Answer:
<h2>C. -5; -135, -10,935</h2>
Step-by-step explanation:
![\text{Substitute}\ n=1,\ n=4\ \text{and}\ n=8\ \text{to}\ A(n)=-5\cdot3^{n-1}:\\\\A(1)=-5\cdot3^{1-1}=-5\cdot3^0=-5\cdot1=-5\\\\A(4)=-5\cdot3^{4-1}=-5\cdot3^3=-5\cdot27=-135\\\\A(8)=-5\cdot3^{8-1}=-5\cdot3^7=-5\cdot2,187=-10,935](https://tex.z-dn.net/?f=%5Ctext%7BSubstitute%7D%5C%20n%3D1%2C%5C%20n%3D4%5C%20%5Ctext%7Band%7D%5C%20n%3D8%5C%20%5Ctext%7Bto%7D%5C%20A%28n%29%3D-5%5Ccdot3%5E%7Bn-1%7D%3A%5C%5C%5C%5CA%281%29%3D-5%5Ccdot3%5E%7B1-1%7D%3D-5%5Ccdot3%5E0%3D-5%5Ccdot1%3D-5%5C%5C%5C%5CA%284%29%3D-5%5Ccdot3%5E%7B4-1%7D%3D-5%5Ccdot3%5E3%3D-5%5Ccdot27%3D-135%5C%5C%5C%5CA%288%29%3D-5%5Ccdot3%5E%7B8-1%7D%3D-5%5Ccdot3%5E7%3D-5%5Ccdot2%2C187%3D-10%2C935)
<h2><u>
PLEASE MARK BRAINLIEST!</u></h2>
Answer:
I'm going to help youuuuu.
Step-by-step explanation:
{1}
Your answer is A) because the rise/run is -2/4x, which simplifies to -1/2x, which is <em>option A)</em>.
{2}
Dario's salary is <em>B) $12 per hour</em>. This is because, in 5 hours, Dario makes 60 dollars. If you find the unit rate of $60 in 5 hours, the answer is $12 per hour.
{3}
A) Between <em>x = -6</em> and <em>x = -2</em>
I hope this helps! I am sorry if any of these are incorrect!
- sincerelynini
The linked answer is wrong because that integral gives you the net displacement of the object, not the total distance.
To get the distance, you have to integrate the speed (as opposed to velocity), which involves integrating the absolute value of the velocity function.
![\mathrm{distance} = \displaystyle\int_1^5 |\sin(t)| \,\mathrm dt](https://tex.z-dn.net/?f=%5Cmathrm%7Bdistance%7D%20%3D%20%5Cdisplaystyle%5Cint_1%5E5%20%7C%5Csin%28t%29%7C%20%5C%2C%5Cmathrm%20dt)
By definition of absolute value,
![|\sin(t)|=\begin{cases}\sin(t)&\text{for }\sin(t)\ge0\\-\sin(t)&\text{for }\sin(t)](https://tex.z-dn.net/?f=%7C%5Csin%28t%29%7C%3D%5Cbegin%7Bcases%7D%5Csin%28t%29%26%5Ctext%7Bfor%20%7D%5Csin%28t%29%5Cge0%5C%5C-%5Csin%28t%29%26%5Ctext%7Bfor%20%7D%5Csin%28t%29%3C0%5Cend%7Bcases%7D)
Over this particular integration interval,
• sin(<em>t</em> ) ≥ 0 for 1 ≤ <em>t</em> < <em>π</em>, and
• sin(<em>t</em> ) < 0 for <em>π</em> < <em>t</em> ≤ 5
so you end up splitting the integral at <em>t</em> = <em>π</em> as
![\mathrm{distance} = \displaystyle\int_1^\pi \sin(t)\,\mathrm dt + \int_\pi^5 (-\sin(t))\,\mathrm dt](https://tex.z-dn.net/?f=%5Cmathrm%7Bdistance%7D%20%3D%20%5Cdisplaystyle%5Cint_1%5E%5Cpi%20%5Csin%28t%29%5C%2C%5Cmathrm%20dt%20%2B%20%5Cint_%5Cpi%5E5%20%28-%5Csin%28t%29%29%5C%2C%5Cmathrm%20dt)
Now compute the distance:
![\mathrm{distance} = -\cos(t)\bigg|_1^\pi + \cos(t)\bigg|_\pi^5](https://tex.z-dn.net/?f=%5Cmathrm%7Bdistance%7D%20%3D%20-%5Ccos%28t%29%5Cbigg%7C_1%5E%5Cpi%20%2B%20%5Ccos%28t%29%5Cbigg%7C_%5Cpi%5E5)
![\mathrm{distance} = -(\cos(\pi) - \cos(1)) + (\cos(5) - \cos(\pi))](https://tex.z-dn.net/?f=%5Cmathrm%7Bdistance%7D%20%3D%20-%28%5Ccos%28%5Cpi%29%20-%20%5Ccos%281%29%29%20%2B%20%28%5Ccos%285%29%20-%20%5Ccos%28%5Cpi%29%29)
![\mathrm{distance} = -2\cos(\pi) + \cos(1) + \cos(5) \approx 2.82](https://tex.z-dn.net/?f=%5Cmathrm%7Bdistance%7D%20%3D%20-2%5Ccos%28%5Cpi%29%20%2B%20%5Ccos%281%29%20%2B%20%5Ccos%285%29%20%5Capprox%202.82)
making B the correct answer.
Answer:
B. ![-\frac{9}{2}](https://tex.z-dn.net/?f=%20-%5Cfrac%7B9%7D%7B2%7D%20)
Step-by-step explanation:
Rate of change of y with respect to x, can be calculated using any two of the pairs of values of the table, say, (-2, 12) and (0, 3).
Rate of change = ![\frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%20)
Let,
![(-2, 12) = (x_1, y_1)](https://tex.z-dn.net/?f=%20%28-2%2C%2012%29%20%3D%20%28x_1%2C%20y_1%29%20)
![(0, 3) = (x_2, y_2)](https://tex.z-dn.net/?f=%20%280%2C%203%29%20%3D%20%28x_2%2C%20y_2%29%20)
Plug in the values
Rate of change = ![\frac{3 - 12}{0 - (-2)} = \frac{-9}{2} = -\frac{9}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%20-%2012%7D%7B0%20-%20%28-2%29%7D%20%3D%20%5Cfrac%7B-9%7D%7B2%7D%20%3D%20-%5Cfrac%7B9%7D%7B2%7D%20)