Answer:
Step-by-step explanation:
If it's on the same line, that means that the slope from each point to the other must be the same.
Using the first given points, we can calculate the slope to be:
![m = \frac{189-111}{15-9}=\frac{78}{6}=13\\](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B189-111%7D%7B15-9%7D%3D%5Cfrac%7B78%7D%7B6%7D%3D13%5C%5C)
We can solve for y
![13 = \frac{111-y}{9--7}\\13=\frac{111-y}{16}\\111 - y = 208\\y = -97\\](https://tex.z-dn.net/?f=13%20%3D%20%5Cfrac%7B111-y%7D%7B9--7%7D%5C%5C13%3D%5Cfrac%7B111-y%7D%7B16%7D%5C%5C111%20-%20y%20%3D%20208%5C%5Cy%20%3D%20-97%5C%5C)
We can double check:
![m = \frac{111--97}{9--7}\\m=\frac{208}{16}=13](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B111--97%7D%7B9--7%7D%5C%5Cm%3D%5Cfrac%7B208%7D%7B16%7D%3D13)
Answer:
The solution is x = e⁶
Step-by-step explanation:
Hi there!
First, let´s write the equation
ln(x⁶) = 36
Apply logarithm property: ln(xᵃ) = a ln(x)
6 ln(x) = 36
Divide both sides of the equation by 6
ln(x) = 6
Apply e to both sides
e^(ln(x)) = e⁶
x = e⁶
The solution is x = e⁶
Let´s prove why e^(ln(x)) = x
Let´s consider this function:
y = e^(ln(x))
Apply ln to both sides of the equation
ln(y) = ln(e^(ln(x)))
Apply logarithm property: ln(xᵃ) = a ln(x)
ln(y) = ln(x) · ln(e) (ln(e) = 1)
ln(y) = ln(x)
Apply logarithm equality rule: if ln(a) = ln(b) then, a = b
y = x
Since y = e^(ln(x)), then x =e^(ln(x))
Have a nice day!
Answer:
20x30xH=7000
11.6666 , depends on how much you need to round it. if 2 sig figs, round it to 12.
Answer:
2
Step-by-step explanation:
Let
be a real number.
equals
if:
![\lim_{x \rightarrow 2^-}f(x)=L](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Crightarrow%202%5E-%7Df%28x%29%3DL)
![\lim_{x \rightarrow 2^+}f(x)=L](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Crightarrow%202%5E%2B%7Df%28x%29%3DL)
----------------------------
means what does
get close to as we move
closer to 2 from the left. Please look at the orange to see what that looks like visually.
We see that
tends to
.
This means:
![\lim_{x \rightarrow 2^-}f(x)=2](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Crightarrow%202%5E-%7Df%28x%29%3D2)
-----------------------------
means what does
get close to as we move
closer to 2 from the right. Please look at the blue to see what that looks like visually.
We see that
tends to
.
This means:
![\lim_{x \rightarrow 2^+}f(x)=2](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Crightarrow%202%5E%2B%7Df%28x%29%3D2)
----------------------------
Therefore,
.