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If y=3x^3e^x; find dy/dx?

Using the product rule we know that dy/dx = uv' + vu' where u = 3x^3; v = e^x. e^x differentiates to itself multiplied by any number in front of the x. u' = 9x^2; v' = e^x. Therefore dy/dx = 3x^3e^x + 9x^2e^...
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Answered by Aimee G. • Maths tutor
6124 Views

Why do you not add the 'plus c' when finding the area under a graph using integration even though you add it when normally integrating?

when integrating with the limits, you substitute in the two limits into the integral and then take them away. As both will have added the constant 'c', you are taking c away from c and so cancel out, so it i...
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Answered by Neha M. • Maths tutor
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For a given function F(x), what does the graph of the function F(x+2) look like in comparrison to F(x)?

F(x+2) is simply F(x) but whenever you see an 'x' replace it with 'x+2'. So when x is say 3, F(x) is F(3) and F(x+2) is F(5). If we draw this out on a graph, we see that this has the effect of shifting the g...
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Answered by James S. • Maths tutor
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Emma wants to buy a radio, the full price is £80. In the shop, she is given a discount. A year later, she sells the radio for £78, giving her a profit of 30% of what she bought it for the year before. What discount did she receive? (4)

Finding what Emma paid for her radio £78 / 1.3 = £60 (M1) (A1) Finding what percentage of £80 that is £60 / £80 = 0.8 or 80% (M1) Recognising the discount is 20% ie. 1-0.8=0.2 (A1)
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Answered by Helena R. • Maths tutor
3516 Views

In a class of 30, the ratio of boys to girls is 2 : 3 , how many girls are there?

If the ratio is 2 : 3 then in a class of 5 there would be 2 boys and 3 girls. So we can say that 2/5 of the class are boys and 3/5 of the class are girls. And we know that to calculate 3/5 of 30 we must firs...
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Answered by Rebecca E. • Maths tutor
49802 Views