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Let Curve C be f(x)=(1/3)(x^2)+8 and line L be y=3x+k where k is a positive constant. Given that L is tangent to C, find the value of k. (6 marks approx)

SO when we see the word tangent we should be thinking about rate of change. Recall that the line being a tangent means they meet and have the same derivative at this point OR we find k such that f(x)-y=0 ...

Answered by Gurbir J. • Further Mathematics tutor

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Using Figure 5, assess whether the decision to install the machine (used in production in an independent fast food shop) will be beneficial for the business and the workers.

It is stated that the production of burgers can be split into different stages following the installation of the machine. This allows for the division of labour and the subsequent specialisation of worker...

Answered by Stefan D. • Economics tutor

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The point P has coordinates (3, 4) The point Q has coordinates (a, b) A line perpendicular to PQ is given by the equation 3x + 2y = 7 Find an expression for b in terms of a.

y = (7-3x)/2m = ^-3/₂therefore:Y = ²/₃ X + cwhen Y = 4 and X = 3, c = 2therefore b = ²/₃

Answered by Dilan P. • Maths tutor

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A pen is the shape of an equilateral triangle. A goat is attached to a corner of the pen on a rope. The goat eats all the grass it can reach. It can just reach the opposite fence of the pen. What percentage of the grass in the pen does the goat eat?

Step 1: Area of the penA triangle’s area is base * height / 2. Let one side (the base) have length x. By splitting the triangle in half and using Pythagoras’s rule, we get x² = (x/2)^...

Answered by Max C. • Maths tutor

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Explain how a change in an allele can stop a protein functioning correctly. (4)

If there is a change in the allele, there will be a change in base sequence of DNA (1) This means there is a change in order of amino acids (1) Therefore the protein shape changes (1) Hence, the protein m...

Answered by Lima H. • Biology tutor

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