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Nimmy J.

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Biology

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Question:

What is mitosis?

Nimmy J.

Answer:

Mitosis is a type of cell reproduction that results in two genetically identical daughter cells. To be genetically identical, each daughter cell must have the same number and kind of chromosomes as the parent cells.

Calculus

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Question:

Find the derivative of $$ f(x) = 6x^3 - 9x +3 $$.

Nimmy J.

Answer:

In this problem, we see that we have a basic polynomial. So the first thing to remember are the basic derivative formulas of: $$ \frac{d}{dx} \ (c) = 0$$ where c is a constant. $$ \frac{d}{dx} \ ax = a(1) =a $$ where a is a constant. $$ \frac{d}{dx} \ x^n =nx^{n-1}$$ Step 1 : Since this is a polynomial, we can separate it into its individual terms to simplify the problem and see which formula goes with which term So let's rewrite $$ f(x) =A+B+C$$ where $$A = 6x^3 $$ $$B = -9x $$ $$C = 3 $$ Step 2: Now we find the derivatives of the individual terms A, B and C because $$ f'(x) = A' +B' + C' $$ $$ \frac{d}{dx} \ A =\frac{d}{dx} \ 6x^3 = 3(6)x^{3-1} = 18x^2 $$ $$ \frac{d}{dx} \ B = \frac{d}{dx} \ -9x = -9(1) = -9 $$ $$ \frac{d}{dx} \ C = \frac{d}{dx} \ 3 =0$$ Step 3: Plug values back into $$f'(x)$$ $$f'(x) = A' +B' + C' = 18x^2 - 9 + 0$$ So, $$ f'(x) = 18x^2 - 9 $$ The derivative of $$ f(x) = 6x^3 - 9x +3 $$ is $$ f'(x) = 18x^2 - 9 $$

Algebra

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Question:

What is the slope of the line that passes through the points (3,5) and (−2,2)?

Nimmy J.

Answer:

First thing to remember in calculating the slope of a line when given two points is the slope formula. Slope = $$ \frac {\Delta Y}{\Delta X} = \frac {Y_1-Y_2}{X_1-X_2} $$ Step 1: Choose one of the two points to be $$X_1 $$ and$$Y_1$$ and set the other point as $$X_2 $$ and $$Y_2$$ So here, we can set $$X_1 =3$$ and $$Y_1 =5$$ That means we can set $$X_2 = -2 $$ and $$Y_2 =2 $$ Step 2: Plug in the values into the slope formula!! Slope = $$ \frac {Y_1-Y_2}{X_1-X_2} $$ = $$ \frac {5-2}{3-(-2)} = \frac {5-2}{3+2} \ = \frac{3}{5} \ $$ Therefore the slope of a line through the points (3,5) and (−2,2) is $$ \frac{3}{5}\ $$

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