Mathematics

X=2t-1/t , y=t+4/t (t is not 0) deduce that dy/dx<1/2

dy/dx = (dy/dt) / (dx/dt) .........= (1 - 4/t^2) / (2 + 1/t^2) .........= (t^2 - 4) / (2t^2 + 1) .........= (t^2 + 1/2 - 9/2) / (2t^2 + 1) .........= [(1/2)(2t^2 + 1) - 9/2] / (2t^2 + 1) .........= 1/

If u have a strait stick and u break it in 2 random places what is the probability u could form a triangle

Needs to be a triangle with equal side lengths. Cant think of the proper term...-An equilateral triangle? Almost impossible, depending on how precise the breaks are or how much fudge-room there is in

Find the equation of the line passing through (6,6) and perpendicular to the 5x-3y-8=0

First, find the slope of the line defined by 5x-3y-8=0 5x - 3y - 8 = 0add 8 to both sides 5x - 3y = 8subtract 5x from both sides -3y = -5x + 8divide both sides by -3 y = (5/3)x - 8/3given that y = mx

Calculus help? Limits and discontinuities

Define a function by stating its rule such that f is discontinuous at x = -1, but f(-1) exists and the limit as x approaches -1 exists. How would you solve this and problems like this? Also, how w

What is the maximum and minimum values of a Quadratic expression

An expression of the type ax2+bx+c is called quadratic expression. The quadratic expression ax2+bx+c takes different values as x takes different values. As x varies from -`prop` to + `prop`ax2+bx+c

Show that tanx>x for 0<x<pi/2

By the Mean Value Theorem, if f is continuous on [a, b] and differentiable on (a, b), (f(b) - f(a))/(b - a) = f(c) for some c with a Let f(t) = tan t, a = 0, and b = x.Then the derivative of f(t),

I need help with a math question involving exact values

These are the questions: (a) tan(csc^-1(2)) (b) sin(2cos^-1(3/5)) Can someone explain how to find the exact value of each of these expressions?-csc⁻¹ always returns a value between -π/2 and π/2 Let

Solve 4x^4 = 256x, using quadratic formula

4x^4 = 256x Okay, Im not completely inept, Ive gotten part of it done: (4x)x^3-64 = 0--> 4x=(x=0) (x-4)(x^2+4x+16)=0 --> x-4=(x=4) -4+/-√16-64 / 2 So, two of the solutions are 4,0 and i know the nex

Chain rule trig functions proof

Use the Chain Rule to show that if x is measured in degrees, then d/dx (sinx) = pi/180*cosx. How would I do this? :P-If x were in radians, it is correct to say that d/dx (sinx)= cosx. Assuming that

Plz solve it plz plz mathematics

divide 56 into parts such that 3 times the ist number exceeds 1/3 times the 2nd number by 48 find the numbers...-let one part be x and the other part be 56-x 3x =1/3(56-x) + 48 9x= 56-x+144 10x=200x

What is the domain of f(t)=ln(sin(t))

The domain of ln(x) is (0, infinity). so we need to solve sin(t) > 0 sin is positive in the first and second quadrants, so the domain is ...(-4π, -3π) U (-2π, -π) U (0, π) U (2π, 3π) U (4π, 5π) ...

What's the domain of g(t)=sqrt(e^t - 1)

Can someone explain how to find the domain of this?-The domain of the square root function is non-negative real numbers. That gives us this restriction: e^t - 1 ≥ 0 e^t ≥ 1 t ≥ 0 The argument of the

Need help with quadratic equations: graphing

Hey so Im having problems with a question regarding quadratic equations. So first off we were given a sum e.g. y=(x - 3)^2 - 4 then we would put it into our calculators graphing function then graph it

Triple time unanswered algebra polynomial problem help

Please Perform the indicated division. 4x^3-8x^2+11x-4/x^2-3x The problem asks me to divide the two polynomials NOT by factoring, please help me, I wasnt able to do it. I asked this question 3 times

How Big Exactly Would 18m2 Be

Im not very good at Maths, and I have to design a sleep-out that has to fit in about 18 SQ. Only problem I dunno how much it is.. haha please help if you know. =)-If you imagine 3metres, then 6 metres