To solve this you would use the pythagorean theorem since the brace is making the frame look like two right triangles. The theorem states that for a triangle with a right angle, A^2+B^2=C^2. A and B are the sides of the frame and C is the brace which is like the hypotenuse of the triangle. It doesn't matter which side is A or B so you can put 6 or 8 in place of either in the equation. 6^2+8^2=C^2. If you simplify this it equals 36+64=C^2, which then simplifies to 100=C^2. Then you take the square root of both sides (what number multiplied by itself = the number you are trying to get, in this case, 100). So then you get C=10 because 10x10=100. So the length of the diagonal brace is 10ft.

4 0

3 years ago

How would you "remove the discontinuity" of f ? In other words, how would you define

balu736 [363]

There is a hole at x=4 because the top factors to (x-4)(x+3)
in the end we get

f(x)=(x-4)(x+3)/(x-4)
the (x-4) cancels out and we get
f(x)=x+3
so baiscally f(x) is y=x+3 but with a hole at (4,7)

one way is to make a piecewise function defined as(x^2-x-12)/(x-4) for all x≠4 and defined as 7 for x=4

or, to just do f(x)=x+3

5 0

3 years ago