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Solve the quadratic inequality: x^2 - 5x + 4 < 0

x 2 -5x+4 &lt;0First we ignore the inequality and try to solve the equation x 2 -5x+4=0, which we do via factorising (x-4)(x-1)=0. x = 4 or x=1We draw the graph using our solution, going through the points o...
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Answered by Hariz H. • Maths tutor
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Find two positive numbers whose sum is 100 and whose product is a maximum.

Call the two numbers x and y. The constraint is that x + y =100, and we need to maximise A=xy. Rearrange the constraint to y = 100 - x, and substitute into the product equation. A = x(100-x) = 100x - x 2 Dif...
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Solve the integral: int(x^3+4x^2+sinx)dx.

First, since there are terms with different factors of x summing together, we can separate these into three individual integrals as follows:int(x 3 dx) + 4int(x 2 dx) + int(sinx dx)Then using the rules of in...
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A curve C has equation: y = x^2 − 2x − 24x^1/2, x > 0; Find (i) dy/dx (ii) d^2y/dx^2

i) let dy/dx = ans, where ans = y, where you multiply the coefficients of each constant of x by the power and reduce the power by 1 in the equation ytherefore dy/dx = 2x - 2 - 12x -1/2 ii) repeat the process...
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Answered by Charles H. • Maths tutor
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Find the tangent to the curve y=(3/4)x^2 -4x^(1/2) +7 at x=4, expressing it in the form ax+by+c=0.

In general, the equation of a line is y-y0=m(x-x0), where m is the gradient and (x0,y0) is a point on the line. We need to find the gradient and a point on our tangent. Step 1: Find gradient. Since our tange...
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Answered by Eleni P. • Maths tutor
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