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Given that 2log2(x+15) -log2(x) = 6, show that x^2-34x+225=0

As we know nlog(a) is the same as log(a)^n, we can rearrange the equation to log2(x+15)^2 -log2(x) = 6. Also, we know that log(a) - log(b) is equal to log(a/b), so we can fu...

Answered by Rafey A. • Maths tutor

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In a village the number of houses and the number of flats are in the ratio 7 : 4 the number of flats and the number of bungalows are in the ratio 8 : 5 There are 50 bungalows in the village. How many houses are there in the village?

first combine into one ratio by finding lowest common multiple between common category so houses:flats:bungalow = 14:8:5. then for every 5 bungalows to every 14 houses so 50/5 = 10 and 10 x 14 = 140. so t...

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A curve is described by f(x) = x^2 + 2x. A second curve is described by g(x) = x^2 -5x + 7. Find the point (s) where both curves intersect.

To find the points where two curves meet a difference function needs to be calculated. This function is formed by subtracting one function from the other: d(x) = f(x) - g(x). It also works the other way a...

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A curve C has equation y = 3x^4 - 8x^3 - 3. Find dy/dx and d2y/dx2. Verify C has a stationary point at x = 2. Determine the nature of this stationary point, giving a reason for the answer.

y = 3x⁴- 8x³- 3Bringing the power down on each term and subtracting one from the power (as to differentiate, nx^m —> nmx^m-1), we get for each derivative:dy/...

Answered by Connor W. • Maths tutor

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Find the x values for stationary points in the curve y=3sin(2x) for 0<x<180

Firstly we differentiate the equation y=3sin(2x) w.r.t. x.By using the chain rule, we find the dy/dx=6cos(2x)Since a stationary point in the curve is a point where the gradient is 0, we can find them by f...

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