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## If a rectangular area is rotated in a uniform electric field from the position where the maximum electric flux goes through it to an orientation where only half the flux goes through it, what has been the angle of rotation?

With a uniform electric field, flux go along parallel paths, then flux is therefore proportional to the cosine of the angle rotated.
0 degree rotation => cos(0)=1 => 100% of flux.
60 degrees rotation => cos(60) => 0.5  => how many % of flux?

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## At a playground, a child slides down a slide that makes a 42° angle with the horizontal direction. the coefficient of kinetic friction for the child sliding on the slide is 0.20. what is the magnitude of her acceleration during her sliding?

Assuming metric units, metre, kilogram and seconds

Best approach: draw a free body diagram and identify forces acting on the child, which are:
gravity, which can be decomposed into normal and parallel (to slide) components
N=mg(cos(theta)) [pressing on slide surface]
F=mg(sin(theta))  [pushing child downwards, also cause for acceleration]
m=mass of child (in kg)
g=acceleration due to gravity = 9.81 m/s^2
theta=angle with horizontal = 42 degrees

Similarly, kinetic friction is slowing down the child, pushing against F, and equal to
Fr=mu*N=mu*mg(cos(theta))
mu=coefficient of kinetic friction = 0.2

The net force pushing child downwards along slide is therefore
Fnet=F-Fr
=mg(sin(theta))-mu*mg(cos(theta))
=mg(sin(theta)-mu*cos(theta))   [ assuming sin(theta)> mu*cos(theta) ]

From Newton’s second law,
F=ma, or
a=F/m
=mg(sin(theta)-mu*cos(theta))  /  m
= g(sin(theta)-mu*cos(theta))   [ m/s^2]

In case imperial units are used, g is approximately 32.2 feet/s^2.
and the answer will be in the same units [ft/s^2] since sin, cos and mu are pure numbers.

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## Which fact is not used to prove that PQR is similar to STR? Segments ST and PQ are parallel. Angle P is congruent to itself due to the reflexive property. RP is a transversal line passing ST and PQ. Angles RTS and RQP are congruent due to the Corresponding Angles Postulate.

The fact that is not used to prove that PQR is similar to STR is that “Angle P is congruent to itself due to the reflexive property.” The statements Segments ST and PQ are parallel, RP is a transversal line passing ST and PQ and Angles RTS and RQP are congruent due to the Corresponding Angles Postulate are all true.

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## ? A body is suspended from the ceiling with two wires that make an angle of 40° with the ceiling. The weight of the body is 150N. What is the tension in each wire?

So, the weight is supported by the tension in the two wires, but only part of the tension goes in holding the body: the vertical component.

If the angle between the ceiling and the wire is 40 deg, then the vertical component is

T_y = T * sin(40),

There are two wires, so together they do

2*T*sin(40)

And all this holds the weight of the body, so:

2*T*sin(40)=150 —-> T = 75/sin(40)~116.68 N,

Notice how it is larger than 150N (both wires is ~ 233 N), as the angle becomes smaller, there is less tension that is vertical, so one needs more tension to make the vertical component as large as (half) the weight of the body

Hope it helps!

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## When any two lines intersect, four angles are formed. If the intersection is perpendicular, then each angle is 90°

When any two lines intersect, four angles are formed. If the intersection is perpendicular, then each angle is 90°

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## At which angle will a hexagon rotate onto itself

At which angle will a hexagon rotate onto itself

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## Which of the following is not an example of approximate simple harmonic motion? a. a toy car rolling across the floor b. a child swinging on a swing c. a piano wire that has been struck d. a pendulum with an angle of less than 15°

Which of the following is not an example of approximate simple harmonic motion? a. a toy car rolling across the floor b. a child swinging on a swing c. a piano wire that has been struck d. a pendulum with an angle of less than 15°

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## The circumference of C is 72 cm. what is the length of arc AB (the minor arc)? The center angle is 45

Arc length (AB ) =  9 cm .

Step-by-step explanation:

Given : The circumference of C is 72 cm and The center angle is 45.

To find : What is the length of arc AB (the minor arc).

Solution : We have given that

circumference of C = 72 cm.

The center angle  =  45.

Formula of arc length  = .

We have circumference = 2 pi r

Substitute the values arc length  = .

Arc length = .

=  9 cm

Therefore ,Arc length (AB ) =  9 cm .

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## Trevor is pulling his younger brother in a wagon. He pulls the wagon 50 m to the corner with a force that is a parallel with the ground. He then turns the wagon around and pulls it 50 m back to the starting point with the same force at an angle of 30 degrees with respect to the ground. How does the amount of work Trevor performs going to the corner compare with the amount of work he performs coming back? A) they are the same because he uses the same amount of force B) they are the same because he travels the same distance C) he does less work coming back because the force moving the wagon is only 50cos30 D)he does more work coming back because the force moving the wagon is only 50cos60

Work has the greatest value when the force done is
parallel to the direction of motion. In this case, the work done in pulling the
wagon to the corner is greater than the amount of work done in pulling the
wagon back to the starting point. This is because an angle of 30 degrees is
applied when pulling it back. The formula for work when angle is applied is:

Wx = W cos θ

Where in this case, θ = 30

Therefore,
the answer to this is letter:

C) he does less work coming back because the force moving
the wagon is only 50cos30

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## An exterior angle of a triangle measures 125° and one of the remote interior angles measures 35°. The triangle must be: Obtuse Acute Right

An exterior angle of a triangle measures 125° and one of the remote interior angles measures 35°. The triangle must be: Obtuse Acute Right

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## What is the measure of an interior angle of a regular three-sided polygon? A. 45° B. 60° C. 75° D. 80°

The formula to find the measure of an interior angle is , where represents the number of sides in the polygon. In this problem, would represent Let’s plug in the value for  Let’s simplify that. Now we know that the measure of an interior angle of a regular three-sided polygon is 60°. Your answer would be B!

Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish

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## Explain why two right triangles, each with an acute angle of 17°, must be similar

A right triangle is a triangle that has 1 90 degree, or “right” angle. Since there are only 3 angles, if you know 2 of the angles, you can subtract them from the total angle amount to get the third angle, which will stay the same in two right triangles if the second angle is the same. This means that they are similar.

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## The triangles below are similar. In each traingle there is a 50 degree angle and a right angle. What is the measure of the third angle in each triangle?

The triangles below are similar. In each traingle there is a 50 degree angle and a right angle. What is the measure of the third angle in each triangle?

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## A pair of parallel lines is cut by a transversal: A pair of parallel lines cut by a transversal is shown. The inside bottom right angle is labeled 80 degrees. The alternate interior angle is cut by a ray and is labeled as x on one side and 20 degrees on the other. What is the measure of angle x?

A pair of parallel lines is cut by a transversal: A pair of parallel lines cut by a transversal is shown. The inside bottom right angle is labeled 80 degrees. The alternate interior angle is cut by a ray and is labeled as x on one side and 20 degrees on the other. What is the measure of angle x?

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## What is the reference angle for 120°?

The reference angle is 60°

Step-by-step explanation:

Given the angle 120°

we have to find the reference angle of 120°

The reference angle is always the smallest angle made from the terminal side of an angle with the x-axis.

Angle 120° lies in second quadrant

To find the reference angle measuring x° for angle in Quadrant II, the formula is (180−x)°

Reference angle=(180-120)°=60°

hence, the reference angle is 60°

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## Which of the following describe an angle with a vertex at A? Check all that apply. A. CAB B. BAC C. ABC D. ACB

Which of the following describe an angle with a vertex at A? Check all that apply. A. CAB B. BAC C. ABC D. ACB

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## Choose two angles that are each separately alternate exterior angles with angle 12

Choose two angles that are each separately alternate exterior angles with angle 12

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## 22. The tangent of an angle is 7.5. What is the measure of the angle to the nearest tenth?

22. The tangent of an angle is 7.5. What is the measure of the angle to the nearest tenth?

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## An engineer on the ground is looking at the top of a building. The angle of elevation to the top of the building is 46°. The engineer knows the building is 250 ft tall. What is the distance from the engineer to the base of the building to the nearest whole foot?

An engineer on the ground is looking at the top of a building. The angle of elevation to the top of the building is 46°. The engineer knows the building is 250 ft tall. What is the distance from the engineer to the base of the building to the nearest whole foot?

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## According to this diagram what is tan 67 It's a right triangle facing left. hypotenuse: 13 opposite:5 adjacent: 12 The angle to the far left is 23 degrees, the one to the far right at the bottom is 90, and the one on the top is 67. options: 12, 5/13, 12/13, 5/12, 13/5, 13/12 Please explain. Thanks so much

According to this diagram what is tan 67 It’s a right triangle facing left. hypotenuse: 13 opposite:5 adjacent: 12 The angle to the far left is 23 degrees, the one to the far right at the bottom is 90, and the one on the top is 67. options: 12, 5/13, 12/13, 5/12, 13/5, 13/12 Please explain. Thanks so much

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## If measure of angle L=64, and measure of angle K = 50, list the sides of triangle jkl in order from smallest to largest

If measure of angle L=64, and measure of angle K = 50, list the sides of triangle jkl in order from smallest to largest

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## From the top of the CN Tower, the angle of depression to to tip of the towers shadow is 88 degrees. The shadow is 19.5m long

From the top of the CN Tower, the angle of depression to to tip of the towers shadow is 88 degrees. The shadow is 19.5m long

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## Kim's route from her front door to the mailbox, the swing set, and back to the front door forms a triangle. Two legs of the triangle are 245 feet long and they meet at an angle of 38°. How long is the entire route?

Kim’s route from her front door to the mailbox, the swing set, and back to the front door forms a triangle. Two legs of the triangle are 245 feet long and they meet at an angle of 38°. How long is the entire route?

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## Which equation can be used to solve for m angle 1?

Which equation can be used to solve for m angle 1?