Tutor profile: Jose G.

What is the value of the unknown angle in the following isosceles triangle: side a = 40 degrees, side b = 40 degrees side c = ?

As a general rule, the sum of the angles from all three sides of a triangle equal to 180 degrees. Another assumption that can be made from the problem statement is that an isosceles triangle is made of two equal sides. Therefore, 40 + 40 + x = 180 80 + x = 180 x = 180 - 80 = 100 Side c is equal to 100 degrees.

Evaluate the following function using integration in order to determine the area under the curve: X^3, with bounds a = 0 and b = 2.

The operation of integration involves integrating the function of interest based on its identity. In this case, a formula of the form a^n will be integrated into a^(n+1)/(n+1). Therefore, integral(x^3) = x^4/4 Considering the bounds of the integral to evaluate the area under the curve, the difference between the integrated formula evaluated at the second bound (b = 0) and the first bound ( a = 0) must be calculated. [(2)^4/4] - [(0)^4/4] = 16/4 - 0 = 4 - 0 = 4

A ball is thrown at a velocity of 12 m/s at an angle of 32 degrees from the horizontal. What are the ball's horizontal and vertical velocities?

In order to evaluate the horizontal and vertical components of the ball being thrown, the cosine and sin functions must be used. The cosine function determines the horizontal component, and the sin function evaluates the vertical component. Using this assumption, Vx = (12 m/s)*cos(32) = 10.18 m/s (horizontal component) Vy = (12 m/s)*sin(32) = 6.36 m/s (vertical component)