Math Answers

Use big 𝑀 method to solve Minimize 𝑍 = 6𝑥1 + 3𝑥2 + 4𝑥3 𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜

𝑥1 ≥ 30; 𝑥2 ≥ 50; 𝑥3 ≥ 20; 𝑥1 + 𝑥2 + 𝑥3 = 120

A sales organizer goes to.one of the three markets A,B and C every day. He never goes to the same market on consecutive days. If he goes to A, then the next day he goes to B. If he goes to either B or C then the next day he is thrice likely to go to A as to other market. If he goes to C on Thursday. Find the probability of his going to A on the next Tuesday.

1. Solve the spherical triangle ABC right angled C given c= 56°13´ and b=48°30´.

 Solve the following spherical triangle using Law of Sine and Cosine.

2. A= 82°, b=100°, c=78° Find: B

Counting subsets of Finite sets: A student can choose a computer project from one of

three lists. The three lists contain 23, 15 and 19 possible projects, respectfully. No project is

on more than one list. How many possible projects are there to choose from?

Suppose that the universal set is U = {1, 2, 3, 4,5, 6, 7, 8, 9, 10}. Express each of these sets with bit

strings where the ith bit in the string is 1 if i is in the set and 0 otherwise.

Using the formula A = P(1 + r)n  where A is the future value of the investment, P is the principal, r is the fixed annual interest rate, and n is the number of years, how many years will it take an investment to double if the interest rate per annum is 20%?

Solution:

1. Find the value of the following logarithmic expression.

1. log5  5= ________

2. log7  1= ________

3. log5  5= ________

Determine the new value of an Hp computer that has discounted 25% of its

original price of Php 20,000 using the decay factor system. The discount

percentage fall under the decay factor: DECAY FACTOR =100%-25%=75%

Evaluate the line integral ∫𝒖(𝑥, 𝑦, 𝑧) × ⅆ𝒓 𝐶 , where 𝒖(𝑥, 𝑦, 𝑧) = (𝑦 2 , 𝑥, 𝑧) and the curve 𝑪 is described by 𝒛 = 𝑦 = 𝑒 𝑥 with 𝑥 ∈ [0,1].