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Solve the equation 5^(2x) - 12(5^x) + 35 = 0

The first step to solving this is equation is to notice that the equation is of a similar to the form of a quadratic equation: ay^2 + by + c = 0 where a, b and c are constants. Next we introduce a new variab...
JG
Answered by Jacob G. • Maths tutor
11098 Views

Differentiate with respect to x: y = ln(x^2+4*x+2).

Let u = x 2 +4x+2 so y = ln(u). Then dy/du = 1/u and du/dx = 2x+4. Using the chain rule we have: dy/dx = (dy/du)*(du/dx) = (1/u)*(2x+4) = (2x+4)/(x 2 +4x+2).
OL
Answered by Okim L. • Maths tutor
5522 Views

The first 4 terms of a different sequence are: 9, 13, 17, 21. Find an expression for the nth term of the sequence

In order to find the nth term of a sequence you need to keep the structure of the nth term sequence in mind (dn+x). The first thing we want to do is find 'd'. In this case 'd' stands for difference, which is...
IB
Answered by India B. • Maths tutor
8291 Views

Prove that sec^2(θ) + cosec^2(θ) = sec^2(θ) * cosec^2(θ)

These problems can be tricky as they use unfamiliar trigonometric functions such as secant and cosecant. It is much easier to approach these problems by replacing these trigonometric functions with more fami...
HR
Answered by Hugh R. • Maths tutor
12981 Views

A cuboid has sides such that the longest side is two units more than the shortest side, and the middle length side is one unit longer than the shortest side. The total surface area of the cuboid is 52 units². What is the length of the shortest side?

A cuboid has sides such that the longest side is two units more than the shortest side, and the middle length side is one unit longer than the shortest side. The total surface area of the cuboid is 52 units²...
RM
Answered by Roseanna M. • Maths tutor
7072 Views