By the Pythagoras theorem, in a right triangle with the sides being a and b,
a² + b² = Hypotenuse²
Hypotenuse² = 4² + 4²
Hypotenuse² = 16 + 16 = 2*16
Hypotenuse = √2 * √16
Thus, hypotenuse = 4√2
Answer:
$7.60
Step-by-step explanation:
- Penny = $0.01
- Nickel = $0.05
- Dime = $0.10
- Quarter = $0.25
( 5 × 0.01 ) + ( 13 × 0.05 ) + ( 14 × 0.10 ) + ( 2 × 0.25 ) + 5
-<em>The 5 at the end represents the </em><u><em>one</em></u><em> five dollar bill.</em>
Simplified: (solve what is in the parenthesis)
0.05 + 0.65 + 1.4 + 0.50 + 5 = $7.60
The first equation is linear:

Divide through by

to get

and notice that the left hand side can be consolidated as a derivative of a product. After doing so, you can integrate both sides and solve for

.
![\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1xy\right]=\sin x](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5B%5Cdfrac1xy%5Cright%5D%3D%5Csin%20x)


- - -
The second equation is also linear:

Multiply both sides by

to get

and recall that

, so we can write



- - -
Yet another linear ODE:

Divide through by

, giving


![\dfrac{\mathrm d}{\mathrm dx}[\sec x\,y]=\sec^2x](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5B%5Csec%20x%5C%2Cy%5D%3D%5Csec%5E2x)



- - -
In case the steps where we multiply or divide through by a certain factor weren't clear enough, those steps follow from the procedure for finding an integrating factor. We start with the linear equation

then rewrite it as

The integrating factor is a function

such that

which requires that

This is a separable ODE, so solving for

we have



and so on.
204.5 or 204 6/11 yep thats it