Answer:
- Function: B
- Not a function: A, C
Step-by-step explanation:
A relation is a function if there is only one y-value for each x-value. If you can draw a vertical line on the graph that intersect more than one point, the relation is not a function. (This is the "vertical line test.")
<h3>Application</h3>
Graph A: there are 3 y-values associated with x=2. Not a function.
Graph B: passes the vertical line test: A function.
Graph C: there are 2 y-values at each of x=1 and x=2. Not a function.
[ Answer ]
![\boxed{3\frac{9}{25} }](https://tex.z-dn.net/?f=%5Cboxed%7B3%5Cfrac%7B9%7D%7B25%7D%20%7D)
[ Explanation ]
Area Of Rectangle: Length * Width
2 4/5 * 1 1/5
=======================
Convert Fractions Into Mixed Numbers:
2 4/5 = 14/5
1 1/5 = 6/5
Multiply Across:
14 * 6
5 * 5
= 84/ 25
Simplify:
3 9/25
![\boxed{[ \ Eclipsed \ ]}](https://tex.z-dn.net/?f=%5Cboxed%7B%5B%20%5C%20Eclipsed%20%5C%20%5D%7D)
a) The value of
as a function of "x" is ![\theta = tan^{-1}\frac{250}{x}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%5E%7B-1%7D%5Cfrac%7B250%7D%7Bx%7D)
b) The rate of change of the angle with respect to x is -0.000308rad/m
Find the complete question and diagram attached
Form the right-angled triangle shown:
Adjacent side = x
Opposite side = 250m
angle of elevation = ![\theta](https://tex.z-dn.net/?f=%5Ctheta)
Using the SOH CAH TOA identity
![tan\theta = \frac{opposite}{hypotenuse} \\tan \theta = \frac{250}{x} \\\theta = tan^{-1}\frac{250}{x}](https://tex.z-dn.net/?f=tan%5Ctheta%20%3D%20%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D%20%5C%5Ctan%20%5Ctheta%20%3D%20%5Cfrac%7B250%7D%7Bx%7D%20%5C%5C%5Ctheta%20%3D%20tan%5E%7B-1%7D%5Cfrac%7B250%7D%7Bx%7D)
Hence the value of
as a function of "x" is ![\theta = tan^{-1}\frac{250}{x}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%5E%7B-1%7D%5Cfrac%7B250%7D%7Bx%7D)
b) If x = 450m
![\theta = tan^{-1}\frac{250}{x}\\tan \theta = \frac{250}{x}\\](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20tan%5E%7B-1%7D%5Cfrac%7B250%7D%7Bx%7D%5C%5Ctan%20%5Ctheta%20%3D%20%5Cfrac%7B250%7D%7Bx%7D%5C%5C)
Differentiate both sides with respect to "x"
![sec^2 \theta \frac{d\theta}{dx} = \frac{-250}{x^2} \\ \frac{d\theta}{dx} = \frac{1}{sec^2\theta} \times \frac{-250}{x^2}](https://tex.z-dn.net/?f=sec%5E2%20%5Ctheta%20%5Cfrac%7Bd%5Ctheta%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-250%7D%7Bx%5E2%7D%20%20%5C%5C%20%5Cfrac%7Bd%5Ctheta%7D%7Bdx%7D%20%3D%20%20%5Cfrac%7B1%7D%7Bsec%5E2%5Ctheta%7D%20%5Ctimes%20%5Cfrac%7B-250%7D%7Bx%5E2%7D)
Substitute x = 450m and
into the resulting expression to have:
![\frac{d\theta}{dx} = \frac{1}{sec^260^0} \times \frac{-250}{450^2}\\\frac{d\theta}{dx} = (cos60)^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} = 0.5^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} =-0.000308](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5Ctheta%7D%7Bdx%7D%20%3D%20%20%5Cfrac%7B1%7D%7Bsec%5E260%5E0%7D%20%5Ctimes%20%5Cfrac%7B-250%7D%7B450%5E2%7D%5C%5C%5Cfrac%7Bd%5Ctheta%7D%7Bdx%7D%20%3D%20%20%28cos60%29%5E2%5Ctimes%20%5Cfrac%7B-250%7D%7B202%2C500%7D%5C%5C%5Cfrac%7Bd%5Ctheta%7D%7Bdx%7D%20%3D%200.5%5E2%5Ctimes%20%5Cfrac%7B-250%7D%7B202%2C500%7D%5C%5C%5Cfrac%7Bd%5Ctheta%7D%7Bdx%7D%20%3D-0.000308)
Hence the rate of change of the angle with respect to x is -0.000308rad/m
Learn more here: brainly.com/question/15580615
Answer:
7483y4
Step-by-step explanation:
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Answer:
a, 4
Step-by-step explanation: