Recent content by disfused_3289

refractive index ny= vx/ vy nx= vy/vx ny/nx= 1 ?

Homework Statement For substance X, the refractive index is nx. For another substance Y the refractive index ny. Show that the refractive index for light passing from x to y is nx/ ny. 2. The attempt at a solution I'm finding it difficult to devise a solution, but I think the answer...

Homework Statement Given (d^2)x/ (dt^2) = 2 for all t>= 0 and dx/dt= -5 and x= 4 when t= 0 find t when a) dx/ dy= 0 b) x= 0 2. The attempt at a solution a) Given (d^2)x/ (dt^2) = 2, then dx/dt= 2x + c = -5 given dx/ dt= 0 then 2x + c= 0 c= -2.5 using 2x + c= 0 and 2x + c =...

Homework Statement The normal to the curve y= (x + 2)^2 at the point A(-3, 1) meets the curve at B. Find the angle at B between the curve and chord AB. 2. The attempt at a solution I found that B is (-0.5, 2.25) and the equation of the normal is 2y= x + 5. I thought the angle at B...

The cost of running a ship at a constant spped of vkm/h is 160 + (v^3)/ 100 dollars per hour. a) Find the most economical speed for the journey, and the minimum cost. b) If the ship were to have maximum speed of 16km/h, find what the minimum cost would be.

Find the area of the largest rectangle that can be inscribed in the region bounded by the parabola with equation y= 4 - x^2

1. The slant edge of a right circular cone is 6 cm in length. Find the height of the cone when the volume is a maximum. 2. Find the maximum volume of a right circular cone whose slant edge has a constant length measure a.

Solved Ah, I now understand it. I never thought of delta before Thanks a lot

Prove that the graph of y= ax^3 + bx^2 + cx + d has two distinct turning points if b^2> 3ac. Find values of a,b,c and d for which the graph of this form has turning points at (0.5, 1) and (1.5, -1)

Here are my solutions, I don;t know if they're correct a) y= 2/ (2x+3)^4 = -4(2x +5)^(-5) x 2 x 2 = -16/ (2x + 5) ^ (-5) b) y= x(x+1)^(1/2) = ( x + 2) (x + 1)^ (1/2) / 2 d) y = 3x^3 + 3x^(-1/2) + 2 = 3x^2 - 3/2x^(1/3)

Yes, I have learned chain rule to differentiate from x you find dy/dx

I'm having trouble with the following questions about differention with respect to x. Differentiate with respect to x: a) y= 2/ (2x+3)^4 b) y= x(x+1)^(1/2) c) y= (x +1)(x^2 + 3x)^3 d) y= 3x^3 + 3x^(-1/2) + 2 Any help would be greatful