In: Math

-Let O (0,0,0) be the origin and A(a+1,b,c) where a,b and c are the last three digits of your student ID. Find, describe and sketch the set of points P such that OP is perpendicular to AP

- Let u=<a , b+1 , c+1> find and describe all vectors v such that |u x v|=|u|

a=1 , b=1 , c=9

Let a, b, c the last three digits of your QUID. Find the
dimension of the rectangular box of maximum volume that can be
inscribed in the ellipsoid (x/a)^2+(y/b)^2+(z/c)^2=1 a=4, b=8,
c=9

Let A be the sum of the last four digits and let B be the last
digit of your 8-digit student ID. (Example: For 20245347, A = 19
and B = 7) On a road trip, a driver achieved an average speed of
(48.0+A) km/h for the first 86.0 km and an average speed of
(43.0-B) km/h for the remaining 54.0 km. What was her average speed
(in km/h) for the entire trip? Round your final answer to three
significant...

(A) Let a,b,c∈Z. Prove that if gcd(a,b)=1 and a∣bc, then
a∣c.
(B) Let p ≥ 2. Prove that if 2p−1 is prime, then p
must also be prime.
(Abstract Algebra)

)
Consider a game where player 1’s possible three strategies are
a, b and c and player 2’s possible
strategies are A, B and C. The players
choose their strategies simultaneously. The payoff matrix of the
game is as follows:
Player 2
A B C
a 8,5
9,7 10,8
player 1 b 6,1
10,3 7,9
c 5,4 8,6 6,4
(5 pts) Is there a dominated strategy for player 1? For player
2? Justify your answer.
(5 pts) Is...

Probability
Let A, B and C be Boolean variables denoting three independent
events with P(A=1) = 0.7, P(B=1) = 0.3, and P(C=1) = 0.1. Let D be
the event that at least one of A and B occurs, i.e., D = A OR B.
Let E be the event that at least one of B and C occurs, i.e., E = B
OR C. Let F be the event that exactly one of A and B occurs, i.e.,
F =...

There are A, B and C, three plastic balls, A and B, B and C, C
and A are attracted to each other, if A is positive: Group of
answer choices
1. Both B and C are negatively charged.
2. One of the B balls and the C balls is going to be negatively
charged and the other one is not charged
3. B ball, C ball has no charge
4. B ball is negatively charged, C ball is positively...

2. (a) Let (a, b, c) denote the result of throwing three dice of
colours, amber, blue and crimson, respectively., e.g., (1, 5, 3)
represents throwing amber dice =1, blue dice = 5, crimson dice = 3.
What is the probability of throwing these three dice such that the
(a, b, c) satisfy the equation b2 − 4ac ≥ 0? [7
marks]
(b) From a survey to assess the attitude of students in their
study, 80% of them are highly...

Let A and C be a pair of matrix where the product AC exists.
1. Show that rank(AC) ≤ rank(A)
2. Give an example such that rank(AC) < rank(A)
3. is rank(AC) ≤ rank(C) always true? if not give a
counterexample.

3.
Let A = D + 1, B = D − 3, C = D + x, where D = dx. Calculate the
differential operators AB, BC, CA and their effect on y(x) =
e^3x

(a) Let U(A,B) = (A)^1/3 (B)^2/3 , where A and B are two
distinct consumption goods. Compute the marginal utility for A,
MU_A and the marginal utility for B, MU_B. Provide an
interpretation for what these mean.
(b) Compute the marginal rate of substitution (MRS) for a
consumer given the preference given in part (a).
(c) Provide an interpretation for what the MRS means.
(d) Explain why at the point (A, B) that maximizes a consumer’s
utility function U(A, B)...

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