Tuesday, January 24, 2017

When solving an SSA triangle, you could possible have 0,1 or 2 triangles

Suppose in triangle ABC, you know side a = 10, b = 16 and angle A is 30 degrees

By the law of sines,

SinB/16 = Sin30/10

10*sinB = (1/2)!6

SinB = 0.8, therefore B = 53.1 degrees. But sine is also positive in the second quadrant, so there is a possible second triangle with B = 126.9 degrees. This can work because C would equal 23.1 degrees in this triangle and C = 96.9 in the first triangle

If angle A was 60 degrees and B came out to 53.1 or 126.9 then only 1 triangle exists since (126.9 + 60 = 186.9) angle C + angle A > 180.

If you try to solve for an angle an get Sin > 1 or < -1 then there are no solutions.

Friday, January 13, 2017

suppose we want a linear approximation for sin(0.3). Look at the function sinx, where x = 0.3 We want to pick a value for a to approximate x, a value for which we know the sin. We know sin0 = 0, so choose a = 0, which is close to x =0.3.

Now use the formula L(x) (linear approximation as function of x) = f(a) + f'(a)(x-a)

f(0) = 0
f'(x) = cosx, so f'(a) = f'(0) = 1

L(x) = 0 + 1(0.3 - 0)

= 0 + 0.3

=0.3

The value of sin(0.3) = .295. so the approximation is close.  Note that the value of x = 0.3 is in radians

Sunday, January 1, 2017

Roger's statement isn't exactly correct, as it doesn't make sense that a movie would make 3.8735 million dollars without any money put into the production of the movie. A movie cannot even be produced with money budgeted.
Looking at the definition of a linear equation of the regression line, y = a + bx or sometimes written as y = b0 +b1(x). The y-intercept is b0, which is the value when x is 0.
In this case by definition x being the budget and y being the revenue, yes with 0 dollars for budget, the revenue is 3.8735.
But we have to look at practicality with our conclusion. Like I mentioned above, this makes no sense in the context of the problem. So, we cannot make this conclusion. The y-intercept in this case is something we shouldn't even consider because you will never have a budget of 0 dollars.