Tutor profile: Danielle M.
Subject: Basic Math
What is 99 + 99 + 99 using mental math only?
This problem may seem daunting at first, but with a little addition and subtraction, we can make this problem much easier on ourselves. First, I'm going to add 1 to each 99, making each 100. Now I have 100+100+100, remembering I've added 3 to make it look this way. The problem seems very doable now, as I know that 100 + 100 +100 is 300! Now, I'm going to take the 3 I added away, to get 297. So 99 + 99 + 99 is 297, and we did this without a calculator!
What is a derivative of a function?
A derivative of a function can be explained in a few different ways. The most approachable is that a derivative is just a way to show the rate of change of a function. In other words, how the y component of a function changes as the x component changes. Another way to understand derivative is as the slope of the tangent line. If we zoom in on a graph of a function, to the point where the function almost looks like a straight line, the derivative is the slope of that line. The derivative itself is also a function, as it can vary from place to place.
A student with a banana goes out in the woods to look for monkeys and sees one hanging in a tree. The student wants to give his banana to the monkey, so he decides to throw it. The monkey releases its grip the instant the student throws his banana. Where should the student aim in order to hit the monkey?
To hit the monkey, the student must aim the banana AT the monkey. This is because gravity is accelerating the monkey and the banana towards the ground at the same rate (9.81m m/s^2). Therefore, the monkey and the banana fall the same distance at the same time. Gravity acts only on an object's vertical velocity, and not its horizontal velocity; the fact that the banana is traveling horizontally makes no difference in how fast it is falling. The horizontal and vertical velocities of the banana are independent! Let's phrase it another way. If you were able to drop the banana from the same spot that the monkey is hanging, you would expect them to hit the ground at the same time... so why should the fact that the banana is moving horizontally make any difference? Velocities in the horizontal and vertical direction of projectiles is an important part of projectile motion, and this understanding of their independence will provide very useful in any projectile motion problems!
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