Work out 6% of $42 which equals to $2.52. The work out what 20% of $42 which is $8.40. Finally add the $8.40 and $2.52 onto $42 to give you your answer of $52.92
Answer:
4.5
Step-by-step explanation:
Use the distance formula to get sqrt(2^2+4^2) or sqrt20, which is 2sqrt5. sqrt5 is approximately 2.236, so 2*2.236 is 4.472 or 4.5.
Answer:
B is -6.
Step-by-step explanation:
y=mx+b
6 is negative and is in the place of the y intercept (b)
Answer: ![\frac{8}{3}\ ft/s](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B3%7D%5C%20ft%2Fs)
Step-by-step explanation:
Given
length of shadow =22 ft
height of woman =5.5 ft
speed of woman ![\frac{dy}{dt}=8\ ft/s](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%3D8%5C%20ft%2Fs)
from the figure, we can write
![\frac{22}{x+y}=\frac{5.5}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B22%7D%7Bx%2By%7D%3D%5Cfrac%7B5.5%7D%7Bx%7D)
at given instant
y=20 ft
so, using similar triangle properties
![\frac{22}{x+20}=\frac{5.5}{x}\\22x=5.5x+110\\16.5x=110\\x=6.67\ ft](https://tex.z-dn.net/?f=%5Cfrac%7B22%7D%7Bx%2B20%7D%3D%5Cfrac%7B5.5%7D%7Bx%7D%5C%5C22x%3D5.5x%2B110%5C%5C16.5x%3D110%5C%5Cx%3D6.67%5C%20ft)
Again we can write
![\dfrac{22}{x+y}=\dfrac{5.5}{x}\\22x=5.5x+5.5y\\16.5x=5.5y\\3x=y\\\text{differentiate w.r.t time} \\3\frac{dx}{dt}=\frac{dy}{dt}\\\frac{dx}{dt}=\frac{1}{3}\times 8=\frac{8}{3}\ ft/s\ \text{away from the woman}](https://tex.z-dn.net/?f=%5Cdfrac%7B22%7D%7Bx%2By%7D%3D%5Cdfrac%7B5.5%7D%7Bx%7D%5C%5C22x%3D5.5x%2B5.5y%5C%5C16.5x%3D5.5y%5C%5C3x%3Dy%5C%5C%5Ctext%7Bdifferentiate%20w.r.t%20time%7D%20%5C%5C3%5Cfrac%7Bdx%7D%7Bdt%7D%3D%5Cfrac%7Bdy%7D%7Bdt%7D%5C%5C%5Cfrac%7Bdx%7D%7Bdt%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Ctimes%208%3D%5Cfrac%7B8%7D%7B3%7D%5C%20ft%2Fs%5C%20%5Ctext%7Baway%20from%20the%20woman%7D)
Answer:
D. 22,417 feet
Step-by-step explanation:
Fine the diagram in the attachment for proper elucidation. Using the SOH, CAH, TOA trigonometry identity to solve for the distance (x) from the plane (P) to the observer (O), the longest side x is the hypotenuse and the side facing the angle of elevation is the opposite.
Hypotenuse = x and Opposite = 15,000feet
According to SOH;
![sin 42^0 = \frac{Opposite}{Hypotenuse} \\\\Sin42^0 = \frac{15000}{x}\\ \\x = \frac{15000}{sin42^0}\\\\ \\](https://tex.z-dn.net/?f=sin%2042%5E0%20%3D%20%5Cfrac%7BOpposite%7D%7BHypotenuse%7D%20%5C%5C%5C%5CSin42%5E0%20%3D%20%5Cfrac%7B15000%7D%7Bx%7D%5C%5C%20%5C%5Cx%20%3D%20%5Cfrac%7B15000%7D%7Bsin42%5E0%7D%5C%5C%5C%5C%20%5C%5C)
![x = \frac{15000}{ 0.6691} \\\\x = 22,417 feet](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B15000%7D%7B%200.6691%7D%20%5C%5C%5C%5Cx%20%3D%2022%2C417%20feet)
Hence the distance (x) from the plane P to the observer O is approximately 22,417 feet