
X8
lim f(x) = 00,
X8+
Calculus
Vector CalculusFind the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.)
a = 3i  8j + k, b = 9i  k
Calculus
Vector CalculusSolve 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
Calculus
Vector CalculusFind 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
Calculus
Vector CalculusFind the value of 3( i  + 2 j  4 k ).
7 +234k)!
3 i6j+ 12 k
037167127
Ⓒ 37+6512 k
Q3 i
k

6 + 12 k
Calculus
Vector CalculusThe symbol "" is used to denote the
O Magnitude
O square
O square root
O subtraction
of a vector
Calculus
Vector CalculusLet 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 :
Calculus
Vector Calculus23. 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]
Calculus
Vector CalculusFind 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 xyplane
intersection with xzplane
intersection with yzplane
70
Calculus
Vector CalculusFind the distance from (4, 9, 7) to, each of the following.
(a) the xyplane
(b) the yzplane
(c) the xzplane.
(d) the xaxis
(e) the yaxis
(f) the zaxis
Calculus
Vector CalculusWhich 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
Calculus
Vector Calculus23. 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]
Calculus
Vector CalculusVector 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.
Calculus
Vector CalculusA 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.
Calculus
Vector CalculusFind an equation of the tangent
y = 2x²  10x + 1,
line to the curve at the given point.
(6,13)
Calculus
Vector CalculusA 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.
[?]°
Calculus
Vector CalculusFind 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
Calculus
Vector CalculusA 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.
Calculus
Vector CalculusSimplify cos(tan¹()).
x
OA.
√x² +1
√x²1
OB.
OC. √√1x²
1
VI
x²
OD.
X
√√x²1
OE √√x².
Calculus
Vector CalculusA vector has a magnitude of
8 in the 95° direction. What are
the horizontal and vertical
components?
([? ], [ ])
Round to the nearest tenth.
Calculus
Vector CalculusProblem 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 sin¹ (
¹ (sin (57)).
a) Lett be a real number and let P
Calculus
Vector CalculusUse the following graph of a function f to determine y to the nearest integer for y = f(2).
Af(x)
Calculus
Vector CalculusLet F= cos(5t)i + tj + 5t'k and G = t cos(5t) i + t'j+5e¹k
Find the cross product
FXG=
Calculus
Vector CalculusDescribe the toolkit function and it's transformation. The function is f(x) = log(x2)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 xaxis
b Vertical Stretch
n
d
f
g
h
Vertical Shrink
Reflection about the yaxis
Horizontal Stretch
Horizontal Shrink
Horizontal Shift Left
Horizontal Shift Right
Calculus
Vector CalculusFinance. 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?
Calculus
Vector CalculusSolve 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
Calculus
Vector Calculus(a) Find expressions for each side of the right triangle that uses x, 8, or both given that 0 = tan¹().
A =
B =
C =
6
C
A
B