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Patricio O.

Freelance software engineer

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Pre-Calculus

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Question:

Find the lope of a line with points (15, 8) and (10,7);

Patricio O.

Answer:

To find the slope of a line first we need to identify the points and match them with the formula. slope = (y2 - y1)/(x2 - x1); In this case the points are (x1, y1) and (x2, y2) so following the formula we will get: slope = (7 - 8) / (10 - 15) solving the problem we will get slope = -1 / -5 division of negative numbers become positive therefore, the final answer is Slope = 1 / 5.

Calculus

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Question:

Take the derivative of f(x) = 3x^2+2x+2

Patricio O.

Answer:

To take the derivative of this problem we can follow the formula d/dx x^n = nx^x-1. This means that first we need to subtract 1 from the exponent and multiply the exponent with 3 like so, 2*3x^(2-1) which will give us 6x^1 or simply 6x. We do the same thing with the next numbers 2x, 1*2x^(1-1), which will result in 2x^0, now any number to the power of 0 is always 1 therefore, now we have 2 alone and finally the number the derivative of number 2 is equal to 0. The reason for this, is because the derivative of a constant number is always 0. We can only take derivatives of variables and reduce them to minimal expressions. The final result is f'(x) = 6x + 2.

Algebra

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Question:

Solve the equation for x: 5x+5=20;

Patricio O.

Answer:

To be able to solve for x first we need to understand what is the question asking. In this problem x is an unknown number that when multiplied by 5 and added 5 will give the result of 20. Therefore, to solve this equation first we need to separate the equation in two parts and then we will subtract 5 from each part. So 5x+5-5 wich will leave the 5x alone and in the other side of the equal sign 20 - 5 ill give us 15. Now we have an equation that looks like so 5x = 15. Next, divide both sides by 5 like so (5x/5) = (15/5), and when we do so it will cancel out the 5, leaving x alone and in the other side 15/5 will give us 3. Therefore, the final result will be x = 3.

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