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Clare buys some shares for $50x. Later, she sells the shares for $(600 + 5x). She makes a profit of x% (a) Show that x^2 + 90x − 1200 = 0

Profit is (New price-Original price)/Original price . As a fraction it is percentage Profit/100. Equate (New price-Original price)/Old Profit to the fraction of Profit in %/100. Cross multiply and come up wi...
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Answered by Raj H. • Maths tutor
13115 Views

The nth term of a sequence is 8(2^n + 2^(6n-7)). a) Without a calculator, find the 2nd term of this sequence, b)​​​​​​​ Express the formula in the form 2^x + 2^y

To find a) just plug in the number two to all places where n appears. In this case 8(2^2 + 2^(6 * 2 - 7)) and then number crunch. 8(4+2^5) -> 8 * (4 + 32) -> 8 * 36= 288. To find part b, we must first ...
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Answered by Tom P. • Maths tutor
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Simplify fully: (7x^2 - 21x)/(x^2 + 2x - 15)

This one is quite complicated to answer typed up like this and i would definitley use a white board Show that 7x^2 - 21x can be come x(7x-21) which can in turn become 7x(x-3) Show that x^2 + 2x - 15 can beco...
DG
Answered by Dominic G. • Maths tutor
5806 Views

A tank is filled with water up to the height H0. At the bottom of the tank, there is a tap which is opened at t=0. How does the height of liquid change with time?(Hint: dH/dt is proportional to -H)

This is a typical C4 differential equation question. The same algorithm could be used for a lot of other problems. First of all, from the hint we have that dH/dt = -kH (1). We need to separate the variables ...
MB
Answered by Maxim B. • Maths tutor
8342 Views

Find the coordinate of the turning point of the curve y = x^2 - 10x + 7, by completing the square

First, we need to complete the square. We take the first part of the equation ignoring the constant ( + 7). y = x 2 - 10x , we want to change the form of this equation from x 2 + ax + (a/2) 2 into ( x + a/2 ...
JP
Answered by James P. • Maths tutor
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