Answer:
1/4
Step-by-step explanation:
Answer:
See Below.
Step-by-step explanation:
We are given that:

Where <em>I₀</em> and <em>k</em> are constants.
And we want to prove that:

From the original equation, take the derivative of both sides with respect to <em>t</em>. Hence:
![\displaystyle \frac{d}{dt}\left[I\right] = \frac{d}{dt}\left[I_0e^{-kt}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5BI%5Cright%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5BI_0e%5E%7B-kt%7D%5Cright%5D)
Differentiate. Since <em>I₀ </em>is a constant:
![\displaystyle \frac{dI}{dt} = I_0\left(\frac{d}{dt}\left[ e^{-kt}\right]\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdI%7D%7Bdt%7D%20%3D%20I_0%5Cleft%28%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5B%20e%5E%7B-kt%7D%5Cright%5D%5Cright%29)
Using the chain rule:

We have:

Substitute:

Distribute and simplify:

Hence proven.
Answer:
(2, 10)
Step-by-step explanation:
y = (x - h)² + k
vertex = (h, k)
= (2, 10)
Since, the function F(x) represents the monthly earnings of sales executive, which consists of a base salary and a commission earned on each scale, where 'x' is the number of sales.
So, the function F(x) can be expressed as:
F(x)= base salary+ commission earned on each sale (x) where 'x' represents the number of sales done.
So, F(0)= base salary + 0 ( As x=0 implies there was no sale)
And the executive earned only his base salary and no commission as he did not make any sale, and the commission was dependent upon the number of sales (x).
Hence, F(0) represents the base salary.
So, Option J is the correct answer.
Answer:
x = 6 is a solution of x - 1
7.
Step-by-step explanation:
First, plug in x = 6 into the inequality.
x - 1
7 for x = 6
6 - 1
7
Now, solve.
6 - 1 = 5
5
7
The statement above is true, so x = 6 is a solution to x - 1
7.
Please inform me of any mistakes.