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3 years ago

If a = 8 in and b = 15 in what is the length of leg c in a right triangle using the

Mathematics

2 answers:

nirvana33 [79]3 years ago

7 0

See attachment for math work and answer.

laila [671]3 years ago

4 0

So a²+b²=c²
8²+15²=c²
64+225=c²
289=c²
±17=c
So c=17 or c=-17

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Why is the answer to this integral's denominator have 1+pi^2

ss7ja [257]

It comes from integrating by parts twice. Let

$I = \displaystyle \int e^n \sin(\pi n) \, dn$

Recall the IBP formula,

$\displaystyle \int u \, dv = uv - \int v \, du$

Let

$u = \sin(\pi n) \implies du = \pi \cos(\pi n) \, dn$

$dv = e^n \, dn \implies v = e^n$

Then

$\displaystyle I = e^n \sin(\pi n) - \pi \int e^n \cos(\pi n) \, dn$

Apply IBP once more, with

$u = \cos(\pi n) \implies du = -\pi \sin(\pi n) \, dn$

$dv = e^n \, dn \implies v = e^n$

Notice that the ∫ v du term contains the original integral, so that

$\displaystyle I = e^n \sin(\pi n) - \pi \left(e^n \cos(\pi n) + \pi \int e^n \sin(\pi n) \, dn\right)$

$\displaystyle I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n - \pi^2 I$

$\displaystyle (1 + \pi^2) I = \left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n$

$\implies \displaystyle I = \frac{\left(\sin(\pi n) - \pi \cos(\pi n)\right) e^n}{1+\pi^2} + C$

6 0

2 years ago

What is the height of a trapezoid with an area of 99 in.2 whose bases are 6 in. and 12 in.?

vladimir1956 [14]

Answer:

trapezoid area = ((sum of the bases) ÷ 2) • height

trapezoid area = ((6 + 12) / 2) * height

trapezoid area = 18 / 2 * height

height = 99/9 = 11

Step-by-step explanation:

7 0

3 years ago

Convert 6500 ounces to liters.

tekilochka [14]

your answer is 192.23

8 0

3 years ago

The product of two positive integers is 176. One number is 5 more than the other. Find the smaller number.

svlad2 [7]

Hello from MrBillDoesMath!

Answer:

Discussion:

Let "n" be the smaller number. Then

n * (n+5) = 176.

My first reaction to this problem was to factor 176 in my head. That's 176 = 16 * 11 and 16 is 5 more than 11. So that's the solution!.... Now let's solve it using the brute force approach:

n(n+5) = 176 =>

n^2 + 5n - 176 = 0 => use the quadratic formula

n = ( -5 +\- sqrt( 5^2 - 4(1)(-176)) ) /2

= ( -5 +\- sqrt( 25 + 704) )/ 2

= ( -5 +\- sqrt (729) ) /2 => as sqrt(729) = 27

= (-5 +\- 27) / 2 =>

= (-5 + 27)/2 or ( -5 -27)/2 =>

= 22/2 or -32/2 =>

= 11 or -16

But -16 is not allowed as the question wants a positive value.

Thank you,

MrB

4 0

3 years ago

Read 2 more answers

Convert 27 cubits to fathoms

topjm [15]

27 cubits =
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5 0

4 years ago