Question

How do I solve this problem?​

Answer 1

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:

$ksin(\frac{\pi}{4})+(\frac{\pi}{4})^2=\frac{\pi}{4}+2$ and

$k(\frac{\sqrt{2} }{2})+\frac{\pi^2}{16}=\frac{\pi}{4}+2$ and we'll multiply everything by 16 to get rid of the fractions. Doing that gives us:

$8k\sqrt{2}=4\pi+32-\pi^2$ and

$k=\frac{4\pi+32-\pi^2}{8\sqrt{2} }$ 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:

$x +2=mlne^x$

We'll sub in e for x. ln of e to the x power is equal to x, so

e + 2 = me and

$m=\frac{e+2}{e}$ so

m = 1.736

Hope that helps!