Math Answers

Find the equation of the line tangent to the curve y = 3x^2 - 4x and parallel to the line
x - 2y + 6 = 0

Find the tangent line to the curve y = x^4 + 4x^3 - 8x^2 + 3x + 70 with slope 3.

Find the tangent line to the curve y = x^4 + 2x^3 - 2x^2 - 3x + 3 perpendicular to the line x - 3y = 2

a) Let Qi = {qi|x² + q²x +4 = 0, q is an element of N, x is aan element of R}.
Find ⋃∞ i=1 Qi and ⋂∞ i=1 Qi.

Let a relation R = (x, -x)|x^2 = x (mod2x), whereby x element of positive integer. Determine whether R is reflexive, symmetric, anti-symmetric or transitive.

You are getting engaged and your fiancee has hidden the engagement ring. If only one statement is true, determine which statement is true? Where is the ring
Statement 1: The ring is in this box -> A
Statement 2: The ring is not in this box -> B
Statement 3: The ring is not in box A -> C

According to Hooke’s law, the force F (in pounds) required to stretch a certain spring x inches
beyond its natural length is given by
F  (4.5)x
. If
10  F 18
, what are the corresponding
values for x?

At the end of a statistics course, Diana sits for two written papers, P1 and P2 and hands in
a piece of course work. Her marks out 100 were 76 for P1 and 67 for P2 and she gained
81 marks for her course work. Her overall percentage is to be weighted so that the two
written papers account for 40% while the course work accounts for 20%.Calculate
Diana’s overall percentage mark.

The variation of incomes of executives is to be compared with the variation of incomes of
unskilled employees. For a sample of executives, mean = Ksh 500,000 and
Standard deviation = Ksh 50,000. For a sample of unskilled employees, the
mean = Ksh 12,000 and standard deviation = Ksh 2000.
Is the variation among the executives greater than the variation among the unskilled
employees? Justify you answer.

A group of students has measured the heights of 90 trees. The class calculate the mean
height to be x = 12.4 m with standard deviation s = 5.35 m. One student notices that
two of the measurements, 44.5 m and 43.2 m, are much too big and must be wrong.
(a) How many standard deviations away from the mean of 12.4 is the value
44.5?(3m
arks)
191
The incorrect measurements of 44.5 m and 43.2 m must be removed from the data.
(b) Calculate the new value of x after removing the two unwanted values.