We have this function here:
![f(x)=x^2-3x-14](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2-3x-14)
We can differentiate this function using the power rule:
![\frac{d}{dx}x^n=nx^{n-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7Dx%5En%3Dnx%5E%7Bn-1%7D)
We will subtract the power/exponent by 1 and multiply the original exponent to the constant in front.
![f^{\prime}(x)=2x-3](https://tex.z-dn.net/?f=f%5E%7B%5Cprime%7D%28x%29%3D2x-3)
The differentiated function is shown above.
Answer:
3 scoop
Step-by-step explanation:
1/2 /1/6=l/2 x 6/1=6/2=3
Answer:
the gcm or greatest common factor is <u>3xy</u> :)
Step-by-step explanation:
Factor 18x2y3−6xy2+3x3y
18x2y3+3x3y−6xy2
=3xy(6xy2+x2−2y)
3xy(6xy2+x2−2y)
3xy
HOPE THIS HELPS
<span>23 identical packets, consisting of 1 sheet of paper and 4 crayons.
The maximum number of packets the teacher can make from 92 crayons and 23 sheets of paper is the greatest common factor of 92 and 23. And for the values of 92 and 23, the GCF is 23.
First, calculate the list of prime numbers that when multiplied together, get each number.
23 = 23
92 = 2 * 2 * 23
Look for the largest set of prime factors in common to both numbers. In this case, it's 23.
So the teach can make 23 identical activity packets. Each packet will contain (92 / 23 = 4) crayons, and (23 / 23 = 1) sheet of paper.</span>
The exponential model would take the form:
![y=Ae^{kt} ](https://tex.z-dn.net/?f=y%3DAe%5E%7Bkt%7D%0A)
A, the initial value is 2, we will use 3 days and 8 tops to find k, or the rate.
![8 = 2e^{k*3}](https://tex.z-dn.net/?f=8%20%3D%202e%5E%7Bk%2A3%7D)
![k = \frac{ln(4)}{3}](https://tex.z-dn.net/?f=k%20%3D%20%20%5Cfrac%7Bln%284%29%7D%7B3%7D%20)
Now, plugging in 6 days:
![y = 2e^{ \frac{ln(4)}{3}*6}](https://tex.z-dn.net/?f=y%20%3D%202e%5E%7B%20%5Cfrac%7Bln%284%29%7D%7B3%7D%2A6%7D%20)
![y = 32](https://tex.z-dn.net/?f=y%20%3D%2032)
The linear would take the form:
y = mx+b
First the slope would be: (8-2)/(3-1) = 3
And to find b we could plug in the point (8,3):
8 = 3(3)+b
b = 8-9
b = -1
y = 3x-1
At x=6
y = 3(6)-1
y = 17
Thus, the exponential is almost double the result of the linear! Hope that helps.