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First, we're going to split this 1 fraction into 2 fractions. Let (x+2)/((x+5)(x-7)) = A/(x+5) + B/(x-7) then multiplying by (x+5)(x-7) gives A(x - 7) + B(x + 5) = x + 2 multiplying this out we achieve Ax...

a prime number is a number which is only divisible by itself and one e.g 2, 3 , 5, 7when writing a number (in this example 36) as a "product of its prime factors" you need to find the prime numb...

Given that the equation is quadratic and has two distinct roots , this implies that the discriminant (b² - 4ac) in the quadratic formula is equal to zero. Comparing terms a = (k+1), b = (5k -3)...

Multiply: First have to make the fraction whole. To do this we multiply the first number by the denominator. Then we add it to the numerator to get a top heavy fraction. Now we can simply multiply the two...

Always a good first step to a problem like this, is to draw a diagram, making sure to label any lengths. The unknown in this question, is the rate at which the surface of water, in the cone, is rising. Ho...