# Tutor profile: Jase M.

## Questions

### Subject: Electrical Engineering

The governing law in Electrical Engineering is Ohm's Law, could you please explain it in detail?

As learned, Ohm's Law is the basis of Electrical Engineering which states that $$V = R * I$$. This law says that voltage (V), equals resistance times current. This may help us find voltage in respect to a circuit, where we want to theoretically know what the voltage should be given resistance and current values. The law also shows that if you want to calculate resistance (R), the equation would be $$R = \frac{V}{I}$$. It also shows that if you want to find current (I), the equation would be $$I = \frac{V}{R}$$. Resistance is measured in ohms ($$\Omega$$), Voltage is measured in volts (V), and Current is measured in amperes (A). The late German Physicist, Georg Simon Ohm, discovered this law.

### Subject: Calculus

What is the first order partial derivative in respect to x of the the following equation? ($$f_x$$): $$ f(x, y) = 10x^4 + xy + 20x^5 $$

Upon observing the question, we must follow the rules of calculus in respect to derivatives. The question asks for the first order partial derivative of x given. Knowing this information, we will break down the original equation given: $$f(x, y)$$. To take the derivative, we first look at the term $$10x^4$$ and must recognize the derivative rule to be used, the power rule. Given by $$\frac{d}{dx} x^n = nx^{n-1}$$. Knowing this rule, the first derivative of the first term gives us $$4*10x^{4-1}$$, which equals $$40x^3$$. Furthermore, now that the first derivative of the first term is solved, we can move onto the second term in the equation: $$xy$$. We must immediately recognize the problem asked us to take the first derivative in respect to x, not y. With this information we can recognize we have another power rule. Due to there being a y in the second term, we must take a partial derivative. Taking the first derivative of $$xy$$ with respect to partial results in: $$(1*x^{0})*(y)$$. $$x^0 = 1$$ $$1 * 1 = 1$$ $$(1)(y) = y$$ The first derivative of x in relation to the second term is: $$y$$. Lastly, we have one more derivative left, being the last term $$20x^{5}$$. We realize this is the same case as our first term. Using the power rule gives us, $$20*5x^{5-1}$$, which equals $$100x^4$$. Therefore, the first order partial derivative in respect to x, $$f_x$$, is equal to $$40x^3+y+100x^4$$.

### Subject: Algebra

Given the following equation: y = 3x + 12, please find the slope of the equation.

Upon looking at the question, we are asked to find the slope of the equation. With knowledge of algebraic principles we can conclude this equation is in the form of slope-intercept. The general formula for slope-intercept is y = mx + b. variables in the formula: y being the y coordinate x being the x coordinate m being the slope b being the y intercept With knowing this information, we can re-observe the following equation and find the desired outcome: the slope of the equation. It is evident 3 is the slope. As the equation y = 3x + 12 shows the m variable being 3, which is the slope.

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