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The block of material shown below has a shear modulus of 50 GPa. Determine the shear

stress and the shear strain induced by the 2 kN shearing force.


Using Data Below, Compute for the following. Show the Correct and Complete solution

a. Mean

b. Median

c. Mode

d. Standard Deviation

21, 27, 28, 20, 18, 18, 19, 17, 22, 24, 23, 27, 26, 25, 26, 25, 22, 21, 22, 26, 28, 26, 20, 19, 17,18, 26, 27, 27, 22, 23, 25, 25, 27, 28, 20, 19, 17, 16,16, 20,16, 21, 26, 27, 26, 28,16, 25, 28


Three vectors a = (3i 4j), b = (-4i + 3j), c = (-3i + 4j) lie on a horizontal plane, pie(ll).
(i) Determine which of the vectors b or a is perpendicular to a.
Two smooth spheres, S and T, each of mass m lie on the plane ll. Sphere S is projected along the plane towards sphere T with velocity 5x(i + 2j) so that it collides obliquely with T. At the instant of collision, the line of impact is parallel to the vector a. Given that the coefficient of restitution between the two spheres is 1/2,
Show that
(ii) the component of the initial velocity of S parallel to a is 11x.
(iii) the component of the final velocity os S parallel to a is (11/4)x.
(iv) the magnitude of the impulse exerted by sphere T on sphere S is (33/4)mx.

what is not a way to show the theoretical proby


A teacher places 10 differently coloured beanbags on the classroom floor. Each 

beanbag is spaced a step apart. The teacher gives Mpho (5 years old) the following 

instructions and observes her: Take 4 steps forward on the mats. Now take 3 more 

steps from where you are. What number mat did you land on? Now, Mpho, take 2 

steps backwards. What is the number of the mat on which you landed?

1) Counting

2) Sorting

3) Ordering

4) Matching


Journalism is a discipline of verification in which commitment to objectivity is crucial -- explain.


a) given the parabola (y+2)²=-8(x + 1), sketch the graph and determine the vertex , focus and directrix line of the parabola .


b)sketch the graph of f(x)=-(|x - 1| - 3) by using transformation technique . begin with f(x).


c)graph the system inequality below and shade the feasible region .

: 3y < 15 - 2x

: y(less and equal than) x + 2

: y < 2

: y is (greater and equal than) 0



Name the different forces present in a fluid flow. For the Euler's equation of motion, which forces are taken into consideration


  1. Juanita needed 3 and 2/3 hours to take a standardized test, and Jordan needed 5 and 1/4 hours. How much more time did Jordan need than Juanita to take the test?
  2. One evening, a restaurant served a total of 1/2 of a loaf of wheat bread and 7/8 of a loaf of white bread. How many loaves were served in all?
  1. Cathy's classroom has an area of 15 and 5/6 square feet. If the length is 8 and 3/4 feet, then what is the width of her classroom?
  2. An airline agent checked in 10 and 1/3 kg of baggage for one passenger and another 8 and 5/6 kg of baggage for his travel companion. How many kilograms of luggage did the agent check-in all?