Question 1

A traffic light weighing 16 pounds is suspended by two cables (see figure).Find the tension in each cable.Approximate the answer to one decimal place. ​
​  ​
Where b = 28°
​
A)18.0 lb
B)17.0 lb
C)16.0 lb
D)19.0 lb
E)15.0 lb

Accepted Answer

We can break the weight of the traffic light into its x and y components:

Weight of the traffic light = Force due to gravity = mg
where m = mass of the traffic light and g = acceleration due to gravity

In the y-axis direction, we have:

T1 sin(b) + T2 sin(b) = mg
where T1 and T2 are the tensions in the cables

In the x-axis direction, we have:

T1 cos(b) = T2 cos(b)

We can solve for T1 and T2 using the above two equations:

T1 = (mg / 2 sin(b)) cos(b)
T2 = (mg / 2 sin(b)) cos(b)

Substituting m = 16 lb and g = 32.2 ft/s^2, we get:

T1 = 16 / (2 sin(b)) cos(b) ≈ 17.0 lb
T2 = 16 / (2 sin(b)) cos(b) ≈ 17.0 lb

Therefore, the tension in each cable is approximately 17.0 lb. The best choice is B.

Question 2

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​
Find F if W = 5,700 pounds and θ = 29°.Approximate the answer to one decimal place.
​
A)2,761.4 lb
B)2,764.4 lb
C)2,763.4 lb
D)2,765.4 lb
E)2,762.4 lb

Accepted Answer

The force required to pull an object up an inclined plane is given by the formula $F = W \sin(\theta)$, where $F$ is the force in pounds, $W$ is the weight of the object in pounds, and $\theta$ is the angle of the incline in degrees. Substituting $W = 5700$ pounds and $\theta = 29^\circ$, we get $F = 5700 \sin(29^\circ)$. Using a calculator, $\sin(29^\circ) \approx 0.4848$, so $F \approx 5700 \times 0.4848 \approx 2763.36$ pounds, which rounds to 2763.4 pounds.

Question 3

A gun with a muzzle velocity of 1700 feet per second is fired at an angle of 4° above the horizontal.Find the vertical and horizontal components of the velocity.(Round your answer to one decimal place.) ​
A)Vertical ≈ 118.6 ft/sec, Horisontal ≈ 1,695.9 ft/sec.
B)​Vertical ≈ 119.6 ft/sec, Horisontal ≈ 1,696.9 ft/sec.
C)​Vertical ≈ 1,695.9 ft/sec, Horisontal ≈ 1,695.9 ft/sec.
D)​Vertical ≈ 1,695.9 ft/sec, Horisontal ≈ 118.6 ft/sec.
E)​Vertical ≈ 118.6 ft/sec, Horisontal ≈ 118.6 ft/sec.

Accepted Answer

To find the vertical and horizontal components of the velocity, we use trigonometric functions. The vertical component $v_v = v \sin(\theta)$ and the horizontal component $v_h = v \cos(\theta)$, where $v = 1700$ ft/sec is the muzzle velocity and $\theta = 4^\circ$ is the angle. Calculating these gives $v_v \approx 1700 \sin(4^\circ) \approx 118.6$ ft/sec and $v_h \approx 1700 \cos(4^\circ) \approx 1695.9$ ft/sec.

Question 4

​Find the magnitude of vector v with initial point (7, 5) and terminal point (-3, -5). ​
A)​ 
B)​14
C)​ 
D)​ 
E)​

Accepted Answer

The answer of ​Find the magnitude of vector v with...

Question 5

Find the component form and the magnitude of the vector v. Initial Point
Terminal Point
(1, 3)
(-8, -9)
A) 
B) 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of Find the component form and the magnitude...

Question 6

Find the magnitude of vector v. ​ 
A) 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of Find the magnitude of vector v. ​...

Question 7

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ​
Magnitude
Angle  0°
​
​
A) 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of Find the component form of v given...

Question 8

The initial and terminal points of vector v are (3, -8) and (7, 1), respectively.Select v in component form. ​
A)​ 
B)​ 
C) 
D) 
E)​

Accepted Answer

The answer of The initial and terminal points of vector...

Question 9

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector.. ​
Initial Point
Terminal Point
(0, -8)
​(9, 12)
​
​
A)​9i + 20j
B)​-9i - 20j
C)​20i - 9j
D)​​20i + 9j
E)​9i - 20j

Accepted Answer

To find the vector from the initial point (0, -8) to the terminal point (9, 12), we subtract the coordinates of the initial point from the coordinates of the terminal point: (9 - 0)i + (12 - (-8))j = 9i + 20j.

Question 10

Find the component form of vector v. ​
​  ​
A) 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of Find the component form of vector v....

Question 11

Find the component form of vector v with initial point (1, -7) and terminal point (-3, 1).
A)​ 
B) 
C)​ 
D)​ 
E)​

Accepted Answer

Using the formula for finding the component form of a vector, we have: v = v = <-3-1, 1-(-7)> v = <-4, 8> Therefore, the component form of vector v is -4i + 8j, which matches the component form in Choice B.

Question 12

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​
Find F if W = 100 pounds and θ = 11°.Approximate the answer to one decimal place.
​
A)18.1 lb
B)21.1 lb
C)19.1 lb
D)20.1 lb
E)17.1 lb

Accepted Answer

The answer of A force of F pounds is required...

Question 13

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​
Find θ if F = 5,100 pounds and W = 14,000 lb.Approximate the answer to one decimal place.
​
A)19.4°
B)​21.4°
C)​23.4°
D)​20.4°
E)​22.4°

Accepted Answer

We can use the formula: 
F = Wsinθ
Rearranging, we get:
θ = sin⁻¹(F/W)
Plugging in the values, we get:
θ = sin⁻¹(5100/14000) = 21.4° (rounded to one decimal place) 
Therefore, the answer is B)​21.4°.

Question 14

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point
Terminal Point
(-9, 7)
​(0, 2)
​
A)-9i - 5j
B)​-5i + 9j
C)​​-5i ​- 9j
D)​9i - 5j
E)​9i + 5j

Accepted Answer

To find the linear combination of i and j that goes from (-9, 7) to (0, 2), we need to find the difference between the x-coordinates and the y-coordinates of the two points. The difference in x-coordinates is 0 - (-9) = 9, and the difference in y-coordinates is 2 - 7 = -5.

Therefore, the linear combination we need is 9i - 5j.

Question 15

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal, find the vertical and horizontal components of the velocity.(Round your answers to one decimal place.) ​
A)Vertical ≈ -55.7 mi/h, Horisontal ≈ 91.7 mi/h.
B)Vertical ≈ 90.7 mi/h, Horisontal ≈ -56.7 mi/h.
C)Vertical ≈ -56.7 mi/h, Horisontal ≈ -56.7 mi/h.
D)Vertical ≈ -56.7 mi/h, Horisontal ≈ 90.7 mi/h.
E)Vertical ≈ 90.7 mi/h, Horisontal ≈ 90.7 mi/h.

Accepted Answer

To find the vertical and horizontal components of the velocity, we use trigonometry. The horizontal component is found using the cosine function (cos(32°) * 107 mi/h), and the vertical component is found using the sine function (sin(32°) * 107 mi/h), but since it's below the horizontal, it's negative. Calculating these gives approximately -56.7 mi/h for the vertical and 90.7 mi/h for the horizontal components.

Question 16

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​
Find W if F = 620 pounds and θ = 20°.Approximate the answer to one decimal place.
​
A)1,812.8 lb
B)1,810.8 lb
C)1,814.8 lb
D)1,811.8 lb
E)1,813.8 lb

Accepted Answer

The answer of A force of F pounds is required...

Question 17

A traffic light weighing 15 pounds is suspended by two cables (see figure).Find the tension in each cable if θ₁ = 40° and θ₂ = 35°.Approximate the answers to one decimal place. A)T_L = 12.7 lb; TR = 12.7 lb B)T_L = 11.9 lb; TR = 11.9 lb C)T_L = 11.9 lb; TR = 12.7 lb D)T_L = 12.7 lb; TR = 11.9 lb E)T_L = 13.7 lb; TR = 12.9 lb

Accepted Answer

The answer of A traffic light weighing 15 pounds is...

Question 18

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ​
Magnitude
Angle   ​
A)​ 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of Find the component form of v given...

Question 19

A loaded barge is being towed by two tugboats, and the magnitude of the resultant is 6,400 pounds directed along the axis of the barge (see figure).Find the tension in the tow lines if they each make an angle 21° with the axis of the barge.Approximate the answer to one decimal place. ​  ​
Where a = 21°.
A)3,425.7 lb
B)3,429.7 lb
C)3,426.7 lb
D)3,428.7 lb
E)3,427.7 lb

Accepted Answer

The answer of A loaded barge is being towed by...

Question 20

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point
Terminal Point
(-9, 9)​
​(10, -10)
A)19i - 19j
B)​-19i + 19j
C)​​-19i - 19j
D)​19i + 19j
E)​-19i - 19j

Accepted Answer

To find the vector from the initial point (-9, 9) to the terminal point (10, -10), we subtract the coordinates of the initial point from the coordinates of the terminal point: (10 - (-9), -10 - 9) = (19, -19). Therefore, the vector is 19i - 19j.

Quiz 3: Additional-Topics-In-Trigonometry

A traffic light weighing 16 pounds is suspended by two cables (see figure) .Find the tension in each cable.Approximate the answer to one decimal place. Where b = 28°

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find F if W = 5,700 pounds and θ = 29°.Approximate the answer to one decimal place.

A gun with a muzzle velocity of 1700 feet per second is fired at an angle of 4° above the horizontal.Find the vertical and horizontal components of the velocity.(Round your answer to one decimal place.)

Find the magnitude of vector v with initial point (7, 5) and terminal point (-3, -5) .

Find the component form and the magnitude of the vector v. Initial Point Terminal Point (1, 3) (-8, -9)

Find the magnitude of vector v.

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Magnitude Angle 0°

The initial and terminal points of vector v are (3, -8) and (7, 1) , respectively.Select v in component form.

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector.. Initial Point Terminal Point (0, -8) (9, 12)

Find the component form of vector v.

Find the component form of vector v with initial point (1, -7) and terminal point (-3, 1) .

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find F if W = 100 pounds and θ = 11°.Approximate the answer to one decimal place.

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find θ if F = 5,100 pounds and W = 14,000 lb.Approximate the answer to one decimal place.

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point Terminal Point (-9, 7) (0, 2)

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal, find the vertical and horizontal components of the velocity.(Round your answers to one decimal place.)

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find W if F = 620 pounds and θ = 20°.Approximate the answer to one decimal place.

A traffic light weighing 15 pounds is suspended by two cables (see figure) .Find the tension in each cable if θ₁ = 40° and θ₂ = 35°.Approximate the answers to one decimal place.

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. Magnitude Angle

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point Terminal Point (-9, 9) (10, -10)

Quiz 3: Additional-Topics-In-Trigonometry

A traffic light weighing 16 pounds is suspended by two cables (see figure) .Find the tension in each cable.Approximate the answer to one decimal place. ​ ​ ​ Where b = 28° ​

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​ Find F if W = 5,700 pounds and θ = 29°.Approximate the answer to one decimal place. ​

A gun with a muzzle velocity of 1700 feet per second is fired at an angle of 4° above the horizontal.Find the vertical and horizontal components of the velocity.(Round your answer to one decimal place.) ​

​Find the magnitude of vector v with initial point (7, 5) and terminal point (-3, -5) . ​

Find the component form and the magnitude of the vector v. Initial Point Terminal Point (1, 3) (-8, -9)

Find the magnitude of vector v. ​

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ​ Magnitude Angle 0° ​ ​

The initial and terminal points of vector v are (3, -8) and (7, 1) , respectively.Select v in component form. ​

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector.. ​ Initial Point Terminal Point (0, -8) ​(9, 12) ​ ​

Find the component form of vector v. ​ ​ ​

Find the component form of vector v with initial point (1, -7) and terminal point (-3, 1) .

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​ Find F if W = 100 pounds and θ = 11°.Approximate the answer to one decimal place. ​

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​ Find θ if F = 5,100 pounds and W = 14,000 lb.Approximate the answer to one decimal place. ​

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point Terminal Point (-9, 7) ​(0, 2) ​

Detroit Tigers pitcher Joel Zumaya was recorded throwing a pitch at a velocity of 107 miles per hour.If he threw the pitch at an angle of 32° below the horizontal, find the vertical and horizontal components of the velocity.(Round your answers to one decimal place.) ​

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​ Find W if F = 620 pounds and θ = 20°.Approximate the answer to one decimal place. ​

A traffic light weighing 15 pounds is suspended by two cables (see figure) .Find the tension in each cable if θ1 = 40° and θ2 = 35°.Approximate the answers to one decimal place. ​ ​

Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ​ Magnitude Angle ​

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point Terminal Point (-9, 9) ​ ​(10, -10)