Answer:
Step-by-step explanation:
1. 56 + 81 = 137
2. The exterior angle theorem means that the 2 angles within a triangle that is on the opposite side of the angle outside the triangle could be added to find the angle that is outside of the triangle.
3. 56 and 81 are on the opposite side of the "x" outside the triangle which means that they could be added together which equals 137 degrees.
Hope this helps!
Answer:
![\sqrt{85}](https://tex.z-dn.net/?f=%5Csqrt%7B85%7D)
Step-by-step explanation:
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (6, - 2)
d = ![\sqrt{(6+1)^2+(-2-4)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%286%2B1%29%5E2%2B%28-2-4%29%5E2%7D)
= ![\sqrt{7^2+(-6)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B7%5E2%2B%28-6%29%5E2%7D)
= ![\sqrt{49+36}](https://tex.z-dn.net/?f=%5Csqrt%7B49%2B36%7D)
=
← exact distance
Answer:
18.66 ft/s
Step-by-step explanation:
The distance between you and the elevator is given by:
![h=\sqrt{x^2+y^2}](https://tex.z-dn.net/?f=h%3D%5Csqrt%7Bx%5E2%2By%5E2%7D)
The rate of change for the distance between you and the elevator is given by:
![\frac{dh}{dt}=\frac{dh}{dy}*\frac{dy}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7Bdh%7D%7Bdy%7D%2A%5Cfrac%7Bdy%7D%7Bdt%7D)
![-16=\frac{dh}{dy}*\frac{dy}{dt}](https://tex.z-dn.net/?f=-16%3D%5Cfrac%7Bdh%7D%7Bdy%7D%2A%5Cfrac%7Bdy%7D%7Bdt%7D)
![\frac{dh}{dy}=\frac{d}{dy} (\sqrt{x^2+y^2})\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdy%7D%3D%5Cfrac%7Bd%7D%7Bdy%7D%20%28%5Csqrt%7Bx%5E2%2By%5E2%7D%29%5C%5C)
Applying the chain rule:
![u=x^2+y^2\\\frac{dh}{dy}=\frac{d\sqrt u}{du} *\frac{du}{dy}\\\frac{dh}{dy}=\frac{1}{2\sqrt u} *2y\\\frac{dh}{dy}=\frac{y}{\sqrt {(x^2+y^2)}}](https://tex.z-dn.net/?f=u%3Dx%5E2%2By%5E2%5C%5C%5Cfrac%7Bdh%7D%7Bdy%7D%3D%5Cfrac%7Bd%5Csqrt%20u%7D%7Bdu%7D%20%2A%5Cfrac%7Bdu%7D%7Bdy%7D%5C%5C%5Cfrac%7Bdh%7D%7Bdy%7D%3D%5Cfrac%7B1%7D%7B2%5Csqrt%20u%7D%20%2A2y%5C%5C%5Cfrac%7Bdh%7D%7Bdy%7D%3D%5Cfrac%7By%7D%7B%5Csqrt%20%7B%28x%5E2%2By%5E2%29%7D%7D)
Therefore, at x=300 and y = 500, dy/dt is:
![-16=\frac{y}{\sqrt {(x^2+y^2)}}*\frac{dy}{dt}\\-16=\frac{500}{\sqrt {(300^2+500^2)}}*\frac{dy}{dt}\\\frac{dy}{dt}=-18.66\ ft/s](https://tex.z-dn.net/?f=-16%3D%5Cfrac%7By%7D%7B%5Csqrt%20%7B%28x%5E2%2By%5E2%29%7D%7D%2A%5Cfrac%7Bdy%7D%7Bdt%7D%5C%5C-16%3D%5Cfrac%7B500%7D%7B%5Csqrt%20%7B%28300%5E2%2B500%5E2%29%7D%7D%2A%5Cfrac%7Bdy%7D%7Bdt%7D%5C%5C%5Cfrac%7Bdy%7D%7Bdt%7D%3D-18.66%5C%20ft%2Fs)
The elevator is descending at 18.66 ft/s.
Answer:
-37- -47=-10
Step-by-step explanation:
Answer:
The answer to your question is x = 14.7
Step-by-step explanation:
Data
∠A = 20°
∠B = 46
a = 7
b = x
Process
To solve this problem use, the law of sines. This law states that the ratio of a side of a triangle to the sine of the opposite angle is the same for all three sides.
The law of sines for this problem is
x / sin 46 = 7 / sin 20
-Solve for x
x = 7 sin 46 / sin 20
-Simplification
x = 7 (0.719) / 0.342
x = 5.035/0.342
-Result
x = 14.7