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Mumz [18]
2 years ago
6

Order 2.32, 2 1/3, 224%, 254%, 2 2/5 From least to greatest.

Mathematics
1 answer:
Kobotan [32]2 years ago
5 0
2.32, 2 1/3, 2 2/5, 224, 254
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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
2 years ago
Show that the dual of the exclusive-OR is equal to its complement.
Rzqust [24]
Solution:XOR: X+Y= XY’ + X’YDual of XOR:= (X +Y’)+(X’+Y)= XX’+XY +X’Y’ +YY’= XY + X’Y’ Complement of XOR (XNOR)= (X+Y)’= (XY’ + X’Y)’=(X’+Y)+(X +Y’)= XX’+ XY + X’Y’+YY’= XY + X’Y’
HOPE IT HELPS



7 0
3 years ago
Solve the following:
olga_2 [115]

Answer:

Do in calculator simple answer

5 0
2 years ago
Is x + 10 a factor of the function f(x) = x3 − 75x + 250? Explain.
PtichkaEL [24]
Yes. When the function f(x) = x3 – 75x + 250 is divided by x + 10, the remainder is zero. Therefore, x + 10 is a factor of f(x) = x3 – 75x + 250. 

According to the remainder theorem when f(x) is divided by (x+a) the remainder is f(-a). 
In this case, 
f(x)=x^3-75x+250 
(x+a)=(x+10) 
Therefore, the remainder f(-a)=f(-10) 

=x^3-75x+250 
=(-10)^3-(75*-10)+250 
=-1000+750+250 
=1000-1000 
=0. 
The remainder is 0. So, (x+10) is a factor of x^3-75x+250.
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3 years ago
Amber borrows $1,450 from the bank. If she repays the loan in 3 years, the annual interest rate is 5%, compounded annually. Howe
Step2247 [10]
The answer is $126 the asked for 20 charaters so
3 0
3 years ago
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