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Solve the following simultaneous equations: y - 2x = 6 and y + 2x = 0

Firstly, label each of our equations: y - 2x = 6 (1) y + 2x = 0 (2)Then we can rearrange (2) to get the following: y = -2x (3)Then, substitute (3) into (1): -2x - 2x = 6Which yields the result: -4x = 6Theref...
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Answered by Ciara C. • Maths tutor
4750 Views

Suppose we have a circle with the equation x^2 +y^2 =25. What is the equation to the tangent to the circle at point (4,3)?

Firstly lets draw it out-Draw a line from the origin to the point. calculate the change in y over change in x =(3-0)/(4-0)=3/4Take negative reciprocal which is equal to m. Then do y-y 1 =m(x-x 1 ) or y = mx ...
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Answered by Nayan M. • Maths tutor
3214 Views

How do you integrate the natural logarithm?

We already know that the derivative of ln(x) is 1/x, so how can this be used for integration?Recall integration by parts uses knowledge of the derivative of one of the parts in the formula.int(u v' dx) = uv ...
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Answered by Josh L. • Maths tutor
3410 Views

Paul buys three pens and one pencil for £11 while Sam buys four pens and two pencil for £16 - what is the price of pens and pencils?

Read the question and translate the information into equations.'Three pens and one pencil for £11' can be written as 3x + y = 11 where x = pens and y = pencils. 'Four pens and two pencils for £16' can be wri...
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Answered by Isabelle S. • Maths tutor
3167 Views

How do I solve a quadratic equation?

In a quadratic equation the highest power is 2. This means that we are looking for up to 2 answers. The first thing we are going to try to do is factorise the equation. We draw two sets of brackets side by s...
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Answered by Leszek W. • Maths tutor
3164 Views