# Tutor profile: Rachel V.

## Questions

### Subject: Basic Math

What does [(7+4)+5]-3 equal?

Using PEMDAS, you must first solve the parenthesis. There for solve 7+4 = 11, resulting in a new equation of: [11+5]-3. Continuing using the parenthesis, you must solve 11+5. This results in a new equation of [16]-3. Next, subtract these two numbers (16-3) to get an answer: 13.

### Subject: Calculus

A plane is flying directly away from you at 500 mph at an altitude of 3 miles. How fast is the plane's distance from you increasing at the moment when the plane is flying over a point on the ground 4 miles from you?

To better understand this related rate problem, it is helpful to draw a schematic. From the question, you can see that the rate (dx/dt) that the plane moves away from you is 500 mph. The distance between you and the plane is equal to y. Therefore, using the pythagorean theorem, you can solve the equation x^2+9=y^2. Since you are given dx/dt, you must take the derivative of this equation, resulting in 2x (dx/dt) = 2y (dy/dt). The problem asks that you find what y is equal to when x = 4. You can plug 4 back into the pythagorean theorem to find that when x=4, y = 5. Then, plug x=4,y=5, and dx/dt =500 into the derivative and solve for dy/dt. Thus, dy/dt = 400 mph.

### Subject: Algebra

What is the equation of the line perpendicular to the line y=3x+4?

Lines that are perpendicular to another have a slop that is the reciprocal to the slope in the equation. In this equation, the slop (m) is equal to 3. To find the reciprocal of this number you need to reverse it. For example, the reciprocal of 3 is 1/3. Therefore, the equation of the line perpendicular to y=3x+4 is equal to y = (1/3)x+4

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