# Tutor profile: Emma E.

## Questions

### Subject: Physics (Newtonian Mechanics)

A water balloon is dropped from a height of 15m. How long will it take to hit the ground?

To answer this question, let's use the equation: $$ d = \frac{1}{2}gt^{2} + vt $$ where $$ d $$ = distance, $$g$$ = acceleration due to gravity, $$t$$ = time, and $$v$$= initial velocity. In this case, we know that: $$d$$=15m, the height from which the water balloon was dropped. $$v$$=0, because the balloon was dropped, rather than thrown down with an initial speed $$g=9.8 m/s^{2}$$, the acceleration due to gravity Plugging these known values into the original equation gives us: $$15=\frac{1}{2}(9.8)t^{2}+0$$ To simplify this equation, we can simplify first by removing the 0 term. $$15=\frac{1}{2}(9.8)t^{2}$$ Then, multiply both sides of the equation by 2 to remove the fraction, yielding: $$30=(9.8)t^{2}$$ Next, divide both sides of the equation by 9.8, giving: $$3.06=t^{2}$$ Finally, take the square root of both sides, to have: $$1.75=t$$ Therefore, it will take 1.75 seconds for the water balloon to reach the ground.

### Subject: Geometry

An isosceles triangle has an interior angle of 75 degrees. What is the measurement of the largest angle in the triangle?

All 3 interior angles of a triangle must always add up to 360 degrees. An isosceles triangle has two angles that are the same measurement. We can set up the following equation to determine measurements of the angles of an isosceles triangle: 2y + x = 360. For this problem, let us consider two possible cases: 1) the known 75 degree angle is one of the two that are the same: If the 75 degree angle is one of the two that are the same, then 2(75) +x = 360. Solving this equation, we have x= 210. 2) the known 75 degree angle is not one of the two angles in the triangle that are the same: If the 75 degree angle is not one of the two that are the same, then 2y + 75 = 360. Solving this equation gives y = 142.5 However, the missing angle is larger in the first scenario, where the triangle is composes of two 75 degree angles and another 210 degree angle. As a result, the answer to this question is 210 degrees.

### Subject: Algebra

Solve the equation: $$ 5(x-2)+4=6 $$

Equations can be solved in a variety of ways. Here is one solution path: First, simplify the equation by subtracting $$ 4 $$ from both sides to have $$ 5(x-2) = 6 $$ Next, utilize the distributive property to multiply $$ 5$$ to both terms inside the parentheses, giving $$ 5x - 10 = 6 $$ Simplify the equation once again by adding 10 to both sides, leaving $$ 5x = 16 $$ Finally, divide the entire equation by 5 to yield $$ x =\frac{16}{5} $$. In this case, the solution is a fraction. The solution can always be verified by plugging in the solution to the original equation, like so: $$ 5 (\frac{16}{5} - 2)+4 = 6 $$

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