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tia_tia [17]
3 years ago
15

Two crews are laying blacktop on a road. They start at the same time at opposite ends of a 18-mile road and work toward one anot

her. One crew lays blacktop at an average rate of 0.4 mile a day faster than the other crew. If the two crews meet after 5 days, find the rate of each crew.
Mathematics
1 answer:
liraira [26]3 years ago
7 0
Total road length is 36 miles.
If one crew’s rate is x miles/day, the other is 1.4x miles/day.
The collective distance per day is x+1.4x,
so in five days the distance is 5(x+1.4x).
Set that equal to the total distance:
5(x+1.4x)=36
simplify:
x+1.4x=7.2
x(1+1.4)=7.2
x(2.4)=7.2
x=3
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AlekseyPX

Given:

Right triangle XYZ has right angle Z.

\sin(x)=\dfrac{12}{13}

To find:

The value of \cos x.

Solution:

We know that,

\sin^2(x)+\cos^2(x)=1

\cos^2(x)=1-\sin^2(x)

\cos(x)=\pm\sqrt{1-\sin^2x}

For a triangle, all trigonometric ratios are positive. So,

\cos(x)=\sqrt{1-\sin^2x}

It is given that \sin(x)=\dfrac{12}{13}. After substituting this value in the above equation, we get

\cos(x)=\sqrt{1-(\dfrac{12}{13})^2}

\cos(x)=\sqrt{1-\dfrac{144}{169}}

\cos(x)=\sqrt{\dfrac{169-144}{169}}

\cos(x)=\sqrt{\dfrac{25}{169}}

On further simplification, we get

\cos(x)=\dfrac{\sqrt{25}}{\sqrt{169}}

\cos(x)=\dfrac{5}{13}

Therefore, the required value is \cos(x)=\dfrac{5}{13}.

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