# Tutor profile: Alexander C.

## Questions

### Subject: Spanish

Conjugate these verbs for all personal pronouns in the preterite tense: Haber, Tener, Poder

Haber (To have) yo hube nosotros hubimos tu hubiste vosotros hubisteis el/ella/ud. hubo ellos.ellas/uds. hubieron Tener (To hold) yo tuve nosotros tuvimos tu tuviste vosotros tuvisteis el/ella/ud. tuvo ellos.ellas/uds. tuvieron Poder (To be able to) yo pude nosotros pudimos tu pudiste vosotros pudisteis el/ella/ud. pudo ellos.ellas/uds. pudieron

### Subject: Calculus

A racecar's position is determined by the equation d(t) = -3t^3 + 2t^2, where d is measured in meters, and t is measured in seconds, at the 5th second what is the velocity of the racecar?

We know that velocity is the rate of change of position (with respect to time) and we have the equation to the position of the racecar. This means that we can take the derivative of the position equation to find the velocity equation We will use the short-way method of taking a derivate (with respect to time) by multiplying the exponent to the coefficient and subtracting 1 from the exponent Which means the derivative of the equation d(t) = -3t^3 + 2t^2 is v(t) = -3*2 t^(3-1) + 2*2 t^(2-1) v(t) = -6t^2 + 4t We are not finished, however, Now we have to figure out the velocity of the racecar, SPECIFICALLY, at the 5th second, (t=5), which we do by plugging in t=5 into the velocity equation v(5) = -6*(5)^2 + 2*(5) v(5) = -6*25 + 10 v(5) = -150 +10 = -140 The velocity of the car is -140 m/s

### Subject: Algebra

The area of a farm plot in Montana is 8 km^2. The width is 2 less than 3 times the length. What are the length and width of the rectangular plot of farmland?

First, we have to define our variables. We will let the length be represented by L, and we will let the width be represented by W. According to the problem, we can represent the length and width in terms of, L, the length. So mathematically, the problem states: the width, W = 3 times L (length) - (less than) 2 --> W = 3L - 2 the length is just L Now we need an equation so we can isolate our variable L, and we know the area, according to the problem, and we know the equation to find the area of a rectangle: A = W*L (Now we can replace W with the above expression and write the area equation as:) A = (3L - 2) * L Now since we know how to distribute and we know what A (the area) is, this can be turned into 8 = 3L^2 - 2L Here we have a quadratic equation! We can move the 8 to make it standard form: 0 = 3L^2 - 2L - 8 Now we can use the FOIL method to solve the quadratic equation 0 = (3L + 4) (L - 2) L = -4/3 , 2 We know that a measurement of a real object can't be negative so our L (length) is 2 km To find W (width), we plug it back into our original expression W = 3 ( 2) - 2 = 4, which means our width is 4 km

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