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How can I show that the lines between sets of points are perpendicular?

For example, A(6/5, 19/5), B(2, 9/5), C(5, 3). Show that the line segments AB and BC are perpendicular. Before we begin the question, it is a good idea to remind ourselves of the definition of two lines bein...
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Describe how the lac operon works when lactose is both present and absent.

When lactose is absent the lac operon is switched off. This is becasue a repressor protein is produced which binds to the operator region. This prevetns RNA polymerase from binding to the operon and therefor...
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Answered by Suzannah E. • Biology tutor
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Find the indefinite integral of sin(2x)(cos^2(x)) with respect to x.

We know from trigonmetric identities that cos(2x) = 2cos^2(x) -1, therefore cos^2(x) = 0.5(1+cos(2x)). Subbing this in gives the following integrand: 0.5(1+cos(2x))sin(2x). We can now split the integral into...
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Answered by Patrick P. • Maths tutor
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How can I solve equations like 2x + 3 = 8x + 21?

Questions like this ask you to solve an equation; this means to find a value of x that when put into the equation allows each side of the equation to be equal. There are three important rules to follow when ...
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Answered by Tutor87017 D. • Maths tutor
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We have the following fractions: 6/16, 9/24, 12/32 and 15/35. Which fraction is not equivalent to 3/8?

Numerator and denominator of a fraction 6/16 can be divided by 2 to get 3/8. Numerator and denominator of a fraction 9/24 can be divided by 3 to get 3/8. Numerator and denominator of a fraction 12/32 can be ...
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Answered by Karolina P. • Maths tutor
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