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2 years ago

Please help me with this.

Mathematics

1 answer:

Valentin [98]2 years ago

8 0

The correct proportion of the corresponding sides is 2 : 3

<h3>How to determine the proportion?</h3>

From the question, we understand that the shapes are similar.

This means that:

Ratio = GHIJ : KLMN

From the figure, we have:

GH = 6 and KL = 9

So, we have:

Ratio = 6 : 9

Simplify the ratio

Ratio = 2 : 3

Hence, the correct proportion of the corresponding sides is 2 : 3

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A force of 4 pound acts in the direction of 48degree to the horizontal. The force moves an object along a straight line from the

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Answer:

<u>Work Done = 27.66 Joules</u>

Step-by-step explanation:

The work done is:

$W=F*d*Cos \theta$

Where

F is the fore

d is the distance moved

$\theta$ is the angle

The force is "4"

The distance is the distance from (1,7) to (8,10)

The distance is the square root of change in y coordinates, squared and sum of change in x coordinates, squared. Hence, distance is:

$\sqrt{(10-7)^2+(8-1)^2}\\=\sqrt{3^2+7^2}\\\sqrt{58}$

The angle is gotten by the formula:

$Cos\phi = \frac{Force in x direction}{Distance}\\Cos\phi = \frac{8-1}{\sqrt{58}}\\Cos\phi=\frac{7}{\sqrt{58}}\\\phi = Cos^{-1}\frac{7}{\sqrt{58}}\\\phi = 23.21$

So, now:

$\theta = 48 - 23.21 = 24.79$

Work Done = $F*d * Cos\theta = 4 * \sqrt{58} * Cos(24.79)$

<u>Work Done = 27.66 Joules</u>

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