Other Math Answers

If a certain number x is multiplied by 6, it will be equal to four less than twice the same number. The

correct equation for the above sentence is:

there are 10 basketball games. On average, each game will sell 3 1/2 cases of water. a case of water has 30 bottles and costs $3.49. Each bottle has a 5 cent deposit charge. During each game, each worker is allowed a bottle of water and each game has 2 workers. Fans at the game will pay $1.00 per bottle. a) if you buy 10 cases of water, how much will you pay?

A poster must have 32 sq. in. of printed matter with margins of 4" each at the top and 2" at each side. Find the dimensions of the whole poster if its area is maximum.

Show that x + y is a factor of x ^5 + y^5 and x ^7 + y^7 . By using synthetic division, find the quotient in each case. 

Solve the following

𝑎) Maximize 𝑓(𝑥, 𝑦) = 2𝑥 + 5𝑦; subject to the constraints.

2𝑦 − 𝑥 ≤ 8; 𝑥 − 𝑦 ≤ 4; 𝑥 ≥ 0; 𝑦 ≥ 0.

𝑏) Minimize 𝑧 = 3𝑥 + 𝑦; subject to the constraints.

3𝑥 + 5𝑦 ≥ 15; 𝑥 + 6𝑦 ≥ 9; 𝑥 ≥ 0; 𝑦 ≥ 0.

determine the point of discontinuity of the function f and the nature of discontinuity at each points

f(x)= { -x^2, when x<=0

{ 4-5x, when 0<x<=1

{ 3x-4x^2 when 1<x<=2

{-12x+2x when x>2

and check whether function f is derivable at x=1

a) ∫𝝅 𝒙𝒔𝒊𝒏𝟐𝒙 𝒅𝒙

𝟎

b)∫𝒙𝟐 𝒅𝒙 (𝒙+𝟏)

c)∫ 𝒙+𝟏 𝒅𝒙 𝒙𝟐 −𝟑𝒙+𝟐

3/4 x 15/16 x 4/7

rOA and rOB are the position vectors of the two particles Aand B at time t.If both particles start moving when t=0,determine whethert the particles collide and,if they do,give the value of t when this occurs and the position vector of the point of collision.If they do not ,find the time and their distance apart when they are closest together .

(a) rOA =3i-7j+(3i+2j)t, rOB=8i-6j+(2i+j)t.

(b) rOA=-5i+2j+9k+(5i-j+2k)t, rOB=i+2j+3k+(3i-j+4k)t.

A man falling vertivally by parachute in a steady downpour of rain observes that when his speed is V1 the rain appears to make angle α with the upward vertical.When his speed is V2(V2>V1) the rain appears to make angle ß with the upward vertical.

Show that the rain actually falls at an angle Θ with the vertical given by

(V2-V1)cotΘ=V2cotα-V1cotß.