A rational expression is undefined if the denominator is zero. Since the denominator is
, the expression is undefined if

Answer:
Step-by-step explanation:
first multiply 1 with 2+5i then multiply 2i with 2+5i and you will get
2+5i+4i+10i^2
then in the next step add 4i and 5i you will get 9i
in the next step put i^2=-1 and you will get -10
in the last step just substract 2-10 you will get -8 and 9i
and your answer will be -8+9i
(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
Step-by-step explanation:
ah, here you go.
come on, now. you know this now ...
again, mutually exclusive attributes in the table (no overlap here) allow us to add the numbers for a total :
4+2+12+10 = 28 students in total.
how many of those 28 fulfill our desired criteria (has a brother) ?
well, it is the sum of the column "has a brother", as it does not matter, if there is also a sister or not.
so, it is 4 + 12 = 16
therefore, the probability to pick a student randomly, who has a brother is
16/28 = 4/7 = 0.571428571...