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x is an integer such that ‎1≤x≤9, Prove that 0.(0x)recurring=x/99

r=0.0 . x . r=0.0x0x0x0x.... 100r=x.0x0x0x (1) 10,000r=x0x.0x0x0x (2) (2) - (1): 9,900r=x00 r=x00/9,990 r=x/99
EE
Answered by Ellie E. • Maths tutor
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Compute the indefinite integral of x^8 ln(3x)dx

Using integration by parts, by substituting ln(3x) as u and x^8 as dv/dx, use the formula to plug in the values and complete the calculation to get (x^9)(ln(3x)-1/9)/9
PP
Answered by Pawel P. • Maths tutor
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How would I differentiate y=2(e^x)sin(5x) ?

We can see that we have the product of two different functions, and so we need to use the product rule. We will separate the function and label each part u and v for clarity. So we let u = 2e x and let v = s...
SP
Answered by Scott P. • Maths tutor
5150 Views

theta = arctan(5x/2). Using implicit differentiation, find d theta/dx.

First, we must rearrange to give 2tan(θ) = 5x. Differentiate both sides with respect to x: 2sec 2 (θ)dθ/dx = 5 Use identity sin 2 (θ) + cos 2 (θ) = 1, dividing through by cos 2 (θ), to get 2(1+tan 2 (θ))dθ/d...
CW
Answered by Callum W. • Maths tutor
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Bob sprints down a 100 metre track as fast as he can and as he arrives at the finish, a light gate cuts a timer that has been active since Bob began his sprint. It reads 12.45 seconds. calculate Bobs average speed during the sprint.

s=distance/time = 100/12.45 =8.03m/s
RW
Answered by Richard W. • Maths tutor
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