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# Tutor profile: Joe B.

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Joe B.
Patient Math and Physics Tutor
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## Questions

### Subject:Trigonometry

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Question:

Find the height of an upright telephone pole if you know that the length of the shadow of the telephone pole on level groun is 30 feet, and the angle between the ground to the imaginary line drawn from the tip of the pole's shadow to the top of the pole is 70 degrees.

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Joe B.

### Subject:Calculus

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Question:

Given the function f(x) = x^3 - 5*x^2 + x - 7 , solve for the slope of the plot of f(x) at x = 5.

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Joe B.

The definition of the derivative is the rate of change of a function with respect to a variable. In this case our variable is x = 5. In order to find the slope of the plot at x = 5 we can find the derivative of the given function and solve for x = 5. First we find the derivative of the given function: f'(x) is the derivative of the function f(x) We can find the derivative of each summed term in the function f(x) to find f'(x). Lets start with x^3. In this case the term is equivalent to 1*x^3 so the exponent is 3 and the leading multiplier is 1. To take the derivative of x^3 we will multiply the exponent by the leading multiplier to find the leading multiplier of the term's derivative (3 * 1 = 3). Then we will subtract 1 from the exponent to find the exponent of the term's derivative (3 - 1 = 2). Therefore, the derivative of the term x^3 is 3*x^2. We repeat this process for each summed term in f(x): -5*x^2 => -10*x x => 1*x^0 = 1 -7 => 0 We sum these term to get f'(x) = 3*x^2 - 10*x + 1 + 0 Now that we have the derivative of the given function, we plug in our variable (x = 5) to find the slope at our desired location: f'(5) = 3*(5)^2 - 10*(5) + 1 f'(5) = 75 - 50 + 1 f'(5) = 26 Our solution for the slope of our function f(x) at x = 5 is 26

### Subject:Physics

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Question:

Describe Newton's laws of motion in your own words and provide a real world situation where each law would apply.

Inactive
Joe B.

Newton's first law of motion states that a stationary object will remain stationary until acted on by a force, and an object in motion will continue in the same direction and rate of motion until acted on by a force. For example, if a asteroid is traveling through deep space it will maintain the same direction and rate of travel until it is influenced by a force such as a gravitational force or an impact from anther object. Newton's second law of motion states that when a force acts on an object, the change in velocity of the object, or acceleration, follows the relationship F=m*a which can be reorganized as a=F/m. where: F = Magnitude of force acting on the object (Newtons) m = mass of the object (kilograms) a = acceleration of the object (meters per second squared) For example, if we know that our asteroid has a mass of 1,000 kilograms, and experiences a force equivalent to 1,000 Newtons in one direction, then the acceleration of our asteroid will be a = F/m = (1,000N) / (1,000kg) = 1 m/s^2 in the same direction that the force is applied for as long as the force is applied. Newton's third law of motion states that "for every action there is an equal and opposite reaction". This can be interpreted as: for every applied force there is an equal and opposite reaction force. For example, lets assume that the force on the asteroid is performed by an astronaut with a mass of 100kg who is using their arms to push the asteroid with a force of 1,000N. The asteroid is still going to accelerate at 1 m/s^2 according to Newton's second law. However, our astronaut will experience the same force that they are exerting on the asteroid in the opposite direction that the asteroid experiences the force. Therefore, we can use Newton's second law applied to the astronaut to find that the astronaut's acceleration is a = F/m = (1,000N) / (100kg) = 10 m/s^2. Also remember that the astronaut's acceleration will be in the opposite direction of the asteroid's acceleration according to Newton's third law. The accelerations of the asteroid and astronaut will continue for as long as the astronaut is pushing on the asteroid. Once the asteroid and astronaut are separated due to their travel in opposite directions they will each travel in their own directions at a constant rate of motion according to Newton's first law.

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