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2 years ago

Max is selling iPhone cases online. He offers two colors red and green. The red

Mathematics

2 answers:

erma4kov [3.2K]2 years ago

6 0

Howdy;)

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stiks02 [169]2 years ago

4 0

Answer:

See below

Step-by-step explanation:

Red cases x = $10 each
Green cases y = $20 each
Minimum target is $500

Required inequality:

10x + 20y ≥ 500

The graph is attached

Some combinations:

50 red or 25 green or 18 of each color etc.
Any combination of positive numbers in the shaded region.

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steposvetlana [31]

The two curves $y=x$ and $y=x^{1/15}$ intersect at $x=0$ and $x=1$ , with $x^{1/15}\ge x$ over $0\le x\le1$ .

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$\displaystyle\pi\int_0^1\left(\left(x^{1/15}\right)^2-x^2\right)\,\mathrm dx=\pi\int_0^1\left(x^{2/15}-x^2\right)\,\mathrm dx=\pi\left(\frac{15}{17}-\frac13\right)=\boxed{\frac{28\pi}{51}}$

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We have $y=x^{1/15}\implies x=y^{15}$ . The curves $x=y$ and $x=y^{15}$ intersect at $y=0$ and $y=1$ , with $y\ge y^{15}$ over $0\le y\le1$ .

$\displaystyle2\pi\int_0^1y\left(y-y^{15}\right)\,\mathrm dy=2\pi\int_0^1\left(y^2-y^{16}\right)\,\mathrm dy=2\pi\left(\frac13-\frac1{17}\right)=\boxed{\frac{28\pi}{51}}$