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Joshua R.
Software Engineer and lover of math
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Linear Algebra
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Question:

What is the main use of practices of Linear Algebra?

Joshua R.

The practices are used to solve systems of linear equations.

Computer Science (General)
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Question:

What is the purpose of a microprocessor in a computer?

Joshua R.

The purpose of a microprocessor is to process given instructions through a series of logical and mathematical operations.

Calculus
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Question:

Find the area under the curve y = -(x^2) + 5x - 4 and above the x axis. a) Find the left end-point of the area. b) Find the right end-point of the area. c) Find the total area.

Joshua R.

First we convert the bounds of the area into functions with respect to x. Change "above the x axis" to "greater than y = 0". Our bounds are then: y = -(x^2) +5x - 4 and y = 0. a) We can find the bounds of the area by setting the two meeting functions equal to eachother. -(x^2) + 5x - 4 = y = 0 Then we can simplify to find which values of x the functions meet at. -1*[-(x^2) + 5x - 4] = -1*(0) x^2 - 5x + 4 = 0 (x - 4)(x - 1) = 0 x = 1, x = 4 Therefore, the left bound of the function is x = 1. b) As is found in the previous explaination, the right bound of the area is x = 4. c) Knowing the bounds and the functions, the specified are can be calculated with: $$A = \int_{1}^{4} (-x^2 + 5x - 4)dx = (-\frac{1}{3}x^3 + \frac{5}{2} x^2 -4x)|_{1}^4$$ $$A = \frac{9}{2}$$

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