Answer:
Step-by-step explanation:
The first 2 pieces of this function agree at pi/4, so we will set them equal to each other and sub in pi/4 for x to solve for k:
[tex]ksin(\frac{\pi}{4})+(\frac{\pi}{4})^2=\frac{\pi}{4}+2[/tex] and
[tex]k(\frac{\sqrt{2} }{2})+\frac{\pi^2}{16}=\frac{\pi}{4}+2[/tex] and we'll multiply everything by 16 to get rid of the fractions. Doing that gives us:
[tex]8k\sqrt{2}=4\pi+32-\pi^2[/tex] and
[tex]k=\frac{4\pi+32-\pi^2}{8\sqrt{2} }[/tex] so
k = 3.067
The next one is a bit tricky if you're not up on your natural log equations.
Again, we set these equal to each other because they meet at the value of e. We sub in e for x and solve for m:
[tex]x +2=mlne^x[/tex]
We'll sub in e for x. ln of e to the x power is equal to x, so
e + 2 = me and
[tex]m=\frac{e+2}{e}[/tex] so
m = 1.736
Hope that helps!
