Do you mean something like y<21?
Answer:
The number which we divide is called the dividend. The number by which we divide is called the divisor. The result obtained is called the quotient.
Step-by-step explanation:
(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
Completing the square follows the principle of taking

and converting it into

where d is the 'correctional number' as I like to call it - i.e. the number that converts the expanded bracket into the +c, since the expanded bracket will give us

.
In this case, 2/2=1 so we have the first part:

.
Expanding this gives us

. We need c to be 9, so we can just add 8.
Putting this together:

Now we can solve it more easily.
Rearranging:
Answer:
B. 4.5
Step-by-step explanation:
(6x + 42)° and (18x - 12)° are alternate interior angles. If line l is parallel to line m, therefore,
6x + 42 = 18x - 12
Solve for the value of x. Combine like terms.
6x - 18x = -42 - 12
-12x = -54
Divide both sides by -12
-12x/-12 = -54/-12
x = 4.5
Therefore, x = 4.5 would prove lines l and m are parallel to each other.