45x50x39/87/2x633x91/20

Mathematics

1 answer:

UkoKoshka [18]3 years ago

8 0

I hope those x's mean multiplication, if so, here is your answer: 1452489.44

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Find the exact area of the surface obtained by rotating the curve about the x-axis.

padilas [110]

$\bf \begin{cases}
y=sin\left( \frac{\pi x}{6} \right)\\
0\le x\le 6\\
\textit{about the x-axis, or }y=0
\end{cases}\\\\
-----------------------------\\\\
\textit{using the disc method}
\\\\
V=\int\limits_{0}^{6}\pi \left[ sin\left( \frac{\pi x}{6} \right) \right]^2\cdot dx\implies \pi\int\limits_{0}^{6} \left[ sin\left( \frac{\pi x}{6} \right) \right]^2\cdot dx
\\\\\\
 \pi\int\limits_{0}^{6} sin^2\left( \frac{\pi x}{6} \right) \cdot dx\\\\
-----------------------------\\\\$

$\bf \textit{now, let us check the double angle identities}
\\\\
cos(2\theta)=
\begin{cases}
cos^2(\theta)-sin^2(\theta)\\
\boxed{1-2sin^2(\theta)}\\
2cos^2(\theta)-1
\end{cases}
\\\\\\
thus\implies cos(2\theta)=1-2sin^2(\theta)\implies 2sin^2(\theta)=1-cos(2\theta)
\\\\\\
sin^2(\theta)=\cfrac{1-cos(2\theta)}{2}\qquad thus\\\\
-----------------------------$

$\bf \pi\int\limits_{0}^{6} \left[ sin\left( \frac{\pi x}{6} \right) \right]^2\cdot dx\implies 
\pi\int\limits_{0}^{6} \cfrac{1-cos\left(2\cdot \frac{\pi x}{6} \right)}{2}\cdot dx
\\\\\\
\pi\int\limits_{0}^{6}\cfrac{1}{2}dx-\pi \cdot \cfrac{1}{2}\pi\int\limits_{0}^{6}cos\left(\frac{\pi x}{3} \right)dx
\\\\\\
\left[\cfrac{\pi x}{2}-\cfrac{\pi }{2}\cdot \cfrac{sin\left(\frac{\pi x}{3} \right)}{\frac{\pi x}{3} } \right]\implies \left[ \cfrac{\pi }{2}x-\cfrac{3sin\left(\frac{\pi x}{3} \right)}{2x} \right]_0^6$

and surely, you'd know how to get the values for the bounds there

5 0

2 years ago

Ill give brainliest

Lera25 [3.4K]

Answer:

Change: subtract old value from new value. Example: You had 5 books, but now have 7. The change is: 7−5 = 2. Percentage Change is all about comparing old to new values.

Step-by-step explanation:

hope this helps :)

8 0

2 years ago

Read 2 more answers

Please can somebody help me with this question

4vir4ik [10]

Answer:

the answer is=21

Step-by-step explanation:
u have to sum all of its sides
(length+breadth+height).

8 0

2 years ago

A horizontal line passes through the point (5, –1). Which point is also on this line?

sweet-ann [11.9K]

Answer:

Step-by-step explanation:

A horizontal line is a "y = " line. So the horizontal line that goes through the point given has the equation y = -1 (-1 being the y coordinate of the point). That means that another point on this line, y = -1, will also have to have a y coordinate of -1. The only one is the last one, (-2, -1).

7 0

2 years ago

The cost CC (in dollars) of making nn watches is represented by C=15n+85C=15n+85. How many watches are made when the cost is $38

dangina [55]

$\bf \stackrel{cost}{C}=15\stackrel{watches}{n}+85\qquad \boxed{C=385}\qquad \stackrel{cost}{385}=15n+85
\\\\\\
380=15n\implies \cfrac{380}{15}=n\implies \cfrac{76}{3}=n\implies 25\frac{1}{3}=n$

so, 25 whole watches and hmmmm just the wristband of another maybe.

5 0

3 years ago