2 bags so each student will at least get one treat
The first graph since it’s increasing rapidly while the second one is a parabola.
A. Is an exponential function
Answer:
- Hypotenuse
- Leg 1
- Leg 2
Step-by-step explanation:
Represent the dimensions as:
![H = Hypotenuse](https://tex.z-dn.net/?f=H%20%3D%20Hypotenuse)
![Other\ Legs = \{S_1,S_2\}](https://tex.z-dn.net/?f=Other%5C%20Legs%20%3D%20%5C%7BS_1%2CS_2%5C%7D)
So, we have:
![S_1 = 2000](https://tex.z-dn.net/?f=S_1%20%3D%202000)
![H = 400 + S_2](https://tex.z-dn.net/?f=H%20%3D%20400%20%2B%20S_2)
Required
Determine the dimensions
Apply Pythagoras theorem
![H^2 = S_1^2 + S_2^2](https://tex.z-dn.net/?f=H%5E2%20%3D%20S_1%5E2%20%2B%20S_2%5E2)
This gives:
![(400 + S_2)^2 = 2000^2 + S_2^2](https://tex.z-dn.net/?f=%28400%20%2B%20S_2%29%5E2%20%3D%202000%5E2%20%2B%20S_2%5E2)
Open bracket
![160000 + 800S_2 + S_2^2 = 4000000 + S_2^2](https://tex.z-dn.net/?f=160000%20%2B%20800S_2%20%2B%20S_2%5E2%20%3D%204000000%20%2B%20S_2%5E2)
![160000 + 800S_2 = 4000000](https://tex.z-dn.net/?f=160000%20%2B%20800S_2%20%3D%204000000)
Collect Like Terms
![800S_2 = 4000000 - 160000](https://tex.z-dn.net/?f=800S_2%20%3D%204000000%20-%20160000)
![800S_2 = 3840000](https://tex.z-dn.net/?f=800S_2%20%3D%203840000)
Solve for S2
![S_2 = \frac{3840000}{800}](https://tex.z-dn.net/?f=S_2%20%3D%20%5Cfrac%7B3840000%7D%7B800%7D)
![S_2 = 4800](https://tex.z-dn.net/?f=S_2%20%3D%204800)
Recall that:
![H = 400 + S_2](https://tex.z-dn.net/?f=H%20%3D%20400%20%2B%20S_2)
![H = 400 + 4800](https://tex.z-dn.net/?f=H%20%3D%20400%20%2B%204800)
![H = 5200](https://tex.z-dn.net/?f=H%20%3D%205200)
Hence, the dimensions are:
![H = 5200](https://tex.z-dn.net/?f=H%20%3D%205200)
![S_1 = 2000](https://tex.z-dn.net/?f=S_1%20%3D%202000)
![S_2 = 4800](https://tex.z-dn.net/?f=S_2%20%3D%204800)
Answer:
![\displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2\sqrt{x^{3}}} \ - \ \displaystyle\frac{12}{x^{5}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdy%7D%7Bdx%7D%20%5C%20%3D%20%5C%203x%5E%7B2%7D%20%5C%20%2B%20%5C%20%5Cdisplaystyle%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%5E%7B3%7D%7D%7D%20%5C%20-%20%5C%20%5Cdisplaystyle%5Cfrac%7B12%7D%7Bx%5E%7B5%7D%7D)
Step-by-step explanation:
![y \ = \ x^{3} \ - \ \displaystyle\frac{1}{\sqrt{x}} \ + \ \displaystyle\frac{3}{x^{4}} \\ \\ y \ = \ x^{3} \ - \ x^{-\frac{1}{2}} \ + \ 3x^{-4} \\ \\ \displaystyle\frac{dy}{dx} \ = \ 3x^{3 \ - \ 1} \ - \ \left(-\displaystyle\frac{1}{2}\right)x^{-\frac{1}{2} \ - \ 1} \ + \ \left(-4 \ \times \ 3\right)x^{-4-1}](https://tex.z-dn.net/?f=y%20%5C%20%3D%20%5C%20x%5E%7B3%7D%20%5C%20-%20%5C%20%5Cdisplaystyle%5Cfrac%7B1%7D%7B%5Csqrt%7Bx%7D%7D%20%5C%20%2B%20%5C%20%5Cdisplaystyle%5Cfrac%7B3%7D%7Bx%5E%7B4%7D%7D%20%5C%5C%20%5C%5C%20y%20%5C%20%3D%20%5C%20x%5E%7B3%7D%20%5C%20-%20%5C%20x%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%20%5C%20%2B%20%5C%203x%5E%7B-4%7D%20%5C%5C%20%5C%5C%20%5Cdisplaystyle%5Cfrac%7Bdy%7D%7Bdx%7D%20%5C%20%3D%20%5C%203x%5E%7B3%20%5C%20-%20%5C%201%7D%20%5C%20-%20%5C%20%5Cleft%28-%5Cdisplaystyle%5Cfrac%7B1%7D%7B2%7D%5Cright%29x%5E%7B-%5Cfrac%7B1%7D%7B2%7D%20%5C%20-%20%5C%201%7D%20%5C%20%2B%20%5C%20%5Cleft%28-4%20%5C%20%5Ctimes%20%5C%203%5Cright%29x%5E%7B-4-1%7D)
![\displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2}x^{-\frac{3}{2}} \ - \ 12x^{-5} \\ \\ \displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2\sqrt{x^{3}}} \ - \ \displaystyle\frac{12}{x^{5}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7Bdy%7D%7Bdx%7D%20%5C%20%3D%20%5C%203x%5E%7B2%7D%20%5C%20%2B%20%5C%20%5Cdisplaystyle%5Cfrac%7B1%7D%7B2%7Dx%5E%7B-%5Cfrac%7B3%7D%7B2%7D%7D%20%5C%20-%20%5C%2012x%5E%7B-5%7D%20%5C%5C%20%5C%5C%20%5Cdisplaystyle%5Cfrac%7Bdy%7D%7Bdx%7D%20%5C%20%3D%20%5C%203x%5E%7B2%7D%20%5C%20%2B%20%5C%20%5Cdisplaystyle%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%5E%7B3%7D%7D%7D%20%5C%20-%20%5C%20%5Cdisplaystyle%5Cfrac%7B12%7D%7Bx%5E%7B5%7D%7D)
Answer:
12 cookies
Step-by-step explanation: if you have 3 minutes and you did 9 it gives you 3 cookies. which if you times 3 times 4 it gives you 12.