Answer:
y = -1/6x - 14
Step-by-step explanation:
The equation for the first line is y = 6x - 14
Convert the slope 6 so it becomes -1/6
Hi there!

To find the indefinite integral, we must integrate by parts.
Let "u" be the expression most easily differentiated, and "dv" the remaining expression. Take the derivative of "u" and the integral of "dv":
u = 4x
du = 4
dv = cos(2 - 3x)
v = 1/3sin(2 - 3x)
Write into the format:
∫udv = uv - ∫vdu
Thus, utilize the solved for expressions above:
4x · (-1/3sin(2 - 3x)) -∫ 4(1/3sin(2 - 3x))dx
Simplify:
-4x/3 sin(2 - 3x) - ∫ 4/3sin(2 - 3x)dx
Integrate the integral:
∫4/3(sin(2 - 3x)dx
u = 2 - 3x
du = -3dx ⇒ -1/3du = dx
-1/3∫ 4/3(sin(2 - 3x)dx ⇒ -4/9cos(2 - 3x) + C
Combine:

Alright, so plugging it in, we get 2(-4)^2=2(2)^4+3^2-(-4)^2+2^4. Use PEMDAS with parenthesis and exponents to then get (2)(16)+9-16+16. Multiplying 1 and 16, we get 32+41-16+16=73
Answer:
centimeters
Step-by-step explanation:
The numerator of the conversion factor always has the "to" units. The denominator has the "from" units. That way, when you multiply, the "from" units cancel:
(xx <em>from</em>) · (yy <em>to</em>)/(zz <em>from</em>) = xx·yy/zz · (<em>from/from</em>) · <em>to</em> = xx·yy/zz · <em>to</em>
Here, you want to convert to centimeters, so centimeters will be the units in the numerator.
10 in · (2.54 cm)/(1 in) = 25.4 cm
_____
The conversion factor is always "1". That is, the numerator and denominator are always <u>equal</u> in value. Here, 2.54 cm = 1 in, so (2.54 cm)/(1 in) = 1. You can multiply by 1 anytime you like. For units conversion, it only has the effect of changing the units.
To calculate the distance between two points on the coordinate system you have to use the following formula:
![d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%5B%5D%7B%28x_1-x_2%29%5E2%2B%28y_1-y_2%29%5E2%7D)
Where
d represents the distance between both points.
(x₁,y₁) are the coordinates of one of the points.
(x₂,y₂) are the coordinates of the second point.
To determine the length of CD, the first step is to determine the coordinates of both endpoints from the graph
C(2,-1)
D(-1,-2)
Replace the coordinates on the formula using C(2,-1) as (x₁,y₁) and D(-1,-2) as (x₂,y₂)
![\begin{gathered} d_{CD}=\sqrt[]{(2-(-1))^2+((-1)-(-2))}^2 \\ d_{CD}=\sqrt[]{(2+1)^2+(-1+2)^2} \\ d_{CD}=\sqrt[]{3^2+1^2} \\ d_{CD}=\sqrt[]{9+1} \\ d_{CD}=\sqrt[]{10} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20d_%7BCD%7D%3D%5Csqrt%5B%5D%7B%282-%28-1%29%29%5E2%2B%28%28-1%29-%28-2%29%29%7D%5E2%20%5C%5C%20d_%7BCD%7D%3D%5Csqrt%5B%5D%7B%282%2B1%29%5E2%2B%28-1%2B2%29%5E2%7D%20%5C%5C%20d_%7BCD%7D%3D%5Csqrt%5B%5D%7B3%5E2%2B1%5E2%7D%20%5C%5C%20d_%7BCD%7D%3D%5Csqrt%5B%5D%7B9%2B1%7D%20%5C%5C%20d_%7BCD%7D%3D%5Csqrt%5B%5D%7B10%7D%20%5Cend%7Bgathered%7D)
The length of CD is √10 units ≈ 3.16 units