Answer:
The transformation on the graph is a reflection across the x-axis.
Step-by-step explanation:
A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane. When reflecting a figure in a line or in a point, the image is congruent to the preimage. A reflection maps every point of a figure to an image across a fixed line.
In this particular figure, you see that each point is the same number of units away from the x-axis. For instance, with A and A' their both 1 unit away from the x-axis. So this is an automatic indicator that this transformation is a reflection.
Answer:
0.007502795
Step-by-step explanation:
We have
N = 10,000
Replacing these values in the expression for k:
So, the intensity is given by the function
The <em>total light intensity</em> is then
Since 
is an <em>even function</em>
and we only have to divide the interval ![\bf [0,10^{-6}]](https://tex.z-dn.net/?f=%20%5Cbf%20%5B0%2C10%5E%7B-6%7D%5D)
in five equal sub-intervals 
with midpoints 
The sub-intervals and their midpoints are
![\bf I_1=[0,\frac{10^{-6}}{5}]\;,m_1=10^{-5}\\I_2=[\frac{10^{-6}}{5},2\frac{10^{-6}}{5}]\;,m_2=3*10^{-5}\\I_3=[2\frac{10^{-6}}{5},3\frac{10^{-6}}{5}]\;,m_3=5*10^{-5}\\I_4=[3\frac{10^{-6}}{5},4\frac{10^{-6}}{5}]\;,m_4=7*10^{-5}\\I_5=[4\frac{10^{-6}}{5},10^{-6}]\;,m_5=9*10^{-5}](https://tex.z-dn.net/?f=%20%5Cbf%20I_1%3D%5B0%2C%5Cfrac%7B10%5E%7B-6%7D%7D%7B5%7D%5D%5C%3B%2Cm_1%3D10%5E%7B-5%7D%5C%5CI_2%3D%5B%5Cfrac%7B10%5E%7B-6%7D%7D%7B5%7D%2C2%5Cfrac%7B10%5E%7B-6%7D%7D%7B5%7D%5D%5C%3B%2Cm_2%3D3%2A10%5E%7B-5%7D%5C%5CI_3%3D%5B2%5Cfrac%7B10%5E%7B-6%7D%7D%7B5%7D%2C3%5Cfrac%7B10%5E%7B-6%7D%7D%7B5%7D%5D%5C%3B%2Cm_3%3D5%2A10%5E%7B-5%7D%5C%5CI_4%3D%5B3%5Cfrac%7B10%5E%7B-6%7D%7D%7B5%7D%2C4%5Cfrac%7B10%5E%7B-6%7D%7D%7B5%7D%5D%5C%3B%2Cm_4%3D7%2A10%5E%7B-5%7D%5C%5CI_5%3D%5B4%5Cfrac%7B10%5E%7B-6%7D%7D%7B5%7D%2C10%5E%7B-6%7D%5D%5C%3B%2Cm_5%3D9%2A10%5E%7B-5%7D)
<em>By the midpoint rule</em>
![\bf \int_{0}^{10^{-6}}I(\theta)d\theta\approx\frac{10^{-6}}{5}[I(m_1)+I(m_2)+...+I(m_5)]](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cint_%7B0%7D%5E%7B10%5E%7B-6%7D%7DI%28%5Ctheta%29d%5Ctheta%5Capprox%5Cfrac%7B10%5E%7B-6%7D%7D%7B5%7D%5BI%28m_1%29%2BI%28m_2%29%2B...%2BI%28m_5%29%5D)
computing the values of I:
Similarly with the help of a calculator or spreadsheet we find
and we have
![\bf \int_{0}^{10^{-6}}I(\theta)d\theta\approx\frac{10^{-6}}{5}[I(m_1)+I(m_2)+...+I(m_5)]=\frac{10^{-6}}{5}(18756.98654)=0.003751395](https://tex.z-dn.net/?f=%20%5Cbf%20%5Cint_%7B0%7D%5E%7B10%5E%7B-6%7D%7DI%28%5Ctheta%29d%5Ctheta%5Capprox%5Cfrac%7B10%5E%7B-6%7D%7D%7B5%7D%5BI%28m_1%29%2BI%28m_2%29%2B...%2BI%28m_5%29%5D%3D%5Cfrac%7B10%5E%7B-6%7D%7D%7B5%7D%2818756.98654%29%3D0.003751395)
Finally the the total light intensity
would be 2*0.003751395 = 0.007502795
13 + 9 = 22 feet
the angle is 50 degrees
multiply 22 x tan(50) to find the height of the lamppost
22 x tan(50) = 26.21
so the lamppost is about 26 feet tall
