# Tutor profile: Faminan T.

## Questions

### Subject: Calculus

The area of a rectangle is 15 square meters and the perimeter is 16 square meters. What are the dimensions of the rectangle?

Let x and y be respectively the length and width of the rectangle. The area of the rectangle is 15 square meters means: xy=15 The perimeter of the rectangle is 16 meters means: 2(x+y)=16 2(x+y) = 16 (x+y) = 8 x = 8 - y "we will replace x by (8 - y)" xy = 15 (8 - y)y = 15 8y - y^2 = 15 -y^2 + 8y -15 = 0 -(-y^2 + 8y -15) = 0 y^2 - 8y + 15 = 0 Now let us solve for y Delta = (8^2) - 4(1)(15) = 64 -60 Delta = 4 sqrt (Delta) = 2 y_1 = (8-2)/2 = 3 y_2 = (8+2)/2 = 5 _______________________CASE 1_____________________________ When y = 3, x = 15/y = 15/3 = 5 or x = 8 - y = 8 - 3 = 5 Both equations verify y=3 and x = 5 ______________________CASE 2________________________________ When y = 5, x = 15/y = 15/5 = 3 or x = 8 - y = 8 - 5 = 3 Both equations verify y=5 and x = 3 ___________________CONCLUSION_____________________________ x being the length and y the width, as a result x > y (x is superior than y) x = 5 y = 3

### Subject: Algebra

Evaluate f(4) - f(1) f(x) = -4(2x+3)

f(4) = -4 (2(4)+3) = -4 (8+3) = -4(11) f(4) = -44 f(1) = -4 (2(1)+3) = -4 (2+3) = -4 (5) f(1) = -20 f(4) - f(1) = (-44) - (-20) = -44+20 f(4) - f(1) = -24

### Subject: Physics

What is the relationship between Distance, Speed, and Acceleration

- As the word speaks for himself, Distance is the difference between two positions. - Speed (in simple terms) is distance over time. For example, you drive 60 miles in 1 hour. The speed is 60 miles per hour (mph). More generally, speed is the variation of position over time. In other words, it is the rate of change of position over time. "Variation" and "rate of change" is the perfect synonym for "Derivative." That is the reason why speed is generally defined as the derivative of distance of time. V=(dx/dt) and the unit is (meter/second) or m/s - Acceleration is the change of speed over time. For example, let suppose you are driving at 60mph. When you accelerate from 60mph to 70mph in 20 seconds, there is an acceleration usually denoted "a". The variation of speed is 10mph and the acceleration is a=(10mph/20s). a=(dv/dt) and the unit is (m/s^2) Note that International System (SI) require distance to be in "meters" and time in "seconds." 10 miles = 16,030 meters 1 hour = 3,600 seconds 10 mph = 16,030 meters / 3,600 seconds 10 mph = 4.45 m/s a = (4.45 m/s)/(20 s) = 0.22 m / s^2 Just view things like in real life

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