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2 years ago

How to find the sides of a 30 60 90 triangle?

Mathematics

1 answer:

Sever21 [200]2 years ago

4 0

All you need to do is plug in the numbers and you'll get the sides.

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Integrala x la a treia ori ln la a doua dx va rog

Studentka2010 [4]

I don't speak Romanian, but the closest translation for this suggests you're trying to compute

$\displaystyle \int x^3 \ln(x)^2 \, dx$

Integrate by parts:

$\displaystyle \int x^3 \ln(x)^2 \, dx = uv - \int v \, du$

where

u = ln(x)² ⇒ du = 2 ln(x)/x dx

dv = x³ dx ⇒ v = 1/4 x⁴

$\implies \displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac12 \int x^3 \ln(x) \, dx$

Integrate by parts again:

$\displaystyle \int x^3 \ln(x) \, dx = u'v' - \int v' du'$

where

u' = ln(x) ⇒ du' = dx/x

dv' = x³ dx ⇒ v' = 1/4 x⁴

$\implies \displaystyle \int x^3 \ln(x) \, dx = \frac14 x^4 \ln(x) - \frac14 \int x^3 \, dx$

So, we have

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac12 \left(\frac14 x^4 \ln(x) - \frac14 \int x^3 \, dx \right)$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac18 \int x^3 \, dx$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac18 \left(\frac14 x^4\right) + C$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac1{32} x^4 + C$

$\boxed{\displaystyle \int x^3 \ln(x)^2 \, dx = \frac1{32} x^4 \left(8\ln(x)^2 - 4\ln(x) + 1\right) + C}$

3 0

1 year ago

Which property is illustrated by the statement<br> (2+3.4)+6=2+(3.4+6)

aleksandrvk [35]

Answer:

Associative property is illustrated.

Step-by-step explanation:

we have been given:

(2+3.4)+6=2+(3.4+6)

This is the associative identity which is:

a+(b+c)=(a+b)+c

Here, we have a=2, b=3.4, c=6

On comparing the values with associative property we get:

(2+3.4)+6=2+(3.4+6)

We club two numbers b and c first and then a and b in same bracket.

6 0

2 years ago

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a football gains 8 yards on their first play. they lose 12 yards on the next play.. which integers represent the two plays?

9966 [12]

8 yards - 12 yards = - 4

The integer is -4

5 0

2 years ago

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Worth 10 points pls help

Olenka [21]

What subject is this

3 0

2 years ago

The square root of 52 is between which two consecutive Integers?

Murrr4er [49]

The answer is 7 and 8

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2 years ago

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