Math Answers

1. Evaluate "\\intop"x²(1 + 2x³)³dx.

2. Evaluate "\\intop"xe^7x dx.

3. Find the volume of the solid of revolution when the curve y = 1 + x2 is revolved around the x-axis on [−2, 2].

Find the area of the paraboloid x2 + y2 = z inside the cylinder x2 + y2 = 9.

1. A line with an angle of inclination of 45° passes through (-5/2 , -9/2). If the ordinate of the point is 6, what is its abscissa?
2. Find the angle from the line through (13/2, 0) and (2, -7) to the vertical line 5 units from the y-axis.
3. The angle from line 1 to line 2 is arctan (2/3) and the slope of line 1 is -1. Find the slope of line 2.
4. The inclination of line 1 is arctan (1/2). If line 2 makes an angle of 45° with line 1, find the slope of line 2.
5. The vertices of a triangle are (7, 4), (1, 7) and (-3, -4) Find the interior angle at the vertex (-3, -4).

Calculate the area under the curve y=x3 +4x+1 from x=-3 to x=3.

Factory produces whiteboard markers. The production process can be modelling by normal distribution with a mean length of 11 cm and a standard deviation of 0.25 cm.

a) What is the probability that a randomly selected whiteboard marker has a length longer than 10.5 cm? (2 marks)

100 whiteboard markers are randomly selected for quality checking.

(b) What are the mean and standard deviation of the sample mean length? (2 marks)

(c) What is the probability that the sample mean length will be between 10.99 cm and 11.01 cm? (2 marks)

(d) If 99.8% of the sample means are more than a specific length Y, find Y. (3 marks)

the weight of a dart to be used in a tournament is normally distributed with a mean of17 grams and a standard deviation of 0.3 grams .find the probability that a dart chosen at random is;

its weight is between 16.55to 17.45 grams

over 18 grams

(D^3 + 3D^2-D-3)y = e^2x+4

Give an example of a subring of a ring, say A, that is not an ideal of A

An insurance company insured 2000 scooter drivers, 4000 car drivers & 6000 truck drivers. The probabilities of their accident are 0.1, 0.3, and 0.2 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?

An insurance company insured 2000 scooter drivers, 4000 car drivers & 6000 truck drivers. The probabilities of their accident are 0.1, 0.3, and 0.2 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?