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Justin R.

Student at Stanford University, Online Tutor for 2 years

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Calculus

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Question:

Find the derivative of 9x - sin(x)

Justin R.

Answer:

Since we are not multiplying or dividing multiple terms with x in them, we simply take the derivative of each term separately. The derivative of 9x is 9 (essentially using the power rule to get 9 * 1 * x^0, which is the same as 9). The derivative of sin(x) is cos(x). Our overall result is d/dx(9x - sin(x)) = 9 - cos(x)

Economics

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Question:

What (if anything) happens in the supply and demand model of the market for cars when there is an increase in the cost of manufacturing engines?

Justin R.

Answer:

Since there was a rise in the price of an input in the car manufacturing process, firms that produce cars are going to produce a smaller quantity of cars at every possible price. The supply curve is going to shift to the left. This will initially create a shortage, and consumers will bid the price of cars up to reach a new equilibrium at a higher price. Overall, quantity supplied decreased and price increased.

Algebra

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Question:

Solve for x: 5x + 29 = 34

Justin R.

Answer:

First, isolate x by subtracting 29 from both sides: 5x = 34 - 29 5x = 5 Now, divide both sides by 5 to get your answer: x = 1

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