Math Answers

 Find all rational solutions of x⁴−6x³+22x²−30x+13=0

Simplify a trigonometric expression sin θ cos2 θ − sin θ

Find the exact value of each expression

sec 30◦ cos 30◦ − tan 60◦ cot 60◦

Solve the logarithmic equation 2^3x-2 =3^2x-1

a) The number of grams of a certain radioactive substance present after t hours is given by the equation Q = Q0e−0.45t, where Q0 represent the ini- tial number of grams. How long will it take 2500 grams to be reduced to 1250.

An investor is considering a $25,000 investment in a start-up company. She estimates that she has

probability 0.05 of a $15,000 loss, probability 0.15 of a $20,000 loss, probability 0.35 of a $35,000 profit,

and probability 0.45 of breaking even (a profit of $0). What is the expected value of the profit?

Suppose p=0.9 and n=4 ,C={0000,1010,1100}.Compute pC,v where

v=1100

Prove that

i) 𝑑 𝑎𝑥 , 𝑎𝑦 = 𝑎 d(x,y)

ii)𝑑 𝑎 + 𝑥 , 𝑎 + 𝑦 = 𝑑 𝑥 , 𝑦

where d is a metric induced by on a normed space X

Consider a project consisting of nine jobs (A, B, C,….,I) with the following precedence 

relations and time estimates.

Job Predecessor Time (Days)

A -- 15

B -- 10

C A,B 10D AB 10

E B 5

F DE 5

G CF 20 

H DE 10

I GH 15

Use big 𝑀 method solve. 𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑍 = 2𝑦1 + 4𝑦2 𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 2𝑦1 – 3𝑦2 ≥ 2,

−𝑦1 + 𝑦2 ≥ 3; 𝑦1

, 𝑦2 ≥ 0