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First begin with rearranging the second equation to put it in terms of Y. Then substitute by putting the second equation (y=3x+13) into equation one as Y^2. Expand (3x+13)^2 and add like terms to form 10x^2 ...

Factorising gives: y = (x+2)(x+1) = 0. y only equals 0 when (x+2)=0 or (x+1)=0. Therefore x=-2 or x=-1

4^(n)-1 factors to (2^(n)-1)(2^(n)+1) by difference of two squares by definition of a prime (only has factors 1 and itself (given that itself isn't 1))So Exactly one of the brackets should = 1 for 4^(n)-1 to...

We use a typical rule for polynomials in the form y = a x b , where a and b are real numbers. Also, for a polynomial equation y = a x b +c x d +.... , dy/dx = d( a x b )/dx + d(c x d )/dx + ...With this info...

e x sin(x) is a product of two functions: e x and sin(x). This means we can use the product rule. Let e x = u and sin(x) = v The differential of uv is u'v + v'u where u' and v' are the two functions differen...