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Integrate the function f(x) = ax^2 + bx + c over the interval [0,1], where a, b and c are constants.

Firstly remember that d/dx(x^n) = nx^(n-1). And so the antiderivative, or integral of x^n, i.e. \int(x^n) = x^(n+1)/(n+1) + C (where C is the integration constant). When integrating with limits, i.e. when we...
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Answered by Anvarbek A. • Maths tutor
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Find the general solution, in degrees, of the equation 2sin(3x+45°)=1. Use your general solution to find the solution of 2sin(3x+45°)=1 that is closest to 200 °.

The first thing to do when we are facing a trigonometry problem is to to draw the sine and cosine diagram on the unit circle. That takes very little time to do and is incredibly helpful to visualize the peri...
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Answered by Francesco S. • Maths tutor
6700 Views

There are 7 white socks and 4 black socks. 2 are taken at random without replacement. What is the probablity that 2 socks of the same colour are taken?

With a more wordy question like this, it is always best to break it up and write down all of the key pieces of information. So we want to work out the probability of picking: white AND white, OR, black AND b...
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Answered by Francesca H. • Maths tutor
4088 Views

Solve x^2+4x-5=0 by completing the square.

x^2+4x-5=0(x+2)^2-(2)^2-5=0subtract 2^2 as (x+2)^2 = x^2+4x+4 when we want x^2+4x(x+2)^2-4-5=0(x+2)^2-9=0(x+2)^2=9square root both sidesx+2=+/-3x=-2+/-3x=-2+3 or x=-2-3x=1 or x=-5
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Answered by Evie M. • Maths tutor
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The radius of a pizza is 12cm, calculate the area of the pizza in terms of pi

To calculate the answer to this question we need to know the formula for the area of the circle. The area of a circle is: A = Pi x r^2 The value of r is given in the question; r = 12. We then just plug this ...
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Answered by Beth B. • Maths tutor
9726 Views