Math Answers

Find the sum of the first 8 terms of the geometric sequences;

5/8, 1 1/4, 2 1/2, 5,........

Insert four geometric means between 10 and 100 such that the sequence form a GP

a) Calculate the sum of all the even numbers from 2 to 100 inclusive
2+ 4+ 6+............+100

b) In the arithmetic series
k+ 2k+ 3k+................+100
k is a positive integer and k is a factor of 100

I) Find in terms of k, an expression for the number of terms in the series

Three bags of wheat, two bags of corn, and one bag of oats weigh the same as one bag of wheat, one bag of corn and five bags of oats. If two bags of corn and one bag of oats weighs 26 pounds and one bag of corn weighs 10 pounds, how much does one bag of wheat weigh?

Q : 5). If f is function from A to B and g is function B to C and both f and g are onto.
Show that go f is also onto. Is go f one-to-one if both f and g are one-to-one.


Q : 6) Let f, g and h: R → R be defined by (R is the set of real numbers)
f(x) = x + 2, g(x) = (1 + x2)
-1, h(x) = 3.
Compute f -1g(x) and hf (g f -1) (hf(x)).

Q : 1) Determine whether each function is one-to-one. The domain of each
function is the set of all real numbers. If the function is not one-to-one,
prove it. Also, determine whether f is onto the set of all real numbers. If f is
not onto, prove it.
a) f(x) = 6x – 9
b) f(x) = 2x3 - 4

Q : 2) Let A = {1, 2, 3}, B = {p, q} and C = {a, b}. Let f: A → B is f = {(1, p), (2, p), (3,
a)} and g: B → C is given by {(p, b), (q, b)}. Find go f and show it pictorially.

Q:1. Determine whether each set is a function from X = {1,2,3,4} to Y = {a,b,c,d}.
If it is a function, find its domain and range, draw its arrow diagram, and
determine if it is one-to-one, onto or both.
a) {(1,a,),(2,a),(3,c),(4,b)}
b) {(1,c),(2,a),(3,b),(4,c),(2,d)}
c) {(1,d),(2,d),(4,a)}

Q:2. List all possible functions from A to B, A = {a, b, c}, B = {0, 1}. Also indicate in
each case whether the function is one-to-one, is onto and one-to-one-onto.

for the circle of radius 9 feet, find the arc length s cut off by a central angle of 6 degrees.

The first three terms of an arithmetic progression are; 2x, x+4, 2x-7......find the value of x and determine T12

Let U={-8,-7,....1,0,1,.....12}
A={x=-2<x<3}
B={x:-8<x<5}
C={x:0<x<12}
Find:
1.AUB
2.ANB
3.A
4.BNA