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A curve C is mapped by the equation ( 1+x)(4-x). The curve intersects the x-axis at x = –1 and x = 4. A region R is bounded by C and the x-axis. Use calculus to find the exact area of R.

First draw the curve. Figure out and write the integration problem. Integral 4 -1 (1+x)(4-x) dx.Expand integral 4 -1 4 + 3x - x 2 dx.= 4 -1 [4x + 3x 2 /2) -x 2 ] = 16 + 30 - 64/3 - (-4 + 3/2 + 1/3)= 125/6
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Answered by Vishesh D. • Maths tutor
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Describe and explain the change in the shape of the graph y=x^2 and y=x^2 + 2.

The graph is translated by two in the positive y-axis direction. For example, for the equation y=x 2 , taking the x-axis values of 0,1,2 and 3, y= 0 2 ,1 2 , 2 2 and 3 2 respectively: These values being 0,1,...
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Answered by Matthew S. • Maths tutor
5367 Views

(a) Find the set of values of k that satisfy the inequality k^2 - k - 12 < 0. (b) We have a triangle ABC, of lengths AC = 4 and BC = 2. Given that cos B < 1/4 , find the range of possible values for AB:

Solution: Let us consider the function f(k) = k 2 - k -12. Firstly, we want to find out the roots of this function. We calculate the discriminant: Δ = b 2 – 4 a c = 49 hence we get the roots: k 1 = (1-7)/(2 ...
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Answered by Alexandru H. • Maths tutor
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Please expand (y+2)(y-3).

We will use the FOIL method. Here FOIL stands for: First, Outside, Inside, Last. This means we start by multiplying the first terms in each bracket together to get y 2 . Then we multiply the outside terms to...
MB
Answered by Mary B. • Maths tutor
8662 Views

Please solve the following simultaneous equations 4x + 7y = 336 y = 6x + 2

Step 1 - through previous experience realise this equation can be solved by the substitution methodStep 2 - rearrange for the part you want to sub in, in this case it is done for us as Y is the variable we w...
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Answered by Eleanor S. • Maths tutor
3628 Views