Answer:
![4\sqrt{2b}](https://tex.z-dn.net/?f=4%5Csqrt%7B2b%7D)
Step-by-step explanation:
![\sqrt{98b}-\sqrt{72b}+\sqrt{18b}](https://tex.z-dn.net/?f=%5Csqrt%7B98b%7D-%5Csqrt%7B72b%7D%2B%5Csqrt%7B18b%7D)
Apply radical rule
:
![\implies \sqrt{98}\sqrt{b} -\sqrt{72}\sqrt{b} +\sqrt{18}\sqrt{b}](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%7B98%7D%5Csqrt%7Bb%7D%20-%5Csqrt%7B72%7D%5Csqrt%7Bb%7D%20%2B%5Csqrt%7B18%7D%5Csqrt%7Bb%7D)
Factor out common term
:
![\implies \sqrt{b}(\sqrt{98} -\sqrt{72}+\sqrt{18})](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%7Bb%7D%28%5Csqrt%7B98%7D%20-%5Csqrt%7B72%7D%2B%5Csqrt%7B18%7D%29)
Rewrite 98, 72 and 18:
![\implies \sqrt{b}(\sqrt{49 \cdot 2} -\sqrt{36 \cdot 2}+\sqrt{9 \cdot 2})](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%7Bb%7D%28%5Csqrt%7B49%20%5Ccdot%202%7D%20-%5Csqrt%7B36%20%5Ccdot%202%7D%2B%5Csqrt%7B9%20%5Ccdot%202%7D%29)
![\implies \sqrt{b}(\sqrt{49}\sqrt{2} -\sqrt{36}\sqrt{2}+\sqrt{9}\sqrt{2})](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%7Bb%7D%28%5Csqrt%7B49%7D%5Csqrt%7B2%7D%20-%5Csqrt%7B36%7D%5Csqrt%7B2%7D%2B%5Csqrt%7B9%7D%5Csqrt%7B2%7D%29)
![\implies \sqrt{b}(7\sqrt{2} -6\sqrt{2}+3\sqrt{2})](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%7Bb%7D%287%5Csqrt%7B2%7D%20-6%5Csqrt%7B2%7D%2B3%5Csqrt%7B2%7D%29)
Factor out common term
:
![\implies \sqrt{b}\sqrt{2}(7 -6+3)](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%7Bb%7D%5Csqrt%7B2%7D%287%20-6%2B3%29)
![\implies \sqrt{b}\sqrt{2}(4)](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%7Bb%7D%5Csqrt%7B2%7D%284%29)
![\implies 4\sqrt{2b}](https://tex.z-dn.net/?f=%5Cimplies%204%5Csqrt%7B2b%7D)
TTese are all parabolas whose axis of symmetry is the y axis. The negative coefficient means they open downwards and the positive mean they open upwards. The higher the absolute value of the coefficient is the greater the slope, so 2x^2 will be steeper than x^2 and -4x^2 will be steeper than - 2x^2.
So h(x) and j(x) are the answers.
The file won't open sorry
9514 1404 393
Answer:
1731 ft
Step-by-step explanation:
The tangent relation is useful in this problem.
Tan = Opposite/Adjacent
The height of the light is found to be ...
tan(11°) = height/(639 ft)
height = (639 ft)·tan(11°) . . . . . solve for height
Then the distance from the light to point B is ...
tan(3°) = height/(B distance)
B distance = height/tan(3°) = (639 ft)·tan(11°)/tan(3°) ≈ 2370 ft
Then the distance from point A to point B is ...
2370 ft -639 ft = 1731 ft . . . AB distance