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A rectangle has sides of length 4x cm and (x+3)cm and has an area less than 112 cm^2, find the set of values x can take

Derive an inequality for the area. 1) As area = width * length then area is 4x * (x+3). 2) Area is less than ( < ) 112 so inequality is 4x* (x+3) < 112. 3) Expand the brackets and then subtract 112 fro...
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Answered by Harry T. • Maths tutor
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The variables x and y are related by y = 5^x. How do I find the value of x when y is set to 15?

15 = 5^x, we can easily solve this equation by using logs on either side which will give us: log15 = x log 5. Then by solving this for x, we get the result of 1.68 to two decimal places.
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Answered by Andrea B. • Maths tutor
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How can I work out the area of a semi-circle with a diameter of 12cm?

For this question we need to remember that the equation to calculate the area of a circle is pi times the radius squared. The radius of a circle is half it's diameter, therefore the radius of the semi-circle...
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Answered by Cosima R. • Maths tutor
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What is the differential of (14x^3-3x^2)^3

Chain Rule - Differential of the bracket x the initial power of the bracket x the initial bracket power-1 --- So Differential of bracket is 42x 2 - 6x--- Power of bracket is 3 ---Initial bracket power-1 is (...
Answered by • Maths tutor
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I don't understand integration by parts - can you explain it please?

(Apologies I don't have the relevant diagrams here so this reads longer than it actually is on paper) 1) First it's important to establish that the prior knowledge is there before explaining something more a...
Answered by • Maths tutor
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