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Alecsey [184]
3 years ago
14

45 mi 28 mi What is the length of the hypotenuse?

Mathematics
1 answer:
solniwko [45]3 years ago
6 0

Answer:

c = 53 miles

Step-by-step explanation:

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Choose the correct simplification of the expression (c2)9.
Lapatulllka [165]
The correct simplification of the expression is 9c^2 i think.
5 0
3 years ago
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Evaluate Dx / ^ 9-8x - x2^
Solnce55 [7]
It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for \sqrt x.

In that case, you want to find the antiderivative,

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}

Complete the square in the denominator:

9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2

Now substitute x+4=5\sin y, so that \mathrm dx=5\cos y\,\mathrm dy. Then

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy

which simplifies to

\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy

Now, recall that \sqrt{x^2}=|x|. But we want the substitution we made to be reversible, so that

x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)

which implies that -\dfrac\pi2\le y\le\dfrac\pi2. (This is the range of the inverse sine function.)

Under these conditions, we have \cos y\ge0, which lets us reduce \sqrt{\cos^2y}=|\cos y|=\cos y. Finally,

\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C

and back-substituting to get this in terms of x yields

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C
4 0
3 years ago
a map distance of 5 inches represents 200 miles of actual distance suppose the distance between two cities on the map is 7in wha
Lesechka [4]

5in : 200mi

7in : xmi

One inch represents 40 miles.

7 * 40 miles = 280 miles.


The two cities are 280 miles apart.

5 0
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Is 9(2k + 3) and 18k + 27 equivalent <br>​
Lunna [17]
Yes, these are equivalent
3 0
3 years ago
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Escribe el número que tenga el mismo valor que 28 decenas
adoni [48]

Answer:

280

Step-by-step explanation:

<u><em>The question in English is</em></u>

Write the number that has the same value as 28 tens

we know that

One tens is equal to the number 10

so

To find out the value of 28 tens, multiply the number 28 by 10

28(10)=280

6 0
3 years ago
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