9) Because the total number of pencils is 180 and you will use them up in 30 days, the equation will have to equal 0 total pencils when 30 is substituted in for the time factor, or x. This already takes our choice 3 because it doesn’t meet this criteria.
The answer to how many pencils in 20 days could be answered by plugging in 20 for x. Choice 4 cannot work because it results in a negative number of pencils. Choices 1 and 2 use the same equation, so by plugging in 20 it is clear choice 2 is the correct answer.
10) A line parallel to the go en equation would have the same slope, -3, which means choices 1 and 4 are out. Plug in (-2,5) into both choices 2 and 3. Plugging -2 into x in choice 2 gives -5, and in choice 3 gives 5 for the y value. Therefore choice 3 is correct.
Answer:
=4/3
Step-by-step explanation:
Step 1
Multiply the denominator by the whole number
6 × 1 = 6
Step 2
Add the answer from Step 1 to the numerator
6 + 2 = 8
Step 3
Write answer from Step 2 over the denominator
8/6
=86
You can also reduce this fraction.
Find the Greatest Common Factor (GCF) of 8 and 6, if it exists, and reduce our fraction by dividing both numerator and denominator by it,
GCF = 2
=8÷2=4
6/2=3
Simplified Solution
=6×1+2/6 =8/6=4/3
hope this helps
you welcome and thanks
Answer:
The value of x that gives the maximum transmission is 1/√e ≅0.607
Step-by-step explanation:
Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.

We need to equalize f' to 0
- k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side
- 2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side
- 2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)
- ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp
- 1/x = e^(1/2)
- x = 1/e^(1/2) = 1/√e ≅ 0.607
Thus, the value of x that gives the maximum transmission is 1/√e.
I'm guessing the second derivative is for <em>y</em> with respect to <em>x</em>, i.e.

Compute the first derivative. By the chain rule,

We have


and so

Now compute the second derivative. Notice that
is a function of
; so denote it by
. Then

By the chain rule,

We have

and so the second derivative is
