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A curve has an equation of y = 20x - x^2 - 2x^3, with one stationary point at P=-2. Find the other stationary point, find the d^2y/dx^2 to determine if point P is a maximum or minium.

We know that a stationary point is found when the gradient of the curve is equal to zero, this is found by equaling the derivative (dy/dx) equal to zero. Differentiating the expression will find a quadrat...

Answered by Georgia S. • Maths tutor

2816 Views

Solve the equation (x+2)/(x-3)=(x-6)/(x+1) for x.

We need to multiply both sides by the denominator (the bottom of the fraction) in both fractions so we get:(x+2)(x-3)(x+1)/(x-3)=(x-6)(x-3)(x+1)/(x+1)Now, we can see that we can cancel each fraction to ge...

Answered by Tom H. • Maths tutor

2667 Views

Consider the infinite series S=Σ(from n=0 to infinite) u(down n) where u(down n)=lim (from n π to (n+1) π) ((sin t)/t) dt. Explain why the series is alternating.

For the first part of the question we need to try and understand what is actually happening – we have the sum of an integral – where we are summing a sequence of definite integrals. So when n = 0 we have ...

Answered by Stuart D. • Maths tutor

5514 Views

Find an equation of the curve with parametric equations x=3sin(A) and y=4cos(A), in the form bx^2+cy^2=d.

x²=9sin²(A) and y²=16cos²(A)Since sin²(A)+cos²(A)=116x²+9y²=16 x 916x²+9y²=144

Answered by Pranav V. • Maths tutor

3408 Views

A shop sells only Apples, Bananas and Mangos. The ratio of Apples to Bananas is 5:11. The next shopper will choose one piece of fruit at random. The probability that they buy a Mango is 0.2. What is the probability that they buy an Apple?

We have the probability of choosing a Mango is 0.2 so the probability of choosing an Apple or Banana is 1-0.2=0.8.Next we use the ratio 5:11 to see that for every (5+11)=16 Apples or Bananas, 5 will be Ap...

Answered by Gregor M. • Maths tutor

3361 Views