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3 years ago

Use Pythagorean theorem to find the height of the missing section

Mathematics

1 answer:

kati45 [8]3 years ago

4 0

Answer:

What is the missing section?

I will edit the answer after you tell me

Step-by-step explanation:

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Loren drove 200 miles at a certain rate, and his wife, Lois, drove 100 miles at a rate 10 mph slower. If Loren had driven for th

NeX [460]

As long as Loren drove, the law of motion was

$200 = st_1 \implies t_1 = \dfrac{200}{s}$

As long as Loid drove, the law of motion was

$100 = (s-10)t_2 \implies t_2 = \dfrac{100}{s-10}$

So, the total time they took is

$t_1+t_2=\dfrac{200}{s}+\dfrac{100}{s-10}$

Had Loren driven the whole time, the law of motion would have been

$300=st_3 \implies t_3 = \dfrac{300}{s}$

And we know that this time would have been 30 minutes (i.e. 0.5 hours) faster. So, we have

$t_3 = t_1+t_2-0.5$

This translates into

$\dfrac{300}{s}=\dfrac{200}{s}+\dfrac{100}{s-10}-\dfrac{1}{2}$

If we subtract 200/s from both sides, we have

$\dfrac{100}{s}=\dfrac{100}{s-10}-\dfrac{1}{2}$

We can simplify the right hand side by summing the two fractions:

$\dfrac{100}{s-10}-\dfrac{1}{2} = \dfrac{200-(s-10)}{2(s-10)}=\dfrac{210-s}{2(s-10)}$

So, we have to solve

$\dfrac{100}{s}=\dfrac{210-s}{2(s-10)}$

If we cross multiply the denominators, we have

$200(s-10)=s(210-s) \iff 200s-2000=210s-s^2 \iff s^2-10s-2000=0$

Which yields the solutions

$s=-40,\quad s=50$

We accept the positive solution, because the negative would mean to travel backwards, so Loren's rate was 50mph

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3 years ago

Read 2 more answers

Larry McCoy desposited three checks to his checking account he remembers that one of the checks was twice the amount of the smal

ddd [48]

$67.50

Step-by-step explanation:

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4 years ago

What is the unit price of a granola bar if 8 granola bars cost $4.16 And show your work

baherus [9]

Answer:

$0.52

Step-by-step explanation:

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2 years ago

Is a diamond a quadrilateral? Parallelogram? Rhombus? Rectangle? Square? Trapezoid? List the applies

Rama09 [41]

Answer:

A diamond is only a quadrilateral and square.

Step-by-step explanation:

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3 years ago

Evaluate arccsc 2

Tasya [4]

Answer:

The answer is option C

arccsc 2 = π/6 , 5π/6

Hope this helps

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3 years ago