s n a ke =4 they are only 4 sound in snake when you sound it out
The number of pretzels that must be sold to maximize the profit is 400.
<h3>What is the number of pretzels to be sold in the quadratic equation?</h3>
The number of pretzels to be sold can be determined by taking the derivative of the quadratic equation.
Given that:
P(x) = -4x^2+3200x-100
P'(x) = -8x + 3200
P''(x) = -8
At the critical point;
P'(x) = 0
Thus;
8x = 3200
x = 3200/8
x = 400
P''(400) = -8
P'' (400) < 0
Therefore, at x = 400, P(x) will be maximum.
Learn more about calculating the derivative of a quadratic equation here:
brainly.com/question/13759985
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Answer:
![\lim\limits_{(x,y)\rightarrow(0,0)}\left(\sqrt{x^2+y^2+49}+7\right)=14](https://tex.z-dn.net/?f=%5Clim%5Climits_%7B%28x%2Cy%29%5Crightarrow%280%2C0%29%7D%5Cleft%28%5Csqrt%7Bx%5E2%2By%5E2%2B49%7D%2B7%5Cright%29%3D14)
Step-by-step explanation:
to find the limit:
![\lim\limits_{(x,y)\rightarrow(0,0)}\left(\dfrac{x^2+y^2}{\sqrt{x^2+y^2+49}-7}\right)](https://tex.z-dn.net/?f=%5Clim%5Climits_%7B%28x%2Cy%29%5Crightarrow%280%2C0%29%7D%5Cleft%28%5Cdfrac%7Bx%5E2%2By%5E2%7D%7B%5Csqrt%7Bx%5E2%2By%5E2%2B49%7D-7%7D%5Cright%29)
we need to first rationalize our expression.
![\dfrac{x^2+y^2}{\sqrt{x^2+y^2+49}-7}\left(\dfrac{\sqrt{x^2+y^2+49}+7}{\sqrt{x^2+y^2+49}+7}\right)](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2%2By%5E2%7D%7B%5Csqrt%7Bx%5E2%2By%5E2%2B49%7D-7%7D%5Cleft%28%5Cdfrac%7B%5Csqrt%7Bx%5E2%2By%5E2%2B49%7D%2B7%7D%7B%5Csqrt%7Bx%5E2%2By%5E2%2B49%7D%2B7%7D%5Cright%29)
![\dfrac{(x^2+y^2)(\sqrt{x^2+y^2+49}+7)}{(\sqrt{x^2+y^2+49}\,)^2-7^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%28x%5E2%2By%5E2%29%28%5Csqrt%7Bx%5E2%2By%5E2%2B49%7D%2B7%29%7D%7B%28%5Csqrt%7Bx%5E2%2By%5E2%2B49%7D%5C%2C%29%5E2-7%5E2%7D)
![\dfrac{(x^2+y^2)(\sqrt{x^2+y^2+49}+7)}{(x^2+y^2)}](https://tex.z-dn.net/?f=%5Cdfrac%7B%28x%5E2%2By%5E2%29%28%5Csqrt%7Bx%5E2%2By%5E2%2B49%7D%2B7%29%7D%7B%28x%5E2%2By%5E2%29%7D)
![\sqrt{x^2+y^2+49}+7](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%2By%5E2%2B49%7D%2B7)
Now this is our simplified expression, we can use our limit now.
![\lim\limits_{(x,y)\rightarrow(0,0)}\left(\sqrt{x^2+y^2+49}+7\right)\\\sqrt{0^2+0^2+49+7}\\7+7\\14](https://tex.z-dn.net/?f=%5Clim%5Climits_%7B%28x%2Cy%29%5Crightarrow%280%2C0%29%7D%5Cleft%28%5Csqrt%7Bx%5E2%2By%5E2%2B49%7D%2B7%5Cright%29%5C%5C%5Csqrt%7B0%5E2%2B0%5E2%2B49%2B7%7D%5C%5C7%2B7%5C%5C14)
Limit exists and it is 14 at (0,0)
Answer:
42.22 (2 repeating)
Step-by-step explanation:
When you are given percentage problems, you deal with the percent (%), base (amount you are starting with), and the amount.
Starting with the most basic equation,
Percent * Base = Amount
In this problem, you are given the amount (38) and the percent (90)
So to find the base, you can do
Base = Amount / Percent
As always, convert the percent to a decimal by dividing by 100.
38/ 0.9 = 42.222 repeating