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2 years ago

8

Maria is planning a party. Nancy, her friend, suggest that she should order three pizzas for every seven people. If she is expec

ting 21 people at the party, how many pizzas should she order?

1 answer:

Eva8 [605]2 years ago

8 0

She should order nine because 21÷7=3 and 3*3=9

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strojnjashka [21]

Answer:

The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.

Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, formulas for the candle are described below:

$V = \pi\cdot r^{2}\cdot h$ (1)

$A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot r \cdot h$ (2)

Where:

$r$ - Radius, in centimeters.

$h$ - Height, in centimeters.

By (1) we have an expression of the height in terms of the volume and the radius of the candle:

$h = \frac{V}{\pi\cdot r^{2}}$

By substitution in (2) we get the following formula:

$A_{s} = 2\pi \cdot r^{2} + 2\pi\cdot r\cdot \left(\frac{V}{\pi\cdot r^{2}} \right)$

$A_{s} = 2\pi \cdot r^{2} +\frac{2\cdot V}{r}$

Then, we derive the formulas for the First and Second Derivative Tests:

First Derivative Test

$4\pi\cdot r -\frac{2\cdot V}{r^{2}} = 0$

$4\pi\cdot r^{3} - 2\cdot V = 0$

$2\pi\cdot r^{3} = V$

$r = \sqrt[3]{\frac{V}{2\pi} }$

There is just one result, since volume is a positive variable.

Second Derivative Test

$A_{s}'' = 4\pi + \frac{4\cdot V}{r^{3}}$

If $\left(r = \sqrt[3]{\frac{V}{2\pi}}\right)$ :

$A_{s} = 4\pi + \frac{4\cdot V}{\frac{V}{2\pi} }$

$A_{s} = 12\pi$ (which means that the critical value leads to a minimum)

If we know that $V = 3217\,cm^{3}$ , then the dimensions for the minimum amount of plastic are:

$r = \sqrt[3]{\frac{V}{2\pi} }$

$r = \sqrt[3]{\frac{3217\,cm^{3}}{2\pi}}$

$r = 8\,cm$

$h = \frac{V}{\pi\cdot r^{2}}$

$h = \frac{3217\,cm^{3}}{\pi\cdot (8\,cm)^{2}}$

$h = 16\,cm$

And the amount of plastic needed to cover the outside of the candle for packaging is:

$A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot r \cdot h$

$A_{s} = 2\pi\cdot (8\,cm)^{2} + 2\pi\cdot (8\,cm)\cdot (16\,cm)$

$A_{s} \approx 1206.372\,cm^{2}$

The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.

3 0

2 years ago

4 If y = 2x + 1, what is X=-3?<br>A 5<br>B - 7<br>C -5<br>D 6<br>

Hoochie [10]

Answer:

c

Step-by-step explanation:

y=2(-3)+1

y=-6+1

y=-5

USE SUBSTITUTION

5 0

2 years ago

Read 2 more answers

Who is the richest president in the world

olga55 [171]

The richest president in the world is Sebastian Pinera, President of Chile with $2.4 billion.

3 0

2 years ago

The polygons are similar. Find the missing side length.

zloy xaker [14]

Answer:

44

Step-by-step explanation:

Since triangles are similar, so their corresponding sides would be in proportion.

Therefore,

$\frac{24}{32} = \frac{33}{?} \\ \\ \\ ? = \frac{32 \times 33}{24} \\ \\ ? = \frac{4\times 33}{3} \\ \\ ? = 4\times 11 \\ \\ ? = 44 \: units$

6 0

2 years ago

Select the assumption necessary to start an indirect proof of the statement. If 3a+7 < 28, then a<7.

pashok25 [27]

When applying indirect proofs, we assume the negation of the conclusion is true, and show that this assumption would lead to nonsense, or contradiction.

In our case we assume a is not smaller than 7, that is we assume a≥7.

a≥7 then, multiplying both sides by 3:
3a≥21, then, adding both sides 7:

3a+7≥28,

which is a contradiction because 3a+7 is smaller than 28.

So our assumption is wrong, which means the opposite of it is correct.

Answer: assume a≥7

7 0

2 years ago