Math Answers

16 a Find the y-intercept of the tangent to f (x) = x In x at the point where: i x = 1 it x = 2 iii x = 3. b Make a conjecture about the y-intercept of the tangent to f (x) = x In x at the point where = a, a > 0. c Prove your conjecture algebraically. 17 Find the axes intercepts of the tangent to y = x2 ex at x = 1. 18 Find the exact area of the shaded triangle. 

the probabilities that a student gets 0, 1,2,3,4, or 5 mistakes are respectively. What is the average number of mistakes that a student makes in this class? What is expected value, variance and standard deviation of this discrete probability distribution?

4. [6] The table below gives ²¹⁰Pb activities in a marine sediment core.

Depth, L(cm)

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

²¹⁰Pb activity, A_L(Bq kg^-1)

247.0

199.0

160.0

123.0

101.0

78.0

62.0

46.0

38.0

Assume the following equation applies

Where A_L is the activity at depth L (Bq kg^-1), A₀ is the activity at zero depth (L = 0 cm), l is the decay constant (0.031 yr^-1 for ²¹⁰Pb), L is the sediment depth (cm) and S is the sediment accumulation rate (cm yr^-1).

(a) Transform the above equation into straight line form.

(b) By plotting the data estimate the value of A₀ and S.

Determine the cost of Labour amounts to R1245 with an equipment rent in free of R250 to produce five devices

suppose a population consists of the numbers 2,3,5,8 and 12 what is the mean of the population?

A dog gave birth of six puppies. Three of them are male while the rest are female. If you are to be

given three puppies at random, list all the elements of the sample space using the letters M and F for

male puppies and female puppies, respectively. Then assign a value x of the random variable X

representing the number of male puppies you receive.

If A={1,2,3}, identify the power set of the given set A.

P(A)=

P(A)={ }

and

P(A)=

Show that Sigma infinity n=1 ( -1)^n+1 5÷7n+2 is conditionally convergent

Show that y= c₁e^x + c₂e^2x is the general solution of y’’-3y’+2y=0 on any interval, and find the particular solution for which y(0)=-1 and y’(0)=1

The volume of a cube is increasing at a rate of 1200 cm3/min at the

moment the lengths of the sides are 20 cm. How fast are the lengths of

the sides increasing at that moment?