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Solve e^(2x) = 5e^(x) - 6, giving your answers in exact form

Solve e^2x = 5e^x- 6e^2x - 5e^x+ 6 = 0(e^x)² - 5e^x<...

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A curve C is mapped by the equation ( 1+x)(4-x). The curve intersects the x-axis at x = –1 and x = 4. A region R is bounded by C and the x-axis. Use calculus to find the exact area of R.

First draw the curve. Figure out and write the integration problem. Integral⁴_-1 (1+x)(4-x) dx.Expand integral⁴_-1 4 + 3x - x² dx.= ⁴_...

Answered by Vishesh D. • Maths tutor

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Describe and explain the change in the shape of the graph y=x^2 and y=x^2 + 2.

The graph is translated by two in the positive y-axis direction. For example, for the equation y=x², taking the x-axis values of 0,1,2 and 3, y= 0²,1², 2

Answered by Matthew S. • Maths tutor

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(a) Find the set of values of k that satisfy the inequality k^2 - k - 12 < 0. (b) We have a triangle ABC, of lengths AC = 4 and BC = 2. Given that cos B < 1/4 , find the range of possible values for AB:

Solution: Let us consider the function f(k) = k²- k -12. Firstly, we want to find out the roots of this function. We calculate the discriminant: Δ = b² – 4ac = 49 hence we ...

Answered by Alexandru H. • Maths tutor

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Please expand (y+2)(y-3).

We will use the FOIL method. Here FOIL stands for: First, Outside, Inside, Last.
This means we start by multiplying the first terms in each bracket together to get y² .
Then we multi...

Answered by Mary B. • Maths tutor

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