Mathematics, 01.08.2019 12:00, darkghostmist

Find the volume v obtained by rotating the region bounded by the given curves about the specified axis. y = 9 sin x, y = 0, π 2 ≤ x ≤ π; about the x−axis

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answered: tcjet

The volume obtained by rotating the region is 9 cubic units.

How to find the volume of a solid of revolution

The volume of a solid of revolution () generated about the x-axis is determined by the following integral formula:

$V = \pi \int\limits^{\pi}_{\frac{\pi}{2} } {f(x)} \, dx$ (1)

Where f(x) is the curve function.

If we know that $f(x) = 9\cdot \sin x$ , then the volume of the solid of revolution is:

$V = 9\int\limits^\pi_{\frac{\pi}{2} } {\sin x} \, dx$

$V = 9\cdot [-\cos \pi + \cos \frac{\pi}{2} ]$

V = 9

The volume obtained by rotating the region is 9 cubic units. $\blacksquare$

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Find the volume obtained by rotating the region bounded by the given curves about the specified axis. $y = 9\cdot \sin x$ , y = 0 , $\frac{\pi}{2}\le x \le \pi$ , about the x-axis.

To learn more on solids of revolution, we kindly invite to check this verified question: link

answered: Guest

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

the function given is y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 = -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

answered: Guest

you ignore the remainder, therefore the answer is y = x+2

step-by-step explanation: