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Hatshy [7]
3 years ago
10

Solve for x x + 4/x = -5

Mathematics
1 answer:
Arlecino [84]3 years ago
5 0

Answer:

x = -4 , x = -1

Explanation:

Multiply by x on both sides to get rid of fraction

x(x + 4/x) = x(-5)

x^2 + 4 = -5x

x^2 + 5x + 4 = 0

Factor

(x+4)(x+1) = 0

x = -4 , x = -1

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(a) Use the reduction formula to show that integral from 0 to pi/2 of sin(x)^ndx is (n-1)/n * integral from 0 to pi/2 of sin(x)^
Sedbober [7]
Hello,

a)
I= \int\limits^{ \frac{\pi}{2} }_0 {sin^n(x)} \, dx = \int\limits^{ \frac{\pi}{2} }_0 {sin(x)*sin^{n-1}(x)} \, dx \\

= [-cos(x)*sin^{n-1}(x)]_0^ \frac{\pi}{2}+(n-1)*\int\limits^{ \frac{\pi}{2} }_0 {cos(x)*sin^{n-2}(x)*cos(x)} \, dx \\

=0 + (n-1)*\int\limits^{ \frac{\pi}{2} }_0 {cos^2(x)*sin^{n-2}(x)} \, dx \\

= (n-1)*\int\limits^{ \frac{\pi}{2} }_0 {(1-sin^2(x))*sin^{n-2}(x)} \, dx \\
= (n-1)*\int\limits^{ \frac{\pi}{2} }_0 {sin^{n-2}(x)} \, dx - (n-1)*\int\limits^{ \frac{\pi}{2} }_0 {sin^n(x) \, dx\\


I(1+n-1)= (n-1)*\int\limits^{ \frac{\pi}{2} }_0 {sin^{n-2}(x)} \, dx \\
I= \dfrac{n-1}{n} *\int\limits^{ \frac{\pi}{2} }_0 {sin^{n-2}(x)} \, dx \\


b)
\int\limits^{ \frac{\pi}{2} }_0 {sin^{3}(x)} \, dx \\
= \frac{2}{3} \int\limits^{ \frac{\pi}{2} }_0 {sin(x)} \, dx \\
= \dfrac{2}{3}\ [-cos(x)]_0^{\frac{\pi}{2}}=\dfrac{2}{3} \\






\int\limits^{ \frac{\pi}{2} }_0 {sin^{5}(x)} \, dx \\
= \dfrac{4}{5}*\dfrac{2}{3} \int\limits^{ \frac{\pi}{2} }_0 {sin(x)} \, dx = \dfrac{8}{15}\\







c)

I_n=  \dfrac{n-1}{n} * I_{n-2} \\

I_{2n+1}=  \dfrac{2n+1-1}{2n+1} * I_{2n+1-2} \\
= \dfrac{2n}{2n+1} * I_{2n-1} \\
= \dfrac{(2n)*(2n-2)}{(2n+1)(2n-1)} * I_{2n-3} \\
= \dfrac{(2n)*(2n-2)*...*2}{(2n+1)(2n-1)*...*3} * I_{1} \\\\

I_1=1\\






3 0
3 years ago
HELPPP ME FIND THE LETTER CODE PLEASE I DONT WANNA FAIL SUMMER SCHOOL
Arlecino [84]

Answer:

Ian SomerhalderHappy “3rd” Birthday to our smart, energetic, lively and mischievous Carmelo!!!

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3 0
2 years ago
W(n) = n + 3; Find the value of w(-5)<br> A) 2 <br> B) -2<br> C) 3<br> D) 1
Lina20 [59]

Answer:

-2

Step-by-step explanation:

-5 + 3 = -2

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below :)

6 0
3 years ago
What is 149/18 in its simplest form
Helga [31]
Its simplest form is 8 5/18
4 0
3 years ago
Read 2 more answers
I’ll mark you brainliest if you answer
ra1l [238]

Answer:

A=Pier^2

a=pie2.5^2

a=19.63

A=Pier^2

a=pie2^2

a=12.57

19.63 - 12.57

=7.07

B

8 0
2 years ago
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