Other Math Answers

Derive the Cardano-Tartaglia formula "x= \\sqrt[3]{\\frac{n}{2}+\\sqrt{(\\frac{n}{2})^2+(\\frac{m}{3})^3}} - \\sqrt[3]{\\frac{-n}{2}+\\sqrt{(\\frac{n}{2})^2+(\\frac{m}{3})^3}}" for solving cubic x³+mx=n

Given the input-output matrix below.

Industry Final

Demand

A B C

Industry A 100 400 240 260

B 100 80 480 140

C 300 160 240 500

Other 500 160 240

a) Find the output matrix if final demand changes to 300 for A, 200 for B, and 400 for C.

b) Find the total value of the other production costs that this involves.

a) Suppose consumers will demand 40 units of a product when the price is K12 per unit

and 25 units when the price is K18 each. Find the demand equation assuming that it is

linear. Find the price per unit when 30 units are demanded. [3]

b) Let

50

100

5

P = q +

be the supply equation for a manufacturer’s product and suppose

the demand equation is

65

100

7

P = − q + .

i. If a tax of K1.50 per unit is imposed on the manufacturer, how will the original

equilibrium price be affected if the demand remains the same? [5]

ii. Determine the total revenue obtained by the manufacturer at the equilibrium

point both before and after the tax [2]

35 track and field athletes from Luzon competed in the North-Phil Olympics. 18 competed in the 100-meter dash, 17 in the relay race, and 16 in the hurdles. Five competed in both hurdles and 100-meter dash events, six in both relay race and hurdles, seven in both 100-meter dash and relay race. Only two athletes competed in all three events. How many athletes competed in the following? In the Venn diagram, let D represent 100-meter dash, R represent relay race, and H represent hurdles.

Construct GF25 using hx=1+x2+x5

Find the number of proper cyclic code of length

n=4,& n=120

Find a parity check matrix for the linear code of length

N=7,with generator polynomial gx=1+x+x2+x4