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jenyasd209 [6]
3 years ago
8

Find the midpoint of the line segment joining the points ​(−2​,−1​) and ​(−8​,4​).

Mathematics
1 answer:
Temka [501]3 years ago
8 0

Answer:

(-5, 1.5)

Step-by-step explanation:

(-2 ,-1) ; (-8 , 4)

Midpoint = (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\\\\

               =(\frac{-2-8}{2}, \frac{-1+4}{2})\\\\=(\frac{-10}{2},\frac{3}{2})\\\\=(-5 , 1.5)

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Consider the following.
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Answer:

Anything in the form x = pi+k*pi, for any integer k

These are not removable discontinuities.

============================================================

Explanation:

Recall that tan(x) = sin(x)/cos(x).

The discontinuities occur whenever cos(x) is equal to zero.

Solving cos(x) = 0 will yield the locations when we have discontinuities.

This all applies to tan(x), but we want to work with tan(x/2) instead.

Simply replace x with x/2 and solve for x like so

cos(x/2) = 0

x/2 = arccos(0)

x/2 = (pi/2) + 2pi*k or x/2 = (-pi/2) + 2pi*k

x = pi + 4pi*k   or    x = -pi + 4pi*k

Where k is any integer.

If we make a table of some example k values, then we'll find that we could get the following outputs:

  • x = -3pi
  • x = -pi
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and so on. These are the odd multiples of pi.

So we can effectively condense those x equations into the single equation x = pi+k*pi

That equation is the same as x = (k+1)pi

The graph is below. It shows we have jump discontinuities. These are <u>not</u> removable discontinuities (since we're not removing a single point).

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3 years ago
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Michael owns a small business selling clothing. He knows that in the last week 39 customers paid cash, 30 customers used a debit
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Answer:

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Step-by-step explanation:

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A frog is climbing out of a well that is 15 feet deep, the frog climbs 4 feet per hour, and then the frog slips back 1 foot whil
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Step-by-step explanation:

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In 2 hours, he is going up 4 feet and down 1 which means he advances 3 feet every two hours.

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Answer: in explanation

Step-by-step explanation

Sandi can perform  1/9 of the task in a day

Eva can perform 1/5 of the task in a day

Working together, they can perform

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So

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