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A=2x^2i−3yzj+xz^2k
and
ϕ=2z−x^3y
, find
A×▽ϕ
at point (1,-1,1).
A company producing a household item has a fixed monthly cost of RM 900 and a variable cost of RM 9.70.
The price-demand equation for the production of LED television sets is given by, 𝑥=520−(16)𝑝
where 𝑥 is the number of sets that can be sold at a price RM 𝑝 per item.
(i) Express the price, 𝑝 as a function of the demand 𝑥. (1 mark)
(ii) Find the cost function, 𝐶(𝑥) and revenue function, 𝑅(𝑥). (2 marks)
(iii) Find the marginal revenue and marginal cost functions. (4 marks)
(iv) Find the profit function, 𝑃(𝑥). (2 marks)
(v) Find the output that gives maximum profit for the company. (1 mark)
(vi) Determine the maximum profit. (2 marks)
(vii) Find the output at break-even point. (5 marks)
(viii) Draw the graph for profit function, clearly showing the breakeven levels, and the maximum profit. (3 marks)
Two fair cubes are rolled. The random variable X represents the difference between the values of the two cubes.
a) Find the mean of this probability distribution. (i.e. Find E[X] )
b) Find the variance and standard deviation of this probability distribution.
(i.e. Find V[X] and SD[X])
The random variables A and B are defined as follows:
A = X-10 and B = [(1/2)X]-5
c) Show that E[A] and E[B].
d) Find V[A] and V[B].
e) Arnold and Brian play a game using two fair cubes. The cubes are rolled, and Arnold records his score using the random variable A and Brian uses the random variable B. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores.
(a) Three multiple-choice questions with four answers option each.ensure that your questions are at different cognitive levels of bloom taxonomy
11 to 15 players and 2 coaches are needed to make a soccer team. Make and extend a table to show the number of coaches and the least and greatest number of players needed for one to five teams.
The temperature of a particular country
n
is the number of the month, starting at n
=
n=0
for January. The temperature in the country is greater than 40 o
C
oC
for months Jun, July, August, and September. It is less than 40 o
C
oC
for months January, February, March, April, November and December, and 40 o
C
oC
for months May and October. If a
a
is a positive integer, then which of the following options might be correct
T
(
n
)
=
a
(
n
−
4
)
(
n
−
9
)
−
40
T(n)=a(n−4)(n−9)−40
T
(
n
)
=
a
(
4
−
n
)
(
n
−
9
)
−
40
T(n)=a(4−n)(n−9)−40
T
(
n
)
=
a
(
4
−
n
)
(
9
−
n
)
+
40
T(n)=a(4−n)(9−n)+40
T
(
n
)
=
a
(
4
−
n
)
(
n
−
9
)
+
40
T(n)=a(4−n)(n−9)+40
The temperature in December is 40
−
14
a
40−14a
.
The temperature in April is 40
−
3
a
40−3a
.
A civil engineer found that the durability d
d
of the road, she is laying depends on two functions y
1
y1
and y
2
y2
as follows: d
=
y
2
2
+
4
y
1
−
21
d=y22+4y1−21
. Functions y
1
y1
and y
2
y2
depend on the amount of plastic (x
x
) mixed in bitumen, and their variations are linear functions of x
x
. Let y
1
=
8
y1=8
and y
2
=
3
y2=3
for x
=
x=0
and y
1
=
y1=0
and y
2
=
7
y2=7
for x
=
7
x=7
. Find the durability of the road (upto 2 decimal points), if the amount of plastic is such that both the functions are equal.
I. Solve for the unknown Fibonacci numbers.
(Show a solution)
Fib 11=
Fib 15=
Fib 20=
Fib 25=
II. Solve for the fallowing terms of the Fibonacci Sequence. ( show your solution)
1. F28 =
2. F31=
3. F35=
4. F40=
5. F47=
Answer the fallowing. Provide mathematical solutuons.
1. What is the 50ᵗʰ term of the Fibonacci sequence?
2. Solve for the 67ᵗʰ term of the Fibonacci sequence.
3. The 80ᵗʰ term of Fibonacci sequence is?
4. What is the 99ᵗʰ term of Fibonacci sequence?
5. The 100ᵗʰ term of Fibonacci sequence is?
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