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The first floor of an ancient japanese tower has 150 steps. Each floor above has 5 fewer floors than the previous. So, the second floor has 145 steps, the third 140 etc. How many floors does the tower have if the final floor has 30 steps leading to it.

Note this is an arithmetic series problem, so we use the equation: x n = a + d(n-1). Number of steps on the first floor is 'a', i.e. a = 150. Difference in the number of steps on each subsequent floor is -5 ...
JF
Answered by Joel F. • Maths tutor
3470 Views

Integrate (12x^5 - 8x^3 + 3)dx giving the terms of the answer in the simplest terms

Integration is essentially differentiation in reverse! So in the simpler cases instead of multiplying by the power of x and subtracting one from the power of x, you add one to the power of x and divide by th...
ES
Answered by Ellen S. • Maths tutor
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(C3) Show that 4csc^2(x) - cot^2(x) = k can be expressed as sec^2(x) = (k-1)/(k-4) where k != 4

The student can answer this in several ways. One using the simple, known identities csc= 1/sin, cot=1/tan, sec=1/cos, tan=sin/cos, sin^2 + cos^2 = 1 and basic algebra is the following: 4csc^2 - cot^2 = k4/si...
FH
Answered by Fearghus H. • Maths tutor
4295 Views

The ratio of Adam's age to Bob's age is 1:2. In 12 years time, the ratio of their ages will be 3:5. Calculate their current ages.

Now: In 12 years:A:B A:B1:2x:2x x+12:2x+12 = 3:5 x+12 = 2x+12 3 55(x+12) = 3(2x+12)5x + 60 = 6x + 36x = 24 A:B Adam = 24, Bob = 48x:2x24:2(24)24:48
AS
Answered by Aaron S. • Maths tutor
5275 Views

Find the binomial expansion of (-8+4x)^(2/3) up to and including the term in x^2.

The formula booklet is useful for this type of question, but only once we've rearranged the expression into the correct form. The formula booklet expression is: (1 + z)^n = 1 + n z + 0.5 n*(n-1) z^2 + .... T...
DM
Answered by David M. • Maths tutor
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