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Daniel [21]
3 years ago
6

I'm not quite understanding how to solve these word problems

Mathematics
1 answer:
scoundrel [369]3 years ago
6 0
I'll help you on the first one.
Anya test scores are 78 and 91.
She has one more test and want to average between an 80-89 inclusive.
Lets set up a inequality and call the remaining test x.
80<=(78+91+x)/3<=89
Multiply everything by 3
240<=169+x<=267
Subtract 169 from everything
71<=x<=98
In interval notation that would be [71,98]
In set notation that would be{x|71<=x<=98}
For the graph, I don't really understand. I think you just graph 71<=x<=98.

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A fire ranger stands atop an observation tower 70 feet above the ground and sees a fire in the distance. She measures the angle
mrs_skeptik [129]

Answer:

103.78\:\mathrm{ft}

Step-by-step explanation:

We can form a right triangle where the distance between the ranger's current position and fire is the hypotenuse of the triangle. In a right triangle, the tangent of an angle is equal to its opposite side divided by the hypotenuse.

Therefore, we have:

\tan 34^{\circ}=\frac{70}{x}, where x is the distance between the base of the tower and the fire.

Solving, we get:

x=\frac{70}{\tan 34^{\circ}}=103.779267796\approx \boxed{103.78\:\mathrm{ft}}

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