Answer:
![\textsf{A)}\quad y=-\sqrt{x}+2](https://tex.z-dn.net/?f=%5Ctextsf%7BA%29%7D%5Cquad%20y%3D-%5Csqrt%7Bx%7D%2B2)
Step-by-step explanation:
Parent function:
![y = \sqrt{x}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%7Bx%7D)
The properties of the parent function are:
- Starts at the origin, so y-intercept is at (0, 0)
- Domain: x ≥ 0
- Range: y ≥ 0
- As x increases, y increases
From inspection of the graph, as the x-values increase, the y-values decrease. Therefore there has been a <u>reflection in the x-axis</u>.
The y-intercept is now at (0, 2), therefore the function has been <u>translated 2 units up</u>.
<u>Translations</u>
For a > 0
![y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}](https://tex.z-dn.net/?f=y%3D-f%28x%29%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Breflected%20in%20the%7D%20%5C%3A%20x%20%5Ctextsf%7B-axis%7D)
![f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}](https://tex.z-dn.net/?f=f%28x%29%2Ba%20%5Cimplies%20f%28x%29%20%5C%3A%20%5Ctextsf%7Btranslated%7D%5C%3Aa%5C%3A%5Ctextsf%7Bunits%20up%7D)
Therefore:
Reflected in the x-axis: ![-f(x)=-\sqrt{x}](https://tex.z-dn.net/?f=-f%28x%29%3D-%5Csqrt%7Bx%7D)
Then translated 2 units up: ![-f(x)+2=-\sqrt{x}+2](https://tex.z-dn.net/?f=-f%28x%29%2B2%3D-%5Csqrt%7Bx%7D%2B2)
So the equation that represents the transformed function is:
![y=-\sqrt{x}+2](https://tex.z-dn.net/?f=y%3D-%5Csqrt%7Bx%7D%2B2)
I might be wrong, but here;
You don’t add your salary until the very end.
4.75•50,000=237,500
Now add the salary,
Your answer should be $238,000
100mi(5280ft/mi)(12in/ft)($1/6.06in)=$1045544.55 (to nearest cent)
Answer:
6 feetand 8 feet wide
Step-by-step explanation:
Answer:
![{\bf e}_{1}=\frac{(-1,1,0)}{\lVert (-1,1,0) \rVert}=\left(\frac{-1}{\sqrt{2}},\frac{1}{\sqrt{2}},0\right)](https://tex.z-dn.net/?f=%7B%5Cbf%20e%7D_%7B1%7D%3D%5Cfrac%7B%28-1%2C1%2C0%29%7D%7B%5ClVert%20%28-1%2C1%2C0%29%20%5CrVert%7D%3D%5Cleft%28%5Cfrac%7B-1%7D%7B%5Csqrt%7B2%7D%7D%2C%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%2C0%5Cright%29)
![{\bf e}_{2}=\frac{{\bf v}_{2}-({\bf v}_{2}\cdot {\bf e}_{1}) {\bf e}_{1}}{\lVert {\bf v}_{2}-({\bf v}_{2}\cdot {\bf e}_{1}) {\bf e}_{1} \rVert}=\left(\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},\sqrt{\frac{2}{3}}\right)](https://tex.z-dn.net/?f=%7B%5Cbf%20e%7D_%7B2%7D%3D%5Cfrac%7B%7B%5Cbf%20v%7D_%7B2%7D-%28%7B%5Cbf%20v%7D_%7B2%7D%5Ccdot%20%7B%5Cbf%20e%7D_%7B1%7D%29%20%7B%5Cbf%20e%7D_%7B1%7D%7D%7B%5ClVert%20%7B%5Cbf%20v%7D_%7B2%7D-%28%7B%5Cbf%20v%7D_%7B2%7D%5Ccdot%20%7B%5Cbf%20e%7D_%7B1%7D%29%20%7B%5Cbf%20e%7D_%7B1%7D%20%5CrVert%7D%3D%5Cleft%28%5Cfrac%7B1%7D%7B%5Csqrt%7B6%7D%7D%2C%5Cfrac%7B1%7D%7B%5Csqrt%7B6%7D%7D%2C%5Csqrt%7B%5Cfrac%7B2%7D%7B3%7D%7D%5Cright%29)
![{\bf e}_{3}=\frac{{\bf v}_{3}-({\bf v}_{3}\cdot{\bf e_{1}}){\bf e}_{1}-({\bf v}_{3}\cdot {\bf e}_{2}){\bf e}_{2}}{\lVert {\bf v}_{3}-({\bf v}_{3}\cdot{\bf e_{1}}){\bf e}_{1}-({\bf v}_{3}\cdot {\bf e}_{2}){\bf e}_{2} \rVert}=\left(-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\right)](https://tex.z-dn.net/?f=%7B%5Cbf%20e%7D_%7B3%7D%3D%5Cfrac%7B%7B%5Cbf%20v%7D_%7B3%7D-%28%7B%5Cbf%20v%7D_%7B3%7D%5Ccdot%7B%5Cbf%20e_%7B1%7D%7D%29%7B%5Cbf%20e%7D_%7B1%7D-%28%7B%5Cbf%20v%7D_%7B3%7D%5Ccdot%20%7B%5Cbf%20e%7D_%7B2%7D%29%7B%5Cbf%20e%7D_%7B2%7D%7D%7B%5ClVert%20%7B%5Cbf%20v%7D_%7B3%7D-%28%7B%5Cbf%20v%7D_%7B3%7D%5Ccdot%7B%5Cbf%20e_%7B1%7D%7D%29%7B%5Cbf%20e%7D_%7B1%7D-%28%7B%5Cbf%20v%7D_%7B3%7D%5Ccdot%20%7B%5Cbf%20e%7D_%7B2%7D%29%7B%5Cbf%20e%7D_%7B2%7D%20%5CrVert%7D%3D%5Cleft%28-%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%2C-%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%2C%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%5Cright%29)
Step-by-step explanation:
We have the basis of
. From this basis we want to determine another orthonormal basis
of
.
The first step is to define
as:
![{\bf e}_{1}=\frac{(-1,1,0)}{\lVert (-1,1,0) \rVert}=\left(\frac{-1}{\sqrt{2}},\frac{1}{\sqrt{2}},0\right)](https://tex.z-dn.net/?f=%7B%5Cbf%20e%7D_%7B1%7D%3D%5Cfrac%7B%28-1%2C1%2C0%29%7D%7B%5ClVert%20%28-1%2C1%2C0%29%20%5CrVert%7D%3D%5Cleft%28%5Cfrac%7B-1%7D%7B%5Csqrt%7B2%7D%7D%2C%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%2C0%5Cright%29)
Now define
by:
![{\bf e}_{2}=\frac{{\bf v}_{2}-({\bf v}_{2}\cdot {\bf e}_{1}) {\bf e}_{1}}{\lVert {\bf v}_{2}-({\bf v}_{2}\cdot {\bf e}_{1}) {\bf e}_{1} \rVert}=\left(\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},\sqrt{\frac{2}{3}}\right)](https://tex.z-dn.net/?f=%7B%5Cbf%20e%7D_%7B2%7D%3D%5Cfrac%7B%7B%5Cbf%20v%7D_%7B2%7D-%28%7B%5Cbf%20v%7D_%7B2%7D%5Ccdot%20%7B%5Cbf%20e%7D_%7B1%7D%29%20%7B%5Cbf%20e%7D_%7B1%7D%7D%7B%5ClVert%20%7B%5Cbf%20v%7D_%7B2%7D-%28%7B%5Cbf%20v%7D_%7B2%7D%5Ccdot%20%7B%5Cbf%20e%7D_%7B1%7D%29%20%7B%5Cbf%20e%7D_%7B1%7D%20%5CrVert%7D%3D%5Cleft%28%5Cfrac%7B1%7D%7B%5Csqrt%7B6%7D%7D%2C%5Cfrac%7B1%7D%7B%5Csqrt%7B6%7D%7D%2C%5Csqrt%7B%5Cfrac%7B2%7D%7B3%7D%7D%5Cright%29)
Now define
by :
![{\bf e}_{3}=\frac{{\bf v}_{3}-({\bf v}_{3}\cdot{\bf e_{1}}){\bf e}_{1}-({\bf v}_{3}\cdot {\bf e}_{2}){\bf e}_{2}}{\lVert {\bf v}_{3}-({\bf v}_{3}\cdot{\bf e_{1}}){\bf e}_{1}-({\bf v}_{3}\cdot {\bf e}_{2}){\bf e}_{2} \rVert}=\left(-\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\right)](https://tex.z-dn.net/?f=%7B%5Cbf%20e%7D_%7B3%7D%3D%5Cfrac%7B%7B%5Cbf%20v%7D_%7B3%7D-%28%7B%5Cbf%20v%7D_%7B3%7D%5Ccdot%7B%5Cbf%20e_%7B1%7D%7D%29%7B%5Cbf%20e%7D_%7B1%7D-%28%7B%5Cbf%20v%7D_%7B3%7D%5Ccdot%20%7B%5Cbf%20e%7D_%7B2%7D%29%7B%5Cbf%20e%7D_%7B2%7D%7D%7B%5ClVert%20%7B%5Cbf%20v%7D_%7B3%7D-%28%7B%5Cbf%20v%7D_%7B3%7D%5Ccdot%7B%5Cbf%20e_%7B1%7D%7D%29%7B%5Cbf%20e%7D_%7B1%7D-%28%7B%5Cbf%20v%7D_%7B3%7D%5Ccdot%20%7B%5Cbf%20e%7D_%7B2%7D%29%7B%5Cbf%20e%7D_%7B2%7D%20%5CrVert%7D%3D%5Cleft%28-%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%2C-%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%2C%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%5Cright%29)