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Relative to a fixed origin O, the point A has position vector (8i+13j-2k), the point B has position vector (10i+14j-4k). A line l passes through points A and B. Find the vector equation of this line.

The vector equation of any line is composed of the addition of a point on the line and some distance in the direction of the line, in the form y=(x,y,z) +d(x_1, y_1, z_1), where (x,y,z) is any point on the l...
CS
Answered by Carlota S. • Maths tutor
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Given the ratio of x : y is 7 : 4 and x + y = 88. Work out the value of x – y

7x = 4yx=4y/7If we insert this into our other equation.4y/7 + y = 8811y/7 =88y = 56As we knowx =4y/7X= 4*56/7 = 32Then we can work out the answer X - Y = 32 - 56 = -24
SK
Answered by Salih K. • Maths tutor
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If f(x)=(x^3−2x)^5 , find f'(x).

f(x)=(x 3 -2x) 5 If we look at this function, we can see that it can be split into two functions, one hiding in the other one. Because of that, to solve this problem we will need the Chain rule: f(g(x))' = f...
RS
Answered by Radovan S. • Maths tutor
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What is the indefinite integral of xlog(x)?

The integral can be split into two different functions of x which is a hint that we must use the integration by parts method. The method is defined as ∫ uv’ dx = uv - ∫ u’v dx . If we let u = log(x) and v’ =...
WH
Answered by William H. • Maths tutor
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Solve the following simultaneous equations: x^2 + y^2 = 29 and y - x =3

This question is slightly trickier than normal simultaneous equations, because we have values to the power of 2. What we can do is make either y or x the subject of the 2nd equation (y-x = 3). For this examp...
TD
Answered by Trushna D. • Maths tutor
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