Answer:
Step-by-step explanation:
Graph the parent function y = |x|. This graph has a v shape with vertex at (0, 0) and opens up.
Now translate the entire graph 6 units to the right. The vertex will now be at (6, 0).
Finally, translate this most recent graph 4 units down. The vertex will now be at (6, -4).
Compare your f(x)=1/2tan (2x+5) to
g(x)=a*tan (bx + c).
Note how b = 2.
The period of the given tangent function is pi/b, which here is pi/2, or 90 degrees. Multiplying x by 2 horizontallyl compresses the graph of tan x by a factor of 1/2.
Using the law os cosines formula b^2 = a^2 + c^2 - 2*a*c*cos(B)
a = 17, b = 8, c = 16
8^2 = 17^2 + 16^2 - 2*17*16* cos(B)
64 = 289 + 256 - 544 * cos(B)
544*cos(B) = 289 + 256 - 64
544 * cos(B) = 481
cos (B) = 481/544
B = arccos(481/544)
B = 27.8 degrees
23/4 miles is as much as 5 3/4 miles. We can also write it as a decimal, because 5 3/4 = 5,75 miles.
If Ammar hikes 5,75 miles in 1 1/4 hour, then we need to find out what distance does he hike in 1/4 hour (15 minutes). To do that we can just divide 5,75 by 5 (because dividing 1 1/4 by 5 will give us 1/4 we're looking for).
5,75 / 5 = 1,15
It means that in one hour Ammar hikes 5,75 - 1,15 = 4,6 miles.
We can also write it as a fraction:
4,6 = 4 6/10 = 4 3/5 = 23/5 miles
Just pick whichever form you like :)
