Top answers

Solve the following equation: 4(sinx)^2+8cosx-7=0 in the interval 0=<x=<360 degrees.

We first use the identity sin 2 x+cos 2 x=1 to substitute for sin^2 in terms of cos. sin^2(x)=1-cos^2(x) -------------&gt; -4cos^2(x)+8cosx-3=0 We use the standard quadratic formula to solve for cos(x): cos(...
NW
Answered by Natalia W. • Maths tutor
14552 Views

ABCDEF is a regular hexagon (I will sketch this in the session). Find the angle DAF

What do we know about hexagons? They have six angles and vertices. The fact that the hexagon is regular implies that all interior angles are the same. We can split the hexagon up into six triangles. These tr...
JM
Answered by Jordan M. • Maths tutor
16053 Views

How do you show that (x+2) is a factor of f(x) = x^3 - 19x - 30, and then factorise f(x) completely?

A1) Showing that (x+2) is a factor of f(x). General Method: If A is a number, then (x- A) is a factor of f(x) if when x=A, f(x=A)=0 &lt;-- This is what we want to show This is because if (x-A) is a factor of...
RW
Answered by Rebecca W. • Maths tutor
9851 Views

f(x) = 2x^3 – 7x^2 + 4x + 4 (a) Use the factor theorem to show that (x – 2) is a factor of f(x). (2) (b) Factorise f(x) completely.

We are presented with a third order polynomial with 4 terms, so we expect 3 solutions for f(x)=0. To prove that (x-2) is a factor we must insert the value of x=2 into the function and if f(2)=0 then we have ...
NA
Answered by Nazar A. • Maths tutor
16383 Views

Consider a cone of vertical height H (in metres) and base radius R (in metres) which is full with water. The cone, at time t=0, starts to leak such that it loses water at a rate of k m^3 per second. Give an expression for the rate of change of H.

L = (H 2 +R 2 ) 1/2 V = (1/3)πR 2 (H 2 +R 2 ) 1/2 dV/dt = -k dH/dt = dH/dV × dv/dt dV/dH = (1/3)πR 2 H(H 2 +R 2 ) 1/2 Thus, dH/dt = -3k/(πR 2 H(H 2 +R 2 ) 1/2 ) ​​​​​ ​​​​ ​​
CE
Answered by Callum E. • Maths tutor
3987 Views