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soldier1979 [14.2K]
4 years ago
7

Which statement correctly describes the relationship between the graph of f(x) and the graph of g(x)=f(x)-1?

Mathematics
2 answers:
AlladinOne [14]4 years ago
8 0

Answer:

The correct answer is C. because the graphs are the same, save that -1 on the graph of g(x), which moves the graph down 1 unit

Step-by-step explanation:

LiRa [457]4 years ago
3 0

Answer:

C.

Step-by-step explanation:

The - 1 means its a translation of 1 units down.

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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
4 years ago
Josh stopped at a booth at the fair. The prices of the items being sold were posted on a sign like the one seen below. Josh was
Vikki [24]

Answer:

i need the full sing to determine the answer

3 0
3 years ago
Question shown below within image.
shepuryov [24]

Answer:

m∠x = 119°

m∠y = 61°

m∠z = 119°

Step-by-step explanation:

Angle x:

  • m∠x = 180° - 61°       (sum of angles in a straight line)
  • m∠x = 119°

Angle y:

  • m∠y = 61°                   (Alternate interior angles)

Angle z:

  • m∠z = 119°               (Sum of angles in a line, corresponding angles)

-Chetan K

7 0
3 years ago
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