What makes this equation true?<br><br> -2n + 1.8 = 3.2<br><br> Im so confused

A 140 kg camera is suspended by two wires over a 40 metre wide football field to get shots of the action from above. At one poin

Katen [24]

Answer:

Please red the answer below

Step-by-step explanation:

In order to determine the length of each cable you use the Newton second law for each component of the forces involved in the situation.

For the x component you have:

$T_1cos\theta_1-T_2cos\theta_2=0$ (1)

T1: tension of the first cable = 1500N

T2: tension of the second cable = 800N

θ1: angle between the horizontal and the first cable

θ2: angle between the horizontal and the first cable

For the y component you have:

$T_1sin\theta_1+T_2sin\theta_2-W=0$ (2)

W: weight of the camera = Mg = (140kg)(9.8m/s^2) = 1372N

You can squared both equations (1) and (2) and the sum the two equations:

$T_1^2cos^2\theta_1=T_2^2cos^2\theta_2\\\\T_1^2sin^2\theta_1=T_2^2sin^2\theta_2-2WT_2sin\theta_2+W^2$

Then, you sum the equations:

$T_1^2(cos^2\theta_1+sin^2\theta_1)=T_2^2(sin^2\theta_2+cos^2\theta_2)-2Wsin\theta_2+W^2$ (3)

Next, you use the following identity:

$sin^2\theta+cos^2\theta=1$

and you obtain in the equation (3):

$T_1^2=T_2^2-2WT_2sin\theta_2+W^2\\\\sin\theta_2=\frac{T_2^2-T_1^2+W^2}{2WT_2}=\frac{(800N)^2-(1500)^2+(1372N)^2}{2(800N)(1372N)}=0.066\\\\\theta_2=sin^{-1}0.066=27.23\°$

With this values you can calculate the value of the another angle, by using the equation (1):

$\theta_1=cos^{-1}(\frac{T_2cos(27.23\°)}{T_1})=cos^{-1}(\frac{(800N)(cos27.23\°)}{1500N})\\\\\theta_1=61.69\°$

Now, you can calculate the length of each cable by using the information about the width of the football field. You use the following trigonometric relation:

$l_1cos\theta_1=40-d\\\\l_2cos\theta_2=d\\\\$

d: distance to the right side of the field

By using the cosine law you can fins a system of equation and then you can calculate the values of l1 and l2.

3 0

3 years ago

The midpoint of AB is M(1, -1). If the coordinates of A are (7,-4), what are the

Lapatulllka [165]

Answer:

work is attached and shown

6 0

3 years ago

PLEASE HELP!!!<br> Find MG.<br> ∆EGF~∆EML.

stiv31 [10]

Answer:

$MG=56\ units$

Step-by-step explanation:

step 1

Find the value of x

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem we have that

∆EGF~∆EML

so

$\frac{EG}{EM}=\frac{EF}{EL}$

substitute the given values

$\frac{5x+2}{16}=\frac{126}{28}$

solve for x

$5x+2=\frac{126}{28}(16)$

$5x+2=72\\5x=70\\x=14$

$EG=5x+2=5(14)+2=72\ units$

step 2

Find MG

we know that

$MG=EG-EM$

substitute

$MG=72-16=56\ units$

3 0

3 years ago

Which points are on a graph where y varies directly with x and y = 3 when x = -3

kondor19780726 [428]

A coordinate system is a method of determining the position of points or other geometric components on a manifold. The points which vary are on a graph where y varies directly with x are (-1, 1), (0, 0), and (-5, 5).

<h3>What are coordinates?</h3>

A coordinate system is a method of determining the position of points or other geometric components on a manifold, such as Euclidean space, by using one or more integers, or coordinates.

Given that y varies directly with x, therefore, we can write,

y∝x

y = kx

Also, y=3 and x=-3, therefore, the value of k can be written as,

3=k(-3)

k=-1

Now, the points which vary are on a graph where y varies directly with x are (-1, 1), (0, 0), and (-5, 5).

Learn more about Coordinates:

brainly.com/question/23450276

#SPJ1

3 0

2 years ago

It is 170 miles from Bruce's house to the city where his brother lives. On his last trip to visit his brother, he drove for 2 ho

Rom4ik [11]

Speed of Bruce for the rest of the trip is 30 miles/hour.

Step-by-step explanation:

Step 1: Total distance = 170 miles. In the trip Bruce's speed = 55 miles/hour. So, in 1 hour, distance covered = 55 miles. Find distance covered in 2 hours and the distance of the last part.

Distance covered in 2 hours = 2 × 55 = 110 miles

Remaining part of the trip = 170 - 110 = 60 miles

Step 2: Find the speed of Bruce in the remaining part of the trip when time = 2 hours and distance = 60 miles.

Speed = Distance/Time = 60/2 = 30 miles/hour

5 0

3 years ago

What makes this equation true? -2n + 1.8 = 3.2 Im so confused