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A cuboid has sides such that the longest side is two units more than the shortest side, and the middle length side is one unit longer than the shortest side. The total surface area of the cuboid is 52 units². What is the length of the shortest side?

A cuboid has sides such that the longest side is two units more than the shortest side, and the middle length side is one unit longer than the shortest side. The total surface area of the cuboid is 52 units²...
RM
Answered by Roseanna M. • Maths tutor
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What is a stratified sample?

Stratified sampling is a technique used in some instances to generate a 'fairer' sample than standard random sampling. Wherein a population is divided into subgroups called 'strata'. These strata are usually...
LS
Answered by Lewis S. • Maths tutor
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The second term of an arithmetic sequence is 7. The sum of the first four terms of the arithmetic sequence is 12. Find the first term, a, and the common difference, d, of the sequence.

Let a be the first term Let d be the common difference a + d = 7 S 4 = 4/2 (2a +3d) = 12 Simultaneous equation: a+d =7 // x 6 4a +6d = 12 Difference btween these two 6a + 6d = 42 4a +6d = 12 2a = 30 a = 15 d...
AT
Answered by Alexander T. • Maths tutor
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Solve the equation x^2-x-56=0

The first step in this solution is to factorise the equation we have been given into the form (ax+b)(cx+d)=0, where a, b, c and d are constants which we need to determine. If we were to expand the brackets w...
RC
Answered by Richard C. • Maths tutor
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(3 + root(a))(4 + root(a)) = 17 + k(root(a)) where a and k are positive integers. Find the value of a and the value of k.

Let's open out the bracket using the FOIL method (first, outside, inside, last): (3 + root(a))(4 + root(a)) = 12 + 3root(a) + 4root(a) + (root(a)) 2 = 12 + 7root(a) + a. Since the answer 17 + k(root(a)) is i...
AJ
Answered by Abhinav J. • Maths tutor
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