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A ball, dropped vertically, falls d metres in t seconds. d is proportional to the square of t. The ball drops 45 metres in the first 3 seconds. How far does the ball drop in the next 7 seconds?

First we form equations from the information given in the question. The first equation we can form is that d is directly proportional to the square of t. This means that d = kt 2 ,where k is a constant of pr...
Answered by • Maths tutor
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Find the gradient of the curve y = sin(2x) + 3 at the point where x = pi

This is a question that relates to the topic of differentiation. Typically students encounter this topic near the end of the first term of the first year of their A Level.The equation of the curve, y = sin(2...
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Answered by Agnieszka S. • Maths tutor
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A Polynomial is defined as X^3-6X^2+11X-6. a)i Use the factor theorem to show that X-3 is a factor. ii Express as a linear and quadratic b)Find the first and second derivative c) Prove there is a maximum at y=0.385 to 3DP

a)i Factor Theorem states that if a polynomial has a factor of X-a, when a is substituted in, the polynomial = 0. Therefore substitute 3 into the polynomial, which then equals 0 ii Long Devision- Unsure how ...
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Answered by Oliver M. • Maths tutor
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The perimeter of a right-angled triangle is 60 cm. The lengths of its sides are in the ratio 3 : 4 : 5. Calculate the area of the triangle.

We are given ratios of side lengths and the total perimeter. The perimeter of the triangle is simply the sum of the side lengths. Imagine that the sides are made up of "units": 3 times a unit + 4 t...
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Answered by Viktoria N. • Maths tutor
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How do I solve a sum of equations with unknowns in the denominator?

First, you need to make sure that each equation has a common denominator. You do this by multiplying the numerators of each equation with the denominators of the others. This allows you to form one algebraic...
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Answered by Kai H. • Maths tutor
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