This is quite a complex problem. I wrote out a really nice solution but I can't work out how to put it on the website as the app is very poorly made. Still, I'll just have to type it all in...
Okay so you need to use a technique called logarithmic differentiation. It seems quite unnatural to start with but the result is very impressive.
Let y = (x+8)^(3x)
Take the natural log of both sides:
ln(y) = ln((x+8)^(3x))
By laws of logarithms, this can be rearranged:
ln(y) = 3xln(x+8)
Next, differentiate both sides. By implicit differentiation:
d/dx(ln(y)) = 1/y dy/dx
The right hand side is harder to differentiate. Using the substitution u = 3x and v = ln(x+8):
d/dx(3xln(x+8)) = d/dx(uv)
du/dx = 3
Finding dv/dx is harder, and involves the chain rule. Let a = x+ 8:
v = ln(a)
da/dx = 1
dv/da = 1/a
By chain rule:
dv/dx = dv/da * da/dx = 1/a = 1/(x+8)
Finally, use the product rule:
d/dx(uv) = u * dv/dx + v * du/dx = 3x/(x+8) + 3ln(x+8)
This overall produces the equation:
1/y * dy/dx = 3x/(x+8) + 3ln(x+8)
We want to solve for dy/dx, achievable by multiplying both sides by y:
dy/dx = y(3x/(x+8) + 3ln(x+8))
Since we know y = (x+8)^(3x):
dy/dx = ((x+8)^(3x))(3x/(x+8) + 3ln(x+8))
Neatening this up a bit, we factorise out 3/(x+8):
dy/dx = (3(x+8)^(3x-1))(x + (x+8)ln(x+8))
Well wasn't that a marathon? It's a nightmare typing that in, I hope you can follow all the steps.
I hope this helped you :)
If you calculate SLE to be $25,000 and that there will be one occurrence every four years (ARO), then the ALE is $40,000.
<h3>What is Single-loss expectancy (SLE)?</h3>
A expected monetary decline each moment an asset is at risk is referred to as single-loss expectancy (SLE). It is a term that is most frequently used during risk analysis and attempts to assign a monetary value to each individual threat.
Quantitative risk analysis predicts the likelihood of certain risk outcomes as well as their approximate monetary cost using relevant, verifiable data.
IT professionals must consider a wide range of risks, including the following:
- Errors caused by humans
- Cyber attacks, unauthorised data disclosure, or data misuse are examples of hostile action.
- Errors in application
- System or network failures
- Physical harm caused by fire, natural disasters, or vandalism.
To know more about the Single-loss expectancy (SLE), here
brainly.com/question/14587600
#SPJ4
Answer:
<u>The </u><u><em>red marbles.</em></u>
Step-by-step explanation:
<u>It is because Red has the</u><u><em> least amount of marbles</em></u><u>, therefore it is most likely for you to </u><u><em>not</em></u><u> pull out a red marble.</u>
Tony will get $8.26 back.
Here's why:
First, let's take $1.85 away from $13.59, because he has a coupon. That leaves us with $11.74
Second, do $20 - $11.74 to get your answer, $8.26
Answer:
12
Step-by-step explanation:
Least common multiple means what is the smallest number that both numbers go into
List the prime factors
4= 2*2
12 = 2*2*3
The factors that are in needed to make both are 2 and 3
We need 2 of the 2's and 1 3
2*2*3 = 12
