Question 6

1 point

In chemistry the volume for a certain gas is given by V=25TV=25T, where VV is measured in cc and TT is temperature in °C°C. If the temperature varies between 90°C90°C and 110°C110°C , find the set of volume values.

Enter the exact answer in interval notation.

To enter ∞∞, type infinity. To enter ∪∪, type U.

Do not enter any commas in your answer.

The range of the volume is cc.

Question 7

1 point

Describe all the xx-values within or including a distance of 44 units from the number 88.

Enter your answer in interval notation.

To enter ∞∞, type infinity. To enter ∪∪, type U.

Question 8

1 point

Write the set in interval notation.

{x|−4<x≤8}x|−42x−3−3x−4x−1+2>2x−3−3x

Enter the exact answer in interval notation.

To enter ∞∞, type infinity. To enter ∪∪, type U.

Question 12

1 point

Solve the inequality involving absolute value.

|x−3|+4≥10x−3+4≥10

Enter the exact answer in interval notation.

To enter ∞∞, type infinity. To enter ∪∪, type U.

Question 13

1 point

Solve the compound inequality.

2x−8<−142x−8x−20−3x+4>x−20

Enter the exact answer in interval notation.

Question 20

1 point

Solve the compound inequality.

−5<2x+3≤30−5<2x+3≤30

Enter the exact answer in interval notation. Improper fractions are acceptable in the interval notation.

## (1) The Set A ={11k+8|k∈Z},B={4m|m∈Z}and C = {11(4n + 1) − 3|n ∈ Z} are given. P

(1) The Set A ={11k+8|k∈Z},B={4m|m∈Z}and C = {11(4n + 1) − 3|n ∈ Z} are given.

Prove that A ∩ B = C.

(2) Given f(x) = x3+2×2+x, find the domain, range, behaviour x2 −x−2

of f(x) and hence sketch the graph of the function.

(3) Determine the values of the real parameter m for which the set A = {X ∈ R|(m−1)x2 −(3m+4)x+12m+3 = 0} has:

(a) one element (b) two elements

(c) has no element.

## solve for α in the oblique triangle ABC; AB = 30; AC = 15, and angle B = 20° typ

solve for α in the oblique triangle ABC; AB = 30; AC = 15, and angle B = 20°

type out the two equations substituting the numbers from the diagram.

First, type out the Law of Sines set of relationships.

Next, type out the most appropriate version to use the Law of Cosines for this solution.

Write both equations and make a prediction of which method will be easier to use in finding a solution and why you think that is the case.