3x+(-2+4x) what is the answer???????

Mathematics

1 answer:

BlackZzzverrR [31]3 years ago

6 0

I am assuming you are meant to factor this.

Distribute 3x to the parentheses.

3x*-2 = -6x

3x*4x = 12x^2

Put it all together, largest sums first.

12x^2 - 6x

Not sure if they want you to simplify it further by dividing the common factor, but most likely not since you just expanded it. You'd be going backwards if so, and you should challenge your instructor on their logic.

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Sketch the region enclosed by y=3x and y=x^2 . Then find the area of the region.

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The integral of a function gives you the area under the curve, the subtraction of one of the areas from the other will give you the area in between.

The limits of integration are the points where the curves intersect each other(take the curves has a system of equation and solve for x and y):

$y=3x, y=x^2\\3x=x^2\\x^2-3x=0\\x(x-3)=0\\x_1=0\\x-3=0\\x_2=3$

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$\int\limits^3_0 {3x-x^2} \, dx =\left\frac{3x^2}{2}-\frac{x^3}{3}\right|^3_0=\frac{3(3)^2}{2}-\frac{(3)^3}{3}-\left(\frac{3(0)^2}{2}-\frac{(0)^3}{3}\right)\\\int\limits^3_0 {3x-x^2} \, dx =\frac{27}{2}-\frac{27}{3} =13.5-9=4.5u^2$