Answer:
The last option
Step-by-step explanation:
Take a look at the graph
![4p+ 1 < -11 \\ 6p+3> 39\\\\\begin{bmatrix}y6\end{bmatrix}\quad \mathrm{No\:Solution}](https://tex.z-dn.net/?f=4p%2B%201%20%3C%20-11%20%5C%5C%206p%2B3%3E%2039%5C%5C%5C%5C%5Cbegin%7Bbmatrix%7Dy%3C-3%5C%5C%20y%3E6%5Cend%7Bbmatrix%7D%5Cquad%20%5Cmathrm%7BNo%5C%3ASolution%7D)
Answer:
0.251 kg
Step-by-step explanation:
To convert from grams to kilograms, we divide the # of grams by 1000, or move the decimal point to the right by 3.
Therefore, the answer is 0.251 kg.
Answer:
The change in the angle of elevation is approximately 63.435°
Step-by-step explanation:
The given parameters are;
The speed of the tightrope walker = 3 ft./sec
The altitude at which the tightrope walker is moving = 100 ft.
The horizontal distance of the tightrope walker from the searchlight = 200 feet
The final angle of elevation, θ, is given by the trigonometric ratio as follows;
![tan\angle \theta = \dfrac{Opposite \ leg \ length}{Adjacent\ leg \ length} = \dfrac{Elevation \ of \, the \ tightrope}{Horizontal \ distance \ to \ the \ tight rope \ walker}](https://tex.z-dn.net/?f=tan%5Cangle%20%5Ctheta%20%3D%20%5Cdfrac%7BOpposite%20%5C%20leg%20%5C%20length%7D%7BAdjacent%5C%20leg%20%5C%20length%7D%20%3D%20%5Cdfrac%7BElevation%20%5C%20of%20%5C%2C%20the%20%5C%20tightrope%7D%7BHorizontal%20%5C%20distance%20%20%5C%20to%20%5C%20the%20%5C%20tight%20rope%20%5C%20walker%7D)
![tan\angle \theta = \dfrac{Elevation \ of \, the \ tightrope}{Horizontal \ distance \ to \ the \ tight rope \ walker} = \dfrac{100}{200} = \dfrac{1}{2}](https://tex.z-dn.net/?f=tan%5Cangle%20%5Ctheta%20%3D%20%20%5Cdfrac%7BElevation%20%5C%20of%20%5C%2C%20the%20%5C%20tightrope%7D%7BHorizontal%20%5C%20distance%20%20%5C%20to%20%5C%20the%20%5C%20tight%20rope%20%5C%20walker%7D%20%3D%20%5Cdfrac%7B100%7D%7B200%7D%20%20%3D%20%5Cdfrac%7B1%7D%7B2%7D)
![\theta = tan^{-1} \left (\dfrac{1}{2} \right ) \approx 26.565 ^ {\circ}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%5E%7B-1%7D%20%5Cleft%20%28%5Cdfrac%7B1%7D%7B2%7D%20%5Cright%20%29%20%5Capprox%20%2026.565%20%5E%20%7B%5Ccirc%7D)
Whereby the tightrope walker was initially vertically overhead the search light, the initial angle of elevation = 90°
The change in the angle of elevation = The initial angle of elevation - The final angle of elevation
Substituting the values gives
The change in the angle of elevation = 90° - 26.565 ≈ 63.435°
Answer:
2048
Step-by-step explanation:
Time to use recursive formula :)
Since a of 1 = 4 and -the recursive formula is
-2(a of n-1) We know that the r = -2
Convert that to explicit is
f(n) = -2 * 4^n-1
Let's use that to get the value for a of 6.
f(6) = -2 * 4^6-1
= -2 * 4^5
= -2048
300% change. 36/12. 100%=12, 12*3=36, therefore 100%*3=300%