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Find the equation of the line that passes through (2, 4) and (7, -11)

Step 1) Write out the general equation of a straight line: y = mx + c where m is the gradient and c is where the line intersects the y-axis. Step 2) Find the gradient: m = change in y / change in x, m = (-11...
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Answered by Romily G. • Maths tutor
4191 Views

A sweet is modelled as a sphere of radius 10mm and is sucked. After five minutes, the radius has decreased to 7mm. The rate of decrease of the radius is inversely proportional to the square of the radius. How long does it take for the sweet to dissolve?

dr/dt propto -1/r^2 and integrate to find equation linking radius and time with boundary conditions. Set r = 0, answer is 7mins 37 seconds.
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Answered by Igor S. • Maths tutor
4222 Views

Write 36 as a product of prime factors. Give your answer in index form.

First write down any two factors of 36 (numbers that multiply together to give 36). Let's use 2 x 18. We now need to break these numbers down into prime factors. 2 is already a prime number, so we only need ...
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Answered by Jennifer A. • Maths tutor
18950 Views

Show that ((sqrt(18)+sqrt(2))^2)/(sqrt(8)-2) can be written in the form a(b + 2) where a and b are integers.

First we expand the brackets on the numerator and collect the terms together. We need to get rid of the square root term on the denominator, and we do this by multiplying the numerator and denominator by sqr...
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Answered by Olivia A. • Maths tutor
19095 Views

Solve the simultaneous equations to find x and y. 4X=8Y+24; 7Y=23-2X

To solve these simultaneous equations I will use the substitution method. This method consists of finding out the value of one of the variables (X and Y) and then substituting this value into the other equat...
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Answered by Callum O. • Maths tutor
3964 Views