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log_10⁡((1/(2√2))*(p+2q))=(1/2)(log_10⁡p+log_10⁡q),p,q>0,find p in terms of q.

log 10 [(1/2√2) (p+2q)]=(1/2)(log 10 p+log 10 q)log 10 [(1/2√2) (p+2q)]=(1/2)(log 10 pq)log 10 [(1/2√2) (p+2q)]=log 10 (pq) 1/2 (1/2√2) (p+2q)=(pq) 1/2 (p+2q) 2 =8pqp 2 +4pq+4q 2 =8pqp 2 -4pq+4q 2 =0(p-2q)=0...
HX
Answered by Henry X. • Maths tutor
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Find the integral of 4/(1-x^2) dx:

The first thing to notice here is that the denominator of the integrand is a case of 'difference of two squares'. The integral, which I will call I, can be rewritten as the integral of 4/((1+x)(1-x)) dx. If ...
JP
Answered by Jemima P. • Maths tutor
6154 Views

Use integration by parts to find the integral of x sin(3x)

Firstly we remind ourselves of the integration by parts formula. The formula used to integrate u dv/dx with respect to x = uv - the integral of v du/dx with respect to x. So the first thing we have to decide...
MS
Answered by Marnie S. • Maths tutor
17344 Views

F(X)= 4/(x-3) g(x)= (x+2)/x solve fg(a)= 1

4/(x-3)*(x+2)/x= 4x+8/ x 2 -3x sub in a for x4a+8/a 2 -3athen equate to 1: 4a+8/a 2 -3a=1Times the bottom half of the equation up4a+8=a 2 -3aThe move the 4a+8 across to get a 2 -7a-8=0Factorise (a+1) (a-8)
EJ
Answered by Esther J. • Maths tutor
8916 Views

Complete the square and hence sketch the graph of f(x) = x^2 + 2x + 7

Consider (x + 1)^2, where we halved the coefficient of x to obtain 1. This gives us x^2 + 2x + 1, which looks similar to our function, except it differs by a constant value of 6, hence, by adding 6 to (x + 1...
JP
Answered by Jordan P. • Maths tutor
4238 Views