Answer:
Part A)
The equation in the point-slope form is:
![y-11=\frac{4}{3}\left(x-\left(-2\right)\right)](https://tex.z-dn.net/?f=y-11%3D%5Cfrac%7B4%7D%7B3%7D%5Cleft%28x-%5Cleft%28-2%5Cright%29%5Cright%29)
Part B)
The graph of the equation is attached below.
Step-by-step explanation:
Part A)
Given
The point-slope form of the line equation is
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
Here, m is the slope and (x₁, y₁) is the point
substituting the values m = 4/3 and the point (-2, 11) in the point-slope form of the line equation
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
![y-11=\frac{4}{3}\left(x-\left(-2\right)\right)](https://tex.z-dn.net/?f=y-11%3D%5Cfrac%7B4%7D%7B3%7D%5Cleft%28x-%5Cleft%28-2%5Cright%29%5Cright%29)
Thus, the equation in the point-slope form is:
![y-11=\frac{4}{3}\left(x-\left(-2\right)\right)](https://tex.z-dn.net/?f=y-11%3D%5Cfrac%7B4%7D%7B3%7D%5Cleft%28x-%5Cleft%28-2%5Cright%29%5Cright%29)
Part B)
As we have determined the point-slope form which passes through the point (-2, 11) and has a slope m = 4/3
The graph of the equation is attached below.
Answer:
a) t₀ = 1.73205 s
b) 1.0 C
Step-by-step explanation:
(A)
The time dilation (t) observed by an observer at rest relative to the time (t₀) measured by observer in motion is;
![t = \frac{t_0}{\sqrt{1 - \frac{V^2}{C^2}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7Bt_0%7D%7B%5Csqrt%7B1%20-%20%5Cfrac%7BV%5E2%7D%7BC%5E2%7D%7D%7D)
time measured by captain
⇒
V = 0.5 c
⇒ t₀ = 1.73205 s
(B)
Speed of the light never exceeds by its real value. The speed of the light in any frame of reference is constant.
∵ It will be "1.0C" or just "C"
Using the shell method, the volume is
![\displaystyle 2\pi \int_0^1 (2-x) \cdot 8x^3 \, dx = 16\pi \int_0^1 (2x^3 - x^4) \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%202%5Cpi%20%5Cint_0%5E1%20%282-x%29%20%5Ccdot%208x%5E3%20%5C%2C%20dx%20%3D%2016%5Cpi%20%5Cint_0%5E1%20%282x%5E3%20-%20x%5E4%29%20%5C%2C%20dx)
Each cylindrical shell has radius
(the horizontal distance from the axis of revolution to the curve
); has height
(the vertical distance between a point on the
-axis in
and the curve
).
Compute the integral.
![\displaystyle 16 \pi \int_0^1 (2x^3 - x^4) \, dx = 16\pi \left(\frac{x^4}2 - \frac{x^5}5\right) \bigg|_{x=0}^{x=1} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = 16\pi \left(\frac12 - \frac15\right) \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \frac{24}5\pi = \boxed{4.8\pi}](https://tex.z-dn.net/?f=%5Cdisplaystyle%2016%20%5Cpi%20%5Cint_0%5E1%20%282x%5E3%20-%20x%5E4%29%20%5C%2C%20dx%20%3D%2016%5Cpi%20%5Cleft%28%5Cfrac%7Bx%5E4%7D2%20-%20%5Cfrac%7Bx%5E5%7D5%5Cright%29%20%5Cbigg%7C_%7Bx%3D0%7D%5E%7Bx%3D1%7D%20%5C%5C%5C%5C%20~~~~~~~~~~~~~~~~~~~~~~~~~~~~%20%3D%2016%5Cpi%20%5Cleft%28%5Cfrac12%20-%20%5Cfrac15%5Cright%29%20%5C%5C%5C%5C%20~~~~~~~~~~~~~~~~~~~~~~~~~~~~%20%3D%20%5Cfrac%7B24%7D5%5Cpi%20%3D%20%5Cboxed%7B4.8%5Cpi%7D)
Answer:
-8 27/100
<u>A mixed number consists of an integer followed by a proper fraction.</u>
Answer:
option B ................
is the correct answer