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John F.

Math, Science, Business Tutor

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HTML Programming

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Question:

What is HTML and how is it used?

John F.

Answer:

HTML stands for Hypertext Markup Language and it is a robust, yet simple language that allows any web connected device to send, interpret, and display information. If you are looking to pursue a career as a web developer or just want to build a website in your free time HTML/CSS is the place to start!

Computer Science (General)

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Question:

FUNCTION BASICS: Write a function to find and return the length of a line, given two coordinate points.

John F.

Answer:

The following answer uses Python syntax. ##Take as input 4 numbers: two x-coordinates, two y-coordinates def line_length(x1, y1, x2, y2): ##Use the formula length = square root((x1 - x2)^2 + (y1 - y2)^2) length = (int(x1)-int(x2))**2 + (int(y1)-int(y2))**2 length = math.sqrt(length) ##return length as a float return length

Calculus

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Question:

Consider a rectangular bathtub whose base is 18ft^2. How fast is the water level rising if the tub fills up at a rate of 0.7 ft^3/min?

John F.

Answer:

To answer this question, it is best to first draw a rectangular prism and set the base equal to 18 ft^2. We do not know the height, nor do we need to. To solve this problem follow these steps: 1. Write down the equation for volume a rectangular prism V = b * h Fill in the variables we have values for. In this case we know the base is 18 ft^2. V = 18h 2. Take the derivative of the volume equation dV/dt = 18dh/dt The derivative of V is dV/dt and the derivative of h is dh/dt. A derivative is a "rate of change" by definition. With this in mind, the derivative of V is the rate at which the volume of water in the tub is increasing. So dV/dt is 0.7 ft^3/min. The equation is now: 0.7 = 18(dh/dt) 3. Isolate dh/dt (the rate at which the water level is increasing) by dividing both sides by 18. This gets you: 1/18(0.7) = dh/dt. 4. Solve! 1/18(0.7) = 0.039 ft/second

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