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First set the equations equal to each other: x^2+4x+4 = 2x+3.Rearrange for x in form ax^2+bx+c : x^2+2x+1=0Factorise: (x+1)^2=0. Repeated root, hence only one intersection. x=-1. Using y=2x+3, y=1. So coo...

First step: n=1 we have 8¹ -1=7 which is divisible by 7. Assumption step: 8^k-1 is divisible by 7. Induction step: Using the previous step we have that 8^k-1=7x. So 8^k<...

Using the general rule d/dx(a*x^n) = a *n * x^(n-1) and the linearity of the derivative operator, we obtain:
6x^5+20x^3+0 = 6x^5+20x^3

(7 + √3)(7 - √3) = 7² + 7√3 - 7√3 - (√3)² = 49 - 3 = 46Alternatively you can go straight to identifying that this is the difference between two squares, using the fact that (a + b)(a...

Draw a diagram of the graph y=sin x between the stated interval. Identify the two extrema. Required interval is in between the two points.