Other Math Answers

Use secant’s method to find solutions accurate to within 10−4 for the following problems. a. x3 − 2x2 − 5 = 0, [1, 4] b. x3 + 3x2 − 1 = 0, [−3, −2] c. x − cos x = 0, [0, π/2] d. x − 0.8 − 0.2 sin x = 0, [0, π/2]

. Use Newton’s method to find solutions accurate to within 10−4 for the following problems. a. x3 − 2x2 − 5 = 0, [1, 4] b. x3 + 3x2 − 1 = 0, [−3, −2] c. x − cos x = 0, [0, π/2] d. x − 0.8 − 0.2 sin x = 0, [0, π/2]

Question 2

A swimming pool 30m long is 1m deepat it's shallow end and 4m deep at the deep end.the pool is 14 m wide.

a) find the volume of water in cubic metres,when the pool is full.

b) A circular pipe of diameter 14cm is used to empty the swimming pool. Water flows through the pipe at the rate of 5 metres per second. Calculate the time it would take to the nearest minute,to empty the pool

Name the included angle of the sides TW and WG. Based on the figure below.

Let the vertices A, B and C of a triangle ABC have position vectors a=-2i + 4j + k, b=4i + j + k and c=-7i + 6k respectively. Find the length of the projection of the side AB onto the side BC.

The integrated curriculum mode, sometimes referred to as integrative teaching, is

both a method of teaching and a way of organising the teaching programme so that

many subject areas and skills provided in the curriculum can be linked to one

another. Provide an example of how you, as the teacher, could use the content in

Natural Sciences as a vehicle for mathematical skills development.

A box of miniature cars contains 5 red cars, 7 blue cars, and 6 black cars. Two cars are drawn, but the first car drawn is not replaced. What is the probability of getting a red car on the first draw and a black car on the second draw?

These are the scores on a test of sensitivity to smell taken by 25 chefs attending a national conference with a mean of 75.20 and a standard deviation of 10.90:

96, 83, 59, 64, 73, 74, 80, 68, 87, 67, 64, 92, 76,

68, 50, 85, 75, 81, 70, 76, 91, 69, 83, 75, 71,

(a) get the relative frequency of the highest raw score and the lowest raw score;

(b) get the T-score of both the highest and lowest raw scores.

A factory uses ingredients A, B, C, D, E, and F to produce products I, II, III, IV, and V.

The following table shows the amounts of each ingredient in stock (in kg) as well as the

amount (in kg) necessary to produce 1 tonne (=1000 kg) of each type of product.

How many tonnes of each type of product should they make to use up all the ingredients

completely?

Hint: Suppose they need to make x1 tonnes of product I, x2 tonnes of product II, etc.

Then set up one equation for each of the ingredients A, B, C etc.

Solve this system of equations to find your answers.

Type of product−→ I II III IV V Amount in stock ↓

Ingredient ↓

A 10 0 8 20 10 507.4

B 10 14 12 16 8 749.2

C 7 5 17 0 7 505.1

D 9 38 7 3 0 848.6

E 15 14 0 8 6 491.7

F 21 0 10 20 10 659.5

A body weighing 4N is supported by a string attached to a fixed point and is pulled from the vertical by a horizontal force of 3N. Find the angle the string will make with the vertical and the tension of the string