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3 years ago

Aisha and some friends are going to the movies. At the theater, they sell a bag of

Mathematics

1 answer:

Lynna [10]3 years ago

6 0

Answer:

price of 5 bags of popcorn = 3.75 x 5 = 18.75

price of 8 drinks = 5 x 8 = 40

price of p bags of popcorn = 3.75 x p

price of d drinks = 5 x d

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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

What is the surface area of the sphere below?

tatiyna

Hey there! I'm happy to help!

To find the surface area of a sphere, here is what you do.

You square the radius.

4²=16

You multiply by 4.

16×4=64

And you multiply by pi!

64×π=64π

Therefore, the surface area of the sphere is A. 64π units². It's that easy!

Now you can find the surface area of a sphere! Have a wonderful day! :D

3 0

3 years ago

What is the midpoint of the line segment with endpoints (-1, 3) and (-5,5)?

Debora [2.8K]

Step-by-step explanation:

it is the ans to the midpoint.

7 0

3 years ago

Which graph represents the function y = cos(4x)?<br><br> Answer is graph B

VARVARA [1.3K]

Answer:

Step-by-step explanation:

Let the equation of the cosine function is,

y = Acos(Bx)

From the graph attached,

A = Amplitude = $\frac{1-(-1)}{2}$

= 1

B = $\frac{2\pi}{\text{Period}}$

B = $\frac{2\pi}{\frac{\pi}{2}-0}$

B = $\frac{4\pi}{\pi}$

B = 4

Therefore, equation of the cosine wave given in the graph will be,

y = 1.Cos(4x)

y = Cos(4x)

7 0

3 years ago

Read 2 more answers

How do I solve this

gladu [14]

Make a proportion

x = the amount of miles walked in 137.5 min

25 137.5
--- = --------
2 x

cross multiply

25x = 275
divide both sides by 25
x = 11

paul walked 11 miles in 137.5 minutes

3 0

3 years ago