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. Ms. Ache is paid $1300 per week but is fined $100 each day she is late to work. Ms. Ache wants to make at least $3,000 over th

DerKrebs [107]

Answer:

1250(3) = 3750

3750 - 100d ≥ 3000

-100d ≥ -750

d ≤ 7.5

She can miss no more than 7 days to make $3000.

Step-by-step explanation:

5 0

4 years ago

The total surface area of a closed cylinder is

Degger [83]

The maximum volume of the cylinder is 27147.355 at the maximum point $r = \frac{50}{\sqrt{3} }$ .

<h3>How do you find the maximum volume of the cylinder?</h3>

The formula for the volume of the cylinder v = $\pi$ $r^{2}$ h, To find the maximum volume of the cylinder we apply the condition of maxima $\frac{\mathrm{d} v}{\mathrm{d} r}$ = 0.

Let r cm be the radius and h cm be the height of the closed cylinder.

Then, Total surface area of the cylinder = $2\pi r(r+h)$

$5000$ = $2\pi r^{2} +2\pi rh$

$h$ = $\frac{5000-2\pi r^{2} }{2\pi rh}$ .............(1)

Volume of the cylinder v = $\pi r^{2} h$

Substitute the value of $h$ in the above equation

$\Rightarrow$ = $\pi r^{2}$ × $\left [ \frac{5000-2\pi r^{2}}{2\pi r} \right ]$

$\Rightarrow$ = $\frac{r}{2}$ × $(5000-2\pi r^{2} )$

$\Rightarrow$ v = $2500r-\pi r^{3}$ ..............(2)

Now, for the maximum volume of the cylinder $\frac{\mathrm{d} v}{\mathrm{d} r}$ = 0

$\Rightarrow$ $\frac{\mathrm{d} (2500r-\pi r^{3})}{\mathrm{d} r} = 0$

$\Rightarrow$ $3\pi r^{2} = 2500$

$\Rightarrow$ $r^{2} = \frac{2500}{3\pi }$

$\Rightarrow$ $r = \frac{50}{\sqrt{3\pi } }$

Volume is maximum for $r = \frac{50}{\sqrt{3\pi } }$

Then, v = $2500r-\pi r^{3}$

$\Rightarrow$ = $2500 \frac{50}{\sqrt{3\pi } } -\pi (\frac{50}{\sqrt{3\pi } } )^{3}$

$\Rightarrow$ = $\frac{125000}{\sqrt{3\pi } } - \frac{125000}{3\sqrt{3\pi } }$

$\Rightarrow$ = $\frac{125000}{\sqrt{3\pi } }$ × $\frac{2}{3}$

$\Rightarrow$ = $\frac{250000}{3\sqrt{3\pi } }$

$\Rightarrow$ v = 27147.355

Hence, The maximum volume of the cylinder is 27147.355 at the maximum point $r = \frac{50}{\sqrt{3} }$ .

To learn more about total surface area and volume of the cylinder from the given link

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3 0

2 years ago

Lucy is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes

Nadusha1986 [10]

The total possible outcomes are there if she rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4, spins a spinner with 5 equal-sized sections is 20.

<h3>What is permutation and combination?</h3>

A permutation can be defined as the number of ways a set can be arranged, order matters but in combination the order does not matter.

We have:

Total number of outcomes for pyramid = 4

Total number of outcomes for spinner = 5

Total outcomes = 4×5 (multiplication rule of counting)

= 20

Thus, the total possible outcomes are there if she rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4, spins a spinner with 5 equal-sized sections is 20.

Learn more about permutation and combination here:

brainly.com/question/2295036

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7 0

2 years ago

[HELP, VERY IMPORTANT]The Baker family started a farm in 1900, and the farm has been passed down from generation to generation.

denpristay [2]

Looking first at the graph, we see that the intial potato production was 25000 lb, and that potato production tapered off to below 20000 lb over time.

Analyzing the equation for corn production: C(t) = 25,000 + 500 ln(t + 1), we see

that the initial production was 25000 lb per year and that this increases steadily with time.

Thus, answer A is false.

Answer B is false because at the outset the amounts of corn and potatoes was equal (25000 lb).

Answer D makes sense. Productions were both 25000 lb at the beginning, but the corn production rose steadily over time, exceeding the potato production.

4 0

4 years ago

Read 2 more answers

Write the statements “If you take away 6 from 6 time a number, you get 60”in the form of equations:.

ratelena [41]

6-6+6x10 explanation

6 0

4 years ago

Read 2 more answers