(a) First find the intersections of

and

:

So the area of

is given by

If you're not familiar with the error function

, then you will not be able to find an exact answer. Fortunately, I see this is a question on a calculator based exam, so you can use whatever built-in function you have on your calculator to evaluate the integral. You should get something around 0.5141.
(b) Find the intersections of the line

with

.

So the area of

is given by


which is approximately 1.546.
(c) The easiest method for finding the volume of the solid of revolution is via the disk method. Each cross-section of the solid is a circle with radius perpendicular to the x-axis, determined by the vertical distance from the curve

and the line

, or

. The area of any such circle is

times the square of its radius. Since the curve intersects the axis of revolution at

and

, the volume would be given by
Multiply both sides by y...
(3/y)y-(6/y)y-2y
Simplify it...
(3/y)y=3
(6/y)y=6
3=6-2y
Subtract 6 from both sides...
-2y=-3
Divide both sides by -2...
y=3/2
The solution is y=3/2
717/3= 239
Divide 717 by 3 to get the price of one night.
Answer: 1/10
Explanation: There are 10 discs in the bag so if you choose a 3 there is a 1 in 10 chance of you getting it
Substitution method is one of the ways to solve this system.
-5x+y=4 and 4x-4y=16.
First we will divide the second equation with number 4 and get
x-y=4 => x=y+4 than we will replace x in the first equation
-5(y+4)+y=4 => -5y-20+y=4 => -4y=4+20 => -4y=24 => y=-6
x-(-6))=4 => x+6=4 => x=4-6=-2 (x,y)=(-2,-6)
Good luck!!!