Keeping in mind that for a cost C(x) and profit P(x) and revenue R(x), the marginal cost, marginal profit and marginal revenue are respectively dC/dx, dP/dx and dR/dx, then
![\bf P(x)=0.03x^2-3x+3x^{0.8}-4400 \\\\\\ \stackrel{marginal~profit}{\cfrac{dP}{dx}}=0.06x-3+2.4x^{-0.2} \\\\\\ \cfrac{dP}{dx}=0.06x-3+2.4\cdot \cfrac{1}{x^{0.2}}\implies \cfrac{dP}{dx}=0.06x-3+2.4\cdot \cfrac{1}{x^{\frac{1}{5}}} \\\\\\ \cfrac{dP}{dx}=0.06x-3+\cfrac{2.4}{\sqrt[5]{x}}](https://tex.z-dn.net/?f=%5Cbf%20P%28x%29%3D0.03x%5E2-3x%2B3x%5E%7B0.8%7D-4400%0A%5C%5C%5C%5C%5C%5C%0A%5Cstackrel%7Bmarginal~profit%7D%7B%5Ccfrac%7BdP%7D%7Bdx%7D%7D%3D0.06x-3%2B2.4x%5E%7B-0.2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06x-3%2B2.4%5Ccdot%20%5Ccfrac%7B1%7D%7Bx%5E%7B0.2%7D%7D%5Cimplies%20%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06x-3%2B2.4%5Ccdot%20%5Ccfrac%7B1%7D%7Bx%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06x-3%2B%5Ccfrac%7B2.4%7D%7B%5Csqrt%5B5%5D%7Bx%7D%7D)
![\bf a)\qquad \cfrac{dP}{dx}=0.06(200)-3+ \cfrac{2.4}{\sqrt[5]{200}} \\\\\\ b)\qquad \cfrac{dP}{dx}=0.06(2000)-3+\cfrac{2.4}{\sqrt[5]{2000}} \\\\\\ c)\qquad \cfrac{dP}{dx}=0.06(5000)-3+\cfrac{2.4}{\sqrt[5]{5000}} \\\\\\ d)\qquad \cfrac{dP}{dx}=0.06(10000)-3+\cfrac{2.4}{\sqrt[5]{10000}}](https://tex.z-dn.net/?f=%5Cbf%20a%29%5Cqquad%20%0A%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06%28200%29-3%2B%20%5Ccfrac%7B2.4%7D%7B%5Csqrt%5B5%5D%7B200%7D%7D%0A%5C%5C%5C%5C%5C%5C%0Ab%29%5Cqquad%20%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06%282000%29-3%2B%5Ccfrac%7B2.4%7D%7B%5Csqrt%5B5%5D%7B2000%7D%7D%0A%5C%5C%5C%5C%5C%5C%0Ac%29%5Cqquad%20%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06%285000%29-3%2B%5Ccfrac%7B2.4%7D%7B%5Csqrt%5B5%5D%7B5000%7D%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%29%5Cqquad%20%5Ccfrac%7BdP%7D%7Bdx%7D%3D0.06%2810000%29-3%2B%5Ccfrac%7B2.4%7D%7B%5Csqrt%5B5%5D%7B10000%7D%7D)
Stop copying the question, it's confusing
so 100 cookies and 20 brownies
what is the greatest number you can divide them both by?
find the GCF
factor them
100=2*2*5*5
20=2*2*5
so the GCF is the common group to both or 2*2*5 or 20
100/20=5
20/20=1
there are 20 groups, each wit 5 cookies and 1 brownie
20 groups
2 x 10=20 60-20=40. 40 treats left
Answer:
x is in (0, 17)
Step-by-step explanation:
The compound inequality is ...
0 < x < 17
The "equal to" case is not included on either end, so round brackets are used:
(0, 17)
The converse of the statement "If it is summer, then it is warm outside' would be "if it is warm outside then it is summer" Hope this helped!
