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2 years ago

Geometry Help Pythagorean

Mathematics

1 answer:

labwork [276]2 years ago

4 0

Answer:

Third side = 7

Step-by-step explanation:

x = third side:

$x=\sqrt{(6)^{2}+(\sqrt{13})^{2} } =\sqrt{36+13} =\sqrt{49} =7$

Hope this helps

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4^5/4^2= (four to the fifth power over four to the second power equals?

Sedbober [7]

Answer:

it is 4^3

Step-by-step explanation:

write it out

Expanding it gives you

4×4×4×4×4 divided by 4×4,

then you can cross out 2 4's from each side of the fraction and get 4×4×4 on the numerator. That is 4³, or 4^3

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4 years ago

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Find sin(2x), cos(2x), and tan(2x) from the given information.

larisa86 [58]

Since $\cot(x)=\frac{2}{3}$ and $\cot^{2} x+1=\csc^{2} x$ , we know that:

$\left(\frac{2}{3} \right)^{2}+1=\csc^{2} x\\\\\frac{13}{9}=\csc^{2} x\\\\\csc x=\frac{\sqrt{13}}{3}$

If $\csc x=\frac{\sqrt{13}}{3}$ , this means that $\sin x=\frac{3}{\sqrt{13}}$ and by the Pythagorean identity,

$\sin^{2} x+\cos^{2} x=1\\\left(\frac{3}{\sqrt{13}} \right)^{2}+\cos^{2} x=1\\\frac{9}{13}+\cos^{2} x=1\\\cos^{2} x=\frac{4}13}\\\cos x=\frac{2}{\sqrt{13}}$

Using the double angle formula for sine, $\sin(2x)=2\left(\frac{3}{\sqrt{13}} \right)\left(\frac{2}{\sqrt{13}} \right)=\boxed{\frac{12}{13}}$
Using the double angle formula for cosine, $\cos(2x)=1-2\left(\frac{3}{\sqrt{13}} \right)^{2}=\boxed{-\frac{5}{13}}$
So, since tan=sin/cos, $\tan (2x)=\frac{\sin(2x)}{\cos(2x)}=\frac{\frac{12}{13}}{-\frac{5}{13}}=\boxed{-\frac{12}{5}}$

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AlladinOne [14]

Answer:

Step-by-step explanation:

no two different lines

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3 years ago

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oksian1 [2.3K]

Answer:

Step-by-step explanation:

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3 years ago

Candice deposited $3,587.39 into a savings account with an interest rate of 4.2% compounded twice a year. About how long will it

Ratling [72]

Time taken for the amount deposited to grow to $5000 will be found as follows:
A=P(1+r/100*n)^nt
where:
A=amount
P=principle
r=rate
n=number of terms
t=time
thus plugging in our values we have:
5000=3587.39=(1+4.2/200)^2t
solving for t we have:
1.393771=1.021^2t
2t=ln1.393771/ln1.021
2t=16.111
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4 years ago