Other Math Answers

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.

To cyclist travelling due north along a straight road at 10km/h,the wind appears to come from the east.When he increases his speed to 15km/h,the wind appears to come from the direction N67°E.Find the speed and the direction of the wind over the ground.

Daisy want to buy a new smart phone .the price of the phone excluding vat is 16 500 as suming that is 15% ,if she purchase the smart phone cash the store offers a 5% discount how much will she save if she buy's the phone?