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Given that f(x) = 1/x - sqrt(x) + 3. Find f'(1).

We are given that f(x) = 1/x - sqrt(x) + 3. Here, f(x) represents a function. A function is a relation or expression involving one or more variables. We are able to differentiate f(x) in order to find the...

Answered by • Maths tutor

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The point P has coordinates (3, 4) The point Q has coordinates (a, b) A line perpendicular to PQ is given by the equation 3x + 2y = 7 Find an expression for b in terms of a.

y = (7-3x)/2m = ^-3/₂therefore:Y = ²/₃ X + cwhen Y = 4 and X = 3, c = 2therefore b = ²/₃

Answered by Dilan P. • Maths tutor

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A pen is the shape of an equilateral triangle. A goat is attached to a corner of the pen on a rope. The goat eats all the grass it can reach. It can just reach the opposite fence of the pen. What percentage of the grass in the pen does the goat eat?

Step 1: Area of the penA triangle’s area is base * height / 2. Let one side (the base) have length x. By splitting the triangle in half and using Pythagoras’s rule, we get x² = (x/2)^...

Answered by Max C. • Maths tutor

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y = 4x^3 - 5/x^2 find dy/dx

First rewrite the equation into an easier form:y = y = 4x^3 - 5x^-2dy/dx means differentiate y with respect to xSo when differentiating, you look at the first term and write the co-efficient of the x term...

Answered by Dennis A. • Maths tutor

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How do I solve inequalities when they're not linear?

Ok, let's talk about quadratic inequalities in particular. Look at the inequality x^2 - 8x + 15 > 0.What does a solution to this mean? It means the curve x^2 - 8x + 15 > 0 is above the x-axis at thi...

Answered by Damon F. • Maths tutor

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