Answer:
k = 7
Step-by-step explanation:
Vertical shift down by 7units, f(x) - 7
g(x) = (0.5)x - 7
g(x) = (0.5)x - k
Comparing both equations, k = 7
We have two similar triangles, the one as a whole and the one inside of it. To calculate the height of the flagpole we can set up a proportion. First calculate the length of the base of the smaller triangle.
16.60 - 12.45 = 4.15m
The height is 1.65m, set up a proportion:
![\sf\dfrac{1.65}{4.15}=\dfrac{x}{16.60}](https://tex.z-dn.net/?f=%5Csf%5Cdfrac%7B1.65%7D%7B4.15%7D%3D%5Cdfrac%7Bx%7D%7B16.60%7D)
Cross multiply:
![\sf 27.39=4.15x](https://tex.z-dn.net/?f=%5Csf%2027.39%3D4.15x)
Divide 4.15 to both sides:
![\sf x=\boxed{\sf 6.6m}](https://tex.z-dn.net/?f=%5Csf%20x%3D%5Cboxed%7B%5Csf%206.6m%7D)
So the height of the flagpole is 6.6 meters tall.
The are of the circle is 3.14
I got this answer from someone else so I’m not sure this is correct but I really hope it helps...
Step-by-step explanation:
Look for patterns in the derivatives.
y=cos2x
y'=-2sin2x
y''=-4cos2x
y'''=8sin2x
y''''=16cos2x
Notice that sin and cos alternate every derivative. Also, they alternate positive and negative every 2 derivatives.
The constant is just 2^(derivative#).
Every odd derivative has sin and every even derivative has cos, so you know that the 30th derivative will be cos.
If you follow the pattern of negatives and positives, you find that the 30th derivative will be negative.
y^(30)= -2^30cos2x
y^(30)= -1073741824cos2x