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3 years ago

14

Shannon is putting a fence around the garden ,except where there is a gate that is 3 feet wide one foot of the fence cost $43 .T

he cost of the gate is $128. Write an expression that represents the total cost of the fence and gate.

1 answer:

tamaranim1 [39]3 years ago

6 0

3x43=129 or is $129.

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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

2 years ago

"Ten subtracted from the quotient of a number<br> and 5 is 18."

Anika [276]

Answer: n/5 - 10 = 18: this would be the equation. Your answer would be 140.

Step-by-step explanation: Let consider the number as ‘X’

Quotient of a number and 5 can be written as

X divided by 5

Ten subtracted from the quotient of a number and 5 can be written as

(X divided by 5)-10

Ten subtracted from the quotient of a number and 5 is 18 can be written as

(X divided by 5)-10=18

By solving the above equation, find ‘X’

(X divided by 5) = 18 + 10

X/5=28

X = 28 x 5 = 140

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Divide each number by 3 Then subtract the numbers you got from the answers that you divided

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AleksandrR [38]

we know that

$1\ yard=3\ feet$

Let

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by proportion

<u>Find the value of y</u>

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therefore

<u>the answer is the option C</u>

$3x$

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