3 years ago

Distance between two points ( phythagorean thereorm)

Mathematics

1 answer:

Ilya [14]3 years ago

3 0

What are the points?

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The coordinates on a map for City A are (57, 11) and those for City B are (121, 79). Note that coordinates represent miles. Find

Juliette [100K]

Answer:

93 miles

Step-by-step explanation:

Use the distance formula:

d = $\sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

Plug in the values:

d = $\sqrt{(121 - 57)^2 + (79 - 11)^2}$

d = $\sqrt{4096 + 4624}$

d = $\sqrt{8720}$

d = 93.4

= 93 miles

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3 years ago

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Does 38 minus 15 and 15 less than 38 mean the same thing? Explain

lana [24]

Answer:

Step-by-step explanation:

38 minus 15

38 - 15

15 less than 38

15 < 38

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3 years ago

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Jamie can work no more than 20 hours a week this summer. She needs to earn at least $256 a week to save enough

ivanzaharov [21]

She will have to get 12.8 per hour

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3 years ago

Can you help me with my math

romanna [79]

I can help if you want me to

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3 years ago

Suppose a and b are both non zero real numbers. Find real numbers c and d such that 1/a+ib= c+id

Thepotemich [5.8K]

$\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

Explanation

$\frac{1}{a+bi}=c+di$

Step 1

multiplicate by the conjugate

$\begin{gathered} \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(bi)^2} \\ \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(-b^2)}=\frac{a-bi}{a^2+b^2} \end{gathered}$

notice that

$\begin{gathered} \frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i \\ \frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i=c+di \\ so \\ \end{gathered}$ $\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

I hope this helsp you

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1 year ago