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How do you prove two straight lines intersect?

There are two ways to prove they intercept (you can choose whichever one you prefer). Say we have two straight lines, for example: r 1 = 3 i + 4 j - 5 k + t ( i - 2 j + 2 k ) => r 1 = (3 + t) i + (4 – 2t)...
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Answered by Nicholas M. • Maths tutor
11826 Views

Solve the simultaneous equations: 6x +2y = 2 and 12x - 3y = 18

6x + 2y = 2 and 12x -3y =18 Start by multiplying the first equation by two in order to balance both equations to have equal numbers of x 12x + 4y = 4 and 12x - 3y = 18 Rearrange both equations so that the x ...
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Answered by Jack H. • Maths tutor
3842 Views

A golf ball is hit at angle θ to the horizontal, with initial velocity u. Stating an assumption, show that the horizontal distance travelled by the ball is directly proportional to u^2.

If we assume there is no air resistance, this means that the horizontal component of the ball's velocity won't change. Resolving horizontally we can see that the horizontal velocity = u cos(θ). We can then u...
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Answered by Douglas B. • Physics tutor
11420 Views

Given that y = x^4 tan(2x), find dy/dx

Here we have a product of two functions - they are being multiplied together - so we need to use the product rule. The product rule is: if y = u·v, dy/dx = v·u' + u·v' (where f' stands for df/dx). u = x^4 du...
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Answered by Douglas B. • Maths tutor
10886 Views

How is DNA replicated?

Scientists have proposed several models of DNA replication but the currently accepted model is called the 'Semi-Conservative' model. The Semi-Conservative model of DNA replication was discovered by two scien...
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Answered by Gurpreet D. • Biology tutor
6237 Views