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Work out 51% of 400? (No calculator)

Finding 51% of 400 is the same as finding 50% of 400, and 1% of 400, and adding them together. Finding 50% of a number is the same as finding half of the number, since half of 100% is 50%. Half of 400 is 200...
CW
Answered by Charlotte W. • Maths tutor
26573 Views

Differentiate y = √(1 + 3x²) with respect to x

To solve this question, we need to use the chain rule, because the function is too complicated to solve simply by inspection. The chain rule says that dy/dx = dy/du × du/dx, where u is a function of x. In th...
WT
Answered by Walter T. • Maths tutor
8961 Views

Given h(x) = 9^x + 9 and g(x) = 10*3^x, find {x | h(x) < g(x)}.

This question is asking to find the values for x, such that h(x) is strictly less than g(x). We can write this as 9^x + 9 &lt; 10 3^x and solve for x as follows. 9^x + 9 &lt; 10 3^x =&gt; 3^(2x) - 10 3^x + 9...
CM
Answered by Carlo M. • Maths tutor
4041 Views

Prove the following identity: (1+cos⁡(x)+cos⁡(2x))/(sin⁡(x)+sin⁡(2x) )=cot⁡(x)

Straight away we notice that two trigonometric terms on the left hand side have 2x but there are no 2x on the right hand side therefore we realise that this question will require double angle formulae. If yo...
JB
Answered by Jessica B. • Maths tutor
19909 Views

Given 1/2 + 1 + 2 + 2^2 + ... + 2^10 = a*2^b + c, find the values of a,b,c.

Consider the Left-Hand-Side (LHS) of the equation first. LHS: 1/2 + 1 + 2 + 2^2 + ... + 2^10. We identify this as a geometric series by noticing that dividing any term u_(n+1) by the preceding term n the res...
CM
Answered by Carlo M. • Maths tutor
4241 Views