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Work out the angle between the two tangents of the curve y = sin(x) at y = 0 and y = 1

First we take the derivative of the function, this gives us dy/dx = cos(x) Now we work out the different x values for y = 0 and y = 1. sin(x) = 0 => x = 0, sin(x) = 1 => x = pi/2 (90 degrees) We then s...
KJ
Answered by Kieran J. • Maths tutor
1618 Views

The perimeter of an isosceles triangle is 16cm. The length of the base of the triangle is x+4 and that of the other two sides is x+3. Find the area of the triangle

16=2(x+3)+(x+4)16=2x+6+x+46=3xx=2 - Therefore the base has length 6 a=6y/2 - where y is the perpendicular heighty^2=5^2-3^2y^2=25-9y^2=16y=4 Therefore a=(6*4)/2 a=12 cm^2
PF
Answered by Philip F. • Maths tutor
4507 Views

Find the coordinates and the point of intersection between the lines 8x + 7y = 11 and y = 5x + 2

Substitute y = 5x + 2 into 8x + 7y = 11 to get, 8x + 7(5x + 2) = 11This simplifies down to 8x + 35x + 14 = 11And further simplifies to 43x = -3 giving the solution x = -3/43Substituting the x solution back i...
AR
Answered by Adam R. • Maths tutor
3188 Views

Integrate lnx with respect to x

= xlnx - the integral 1/x X x with respect to x= xlnx - the integral of 1 with respect to x= xlnx - x + c
SB
Answered by Sam B. • Maths tutor
1529 Views

a)By completing the square, prove the quadratic formula starting from ax^2+bx+c=0, b) hence, or otherwise solve 3x^2 + 7x -2= 9, to 3s.f.

a)starting from ax 2 +bx+c=0, divide through by a, x 2 +(b/a)x+c/a=0, complete the square (x+(b/2a)) 2 -(b/2a) 2 +c/a=0, expand (x+(b/2a)) 2 -(b 2 /4a 2 )+c/a=0, Combine fractions and rearrange,(x+(b/2a)) 2 ...
YH
Answered by Yusuf H. • Maths tutor
3974 Views