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Nikhil C.
Student at University of Pittsburgh
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Calculus
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Question:

$$\int tan^2(x)*sec^2(x) dx$$

Nikhil C.

Let $$u=tan(x)$$, $$du=sec^2(x)dx$$. Thus, $$\int tan^2(x)*sec^2(x) dx$$ = $$\int u^2 du$$ $$=u^3/3$$ Substitute $$u=tan(x)$$. $$=tan^3(x)/3$$

Economics
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Question:

What is the classic Keynesian response to a recession?

Nikhil C.

The Keynesian side of economics is also known as demand side economics because Keynesian economists try to implement changes in the economy by increasing or decreasing aggregate demand. Thus, since the question states that the economy is currently in a recession, the response should be to increase aggregate demand. This can be done by either increasing government spending or decreasing taxes so that consumers have greater disposable income and spend more.

Physics
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Question:

Suppose a fast moving car encounters a strip of black ice. Would it be more desirable for the driver to keep the wheels rolling or slam the brakes causing the wheels to lock up?

Nikhil C.

The driver should definitely keep the wheels rolling. This action may seem illogical but makes sense after some thought. This is primarily true because static friction is greater than kinetic friction. Static friction exists when the wheels are rolling without locking up on the ice, resulting in the maximum braking force. On the other hand, using the brakes strongly causes the wheels to lock up which results in relative slipping between the car and the surface and causes kinetic friction to take over. This means that the braking force is not maximal, and thus, the car will take longer to stop. The wheels locking up is also harmful because the driver then has less control of the vehicle and cannot steer properly. Thus, the odds of an accident are clearly higher when the driver slams the brakes.

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