Integrals and Motion
Triangles
Mixed
Area
Bearings
100
Evaluate definitenintegral
∫sin(x) , 0->pi
= - cos (0) - - cos (pi)
= |-1 - 1|
2 u^2
100
Find the area of a triangle with:
Side a=3 cm, b=4 cm and angle C = 90 degrees.
= 0.5 x 3 x 4 x sin (90)
= 6 cm^2
100
A pdf is
f(x) = x/2, 0<x<2
find E(X)
E(X)=∫x(x/2)dx, 0 ->2
=1/2 ∫ x^2 dx, 0 ->2
=1/2 [(x^3)/3], 0->2
=1/2 * 8/3
=4/3
100
Find the intersection for the functions:
f(x) = x, g(x) = 4-x
2
100
At the point of origin, what is the smallest angle between two ships, when ship A travels at a bearing of S30∘E and ship B travels at a bearing of N50∘W.
80∘
200
Evaluate definite integral
∫cos(x)dx, 0 -> pi/2
= sin (0) - 1
absolute
= 1 u^2
200
Which rule is the most suited to find an angle of a triangle when three sides are known?
Cosine Rule
200
If E(X)=5 and
E(X^2)=29
find: Var(X)
Answer
29-5^2 = 4
200
Using the trapezoidal rule calculate the approximate area for a function with the follow values:
x = 0, f(0) = 2
x = 1, f(1) = 3
x = 2, f(2) = 5
x = 3, f(3) = 8
x = 4, f(4) = 6
w = 1
approx area = 1/2 (2 + 2(3+5+8) + 6)
= 20
200
Draw a diagram of a car that travels:
5 km, S35^oW
then 15km on a bearing of
N30^0W
300
Find v(t) when a particle has:
a(t) = 4, v(0) = 3
v(t) = 4t + 3
300
Find the area of triangle with:
sides b = 8, c = 2, Angle A = 30 degrees
= 1/2 * 8 * 2 * 1/2
= 4
300
P(A)=0.5 , P(B|A)=0.8
P(A∩B)
0.4
300
An enclosed area must always be?
Absolute or positive
300
What is the angle formed between two lines that travel in the directions of:
A = 060^0T , and B;=170^0T
110^0
400
Find s(t) when a particle has:
v(t) = 5t, s(0) = 0
s(t) = 5/2 t^2
400
How many possible triangles exist and give reasoning why, for:
a = 8, b = 10 and angle A = 30 degrees
2 as the opposite is smaller than the adjacent.
400
A continuous random variable has pdf
f(x)=kx, 0<x<2
and total area under curve is 1. Find k.
integration (kx) dx = 1 between 2 and 0
2k - 0k = 1
k = 1/2
400
Calculate the area between two functions between 0 and 5.
f(x)=-x+6, g(x)=x-4
bound y-axis, x-axis, intercept x = 3
(-1/2(5)^2+6(5)) - (1/2(5)^2-4(5))
(-12.5+30)-(12.5-20)
25 u^2
400
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