Pre - Calculus Part 2: Lesson 3 and Lesson 4 Quizzes
Find the rectangular coordinates of (5, 30°)
( 5√3 / 2 , 5/2 )
Find the rectangular coordinates of (7, 150°)
(- 7√3 / 2, 7/2 )
Which of the following vectors is shown in the graph below?
(-2, 1, -4)
Which of the following points is shown in the graph below?
(4, -5, 6)
Find a pair of polar coordinates for the point with rectangular coordinates (5, -5).
(5√2, 7π/4)
Write 5(cos109° + isin109°) in rectangular form. Round numerical entries in the answer to two decimal places.
-1.63 + 4.73i
Which of the following is the dot product of u = 4i + 6j - 5k and v = -10i - 8j + 10k?
-138
Find v × w if v = 3i + 8j - 6k and w = -4i - 2j - 3k.
-36i + 33j + 26k
Let DE be the vector with initial point D(8, 6) and terminal point E(-1, 5). Write DE as a linear combination of the vectors iand j.
-9i - j
Determine the eccentricity for r = 5 / 2 + 1sinθ
0.5
Find the angle θ between u = <7, -2> and v = <-1, 2>.
132.5°
Find the direction angle of 3i + j.
18.43°
Find the distance between P1(1, -91°) and P2(3, 335°) on the polar plane.
2.749
Find the angle θ between u and v if u = <-9, -8 , 9> and v = <-5, -3, 9>.
21.5°
Find the length and midpoint of the segment with the given endpoints.(-7, -10, 9), (-2, 9, -9)
26.65, (-4.5, -0.5, 0)
Find the dot product of u = <-8, -8, -9> and v = <-7, -7, 12>. Are u and v orthogonal?
4; not orthogonal
Determine the polar form of the complex number 5 - 3i. Express the angle θ in degrees, where 0 < θ < 360°, and round numerical entries in the answer to two decimal places.
5.83(cos329.04° + isin329.04°)
An airplane is traveling due east with a velocity of 583 miles per hour. The wind blows at 75 miles per hour at an angle of S58°. What is the resultant speed and direction of the plane?
647.8 miles per hour; S86.5°E
Find the volume of the parallelepiped with adjacent edges t = 3j - 4j - 6k, u = 3i - 7j - 7k and v = 5i + j + 3k.
94 cubic units
Find the projection of u = <-6, -7> onto v = <1, 1>.
< - 13/2 , - 13/2 >
Find a unit vector u with the same direction as x =<40, 9>.
< 40,41, 9/41 >
Find the component form of AB with initial point A(8, -2) and terminal point B(-2, -2).
<-10, 0>
Given vectors a = <9, 9> and b = <-4, 7>, find 3a − 2b.
<35, 13>
Find the cross product <-1, -3, -8> × <7, 4, -5>. Is the resulting vector perpendicular to the given vectors?
<47, -61, 71>; yes
Which of the following points is shown in the graph below?
IT IS NOT (1, -5, 3) OR (-1, 5, 3)
A commercial passenger jet is flying with an airspeed of 185 miles per hour on a heading of 036°. If a 47-mile-per-hour wind is blowing from a true heading of 120°, determine the velocity and direction of the jet relative to the ground.
IT IS NOT 195.6 mph, 069°
Find the component form of the vector v with magnitude 6 and direction angle 235°.
IT IS NOT <-4.91, -3.44>
Identify the type of curve given by each equation. r = 4 + 13sin θ
Limacon
Graph the polar equation r = 1 - 3sinθ
Put the equation into Mathway.com and select graph and you will get the answer
Graph the polar equation r = 3.
Put the equation into Mathway.com and select graph and you will get the answer
Identify the type of curve given by each equation. r = -12sin 2θ
Rose
While moving, Jacob pushes a dolly up a ramp with a constant force of 55 N. If the ramp has an incline of 20° with the horizontal, what amount of work (in joules) will Jacob have do to push the dolly 20 meters?
about 1034 joules
Find the area of the parallelogram with adjacent sides u = -4i - 9j + k and v = -6i + j + 5k.
about 75.3 square units
Identify the graph and type of curve for r = 8sinθ
circle (choose the graph with the circle on the top not on the right!)
Find the magnitude of the horizontal and vertical components of a force of 465 newtons at a bearing of 19° from the horizontal. Round to the nearest whole number.
horizontal component: 440 N, vertical component: 151 N
Identify the graph and type of curve for r^2 = 64cosθ
lemniscate
Write the rectangular equation (x + 5)^2 + y^2 = 25 in polar form.
r = -10cos θ
Write a polar equation for the conic with the given characteristics. e = 1.6; directrix: y = 4
r = 6.4 / 1 + 1.6sinθ
Determine the symmetry of each function. r = 14 + 14cosθ
symmetric with respect to the polar axis
Write the polar equation in rectangular form.r = 6 sin θ
x^2 + (y - 3)^2 = 9
Write each equation in rectangular form. θ = - 5π/6
y = √3 / 3 x
Determine the maximum r-values of r = 7cos4θ
θ = 0, π/4, π/2, 3π/4, π
Determine the zeros of r = 2 sin 5 θ
θ = 0, π/5, 2π/5, 3π/5, 4π/5, π
Find the magnitude of AB with initial point A(3, -1) and terminal point B(-2, 6).
√74 ≈ 8.6023