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Given that y = arcos(x/2) find dy/dx of arccos(x/2) and hence find the integral from 0 to 1 of arcos(x/2)dx

a) First we can rewrite y=arccos(x/2) as cosy = x/2 which allows us to use implicit differentiation to easily differentiate each side. Taking d/dx of each side gives us -siny*(dy/dx) = 1/2 . Rearranging this...
OP
Answered by Olivia P. • Maths tutor
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Find the tangent to the curve y=(3/4)x^2 -4x^(1/2) +7 at x=4, expressing it in the form ax+by+c=0.

In general, the equation of a line is y-y0=m(x-x0), where m is the gradient and (x0,y0) is a point on the line. We need to find the gradient and a point on our tangent. Step 1: Find gradient. Since our tange...
EP
Answered by Eleni P. • Maths tutor
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Three girls and four boys are seated randomly on a straight bench. Find the probability that the girls sit together and the boys sit together.

There is a total of 7! possible ways in which the seven children can be seated on the bench. The number of favourable arrangements when four boys are seated on one side and three girls on the other side is 4...
Answered by • Maths tutor
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How would you plan a 'to what extent' essay?

Firstly, take a look at the essay title and go through with a highlighter, picking out any key words you think you will need to address when writing the essay. For example, say the question was: 'The size of...
RM
Answered by Romy M. • Geography tutor
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5.00 g of copper(II) carbonate decomposes to form copper(II) oxide and carbon dioxide: CuCO3(g) → CuO(s) + CO2(g). Calculate the maximum mass of carbon dioxide that can be produced. (Mr of CuCO3 = 123.5, Mr of CO2 = 44.0)

Moles of CuCO3 (using triangle) = 5.00/123.5 = 0.0450 mol.1 mol of CuCO3 makes 1 mol of CO2, therefore 0.0450 mol of CuCO3 makes 0.0450 mol of CO2.Using the triangle, mass of CO2 = 44 x 0.0450 = 1.78 grams
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Answered by Clemmie B. • Chemistry tutor
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