# Tutor profile: Pablo D.

## Questions

### Subject: Spanish

Choose the right word to complete the sentence: "A Miguel se le rompió el vaso. Yo no tengo la ______" $$a)$$ confianza $$b)$$ vergüenza $$c)$$ razón $$d)$$ culpa

1) What does the sentence say? Miguel broke the glass. It's not my____ 2) What are the available options? $$a)$$ trust $$b)$$ embarrasment $$c)$$ reason $$d)$$ fault ANSWER: $$d)$$ culpa

### Subject: Electrical Engineering

What is the valuer of capacitance of a capacitor with 8V voltage and 16C of charge?

1) Establish relevant equations $$ Q = CV $$ $$ Q = $$ Charge held by the conductor $$ C = $$ Capacitance $$ V = $$ Electric Potential 2) Solve for missing variable $$ C = \frac{Q}{V} $$ 3) Substitute and find answer $$ C = \frac{Q}{V} = \frac{16}{8} = 2F $$ ANSWER: 2F

### Subject: Algebra

Solve the system with two variables using Cramer's Rule: $$4x - 3y = 11$$ $$6x + 5y = 7$$

1) Create the relevant matrices: coefficients, x, y $$$$ * Coefficient Matrix: \begin{bmatrix} 4 & -3\\ 6 & 5 \end{bmatrix} * X Matrix: \begin{bmatrix} 11 & -3\\ 7 & 5 \end{bmatrix} * Y Matrix: \begin{bmatrix} 4 & 11\\ 6 & 7 \end{bmatrix} 2) Find the Determinant of each matrix * Coefficient Matrix $$(D): (4)(5) - (-3)(6) = 38$$ * X Matrix $$(D_x): (11)(5) - (-3)(7) = 76$$ * Y Matrix $$(D_y): (4)(7) - (11)(6) = -38$$ 3) Solver for X and Y using the Cramer's rule formula $$ x = \frac{D_x}{D} = \frac{76}{38} = 2 $$ $$ y = \frac{D_y}{D} = \frac{-38}{38} = -1 $$ ANSWER: $$(x,y) = (2, -1)$$

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