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Find dy/dx in terms of t for the curve given by the parametric equations x = tan(t) , y = sec(t) for -pi/2<t<pi/2.

We know that dy/dx = (dy/dt) * (dt/dx). Differentiating each of the equations with respect to t gives. dy/dt = sec(t) tan(t) and dx/dt = sec 2 (t). Since dt/dx = 1 / (dx/dt) we have that dt/dx = 1/(sec 2 (t)...
OC
Answered by Oliver C. • Maths tutor
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7x+5y-3z =16, 3x-5y+2z=-8, 5x+3y-7z=0. Solve for x,y and z.

There are three methods to solve these types of silmultaneous equation questions, substitutution, elimination and matrices. In this example we use substitution and elimination.Elimination example.Eq1). 7x+5y...
HM
Answered by Holly May B. • Maths tutor
9653 Views

Show x^2 + 8x +15 = 0 in the form of (x+b)^2 +c (complete the square) and then solve the equation

x 2 +8x +15 = 0 (x+4) 2 -16 +15=0 (x+4) 2 -1=0 (x+4)= (+/-)1 x = -3 or -5
OA
Answered by Omar A. • Maths tutor
4208 Views

How do I work out the area of a quarter circle with radius 6cm?

The easiest way to do this is to first work out the area of the whole circle. To work out the area of a circle, the equation is area = πr 2 , where r is the radius. So, to work out the area we work out π x 6...
CC
Answered by Carla C. • Maths tutor
14034 Views

The line PQ is the diameter of a circle, where points P and Q have the coordinates (4,7) and (-8,3) respectively. Find the equation of the circle.

Start by using the formula d = sqrt((x 2 -x 1 ) 2 +(y 2 -y 1 ) 2 )Therefore, substituting in our coordinates from P and Q:Length PQ = sqrt((-8-4) 2 +(3-7) 2 )= sqrt((-12) 2 +(-4) 2 )= sqrt(160)= sqrt(16) x s...
MC
Answered by Matt C. • Maths tutor
11167 Views