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3 years ago

15

What is the area of a circle of the diameter is 2

1 answer:

Alja [10]3 years ago

5 0

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A pizza place has pizzas in 2 different sizes, with 8 different flavors for the crust, and 8 different toppings.

mamaluj [8]

Use multiplication:

$2\text{ sizes}*8\text{ flavors}*8\text{ toppings}=\large\boxed{128\text{ pizzas}}$

This question is basically the same as the other question of yours that I answered, so the explanation is very similar:

You can imagine the possibilities as leaves on a tree. Your tree has 2 large branches to represent the two possible sizes. Each of those branch off into 8 smaller branches, each representing a crust flavor. Each one of the smaller branches has 8 leaves to represent a different topping. Each leaf is a combination of a size, a crust flavor, and a topping, so it represents a complete pizza. Your job is to calculate the number of leaves.

5 0

2 years ago

The surface area of a right circular cone of radius r and height h is S = πr√ r 2 + h 2 , and its volume is V = 1 3 πr2h. What i

kirill115 [55]

Answer:

Required largest volume is 0.407114 unit.

Step-by-step explanation:

Given surface area of a right circular cone of radious r and height h is,

$S=\pi r\sqrt{r^2+h^2}$

and volume,

$V=\frac{1}{3}\pi r^2 h$

To find the largest volume if the surface area is S=8 (say), then applying Lagranges multipliers,

$f(r,h)=\frac{1}{3}\pi r^2 h$

subject to,

$g(r,h)=\pi r\sqrt{r^2+h^2}=8\hfill (1)$

We know for maximum volume $r\neq 0$ . So let $\lambda$ be the Lagranges multipliers be such that,

$f_r=\lambda g_r$

$\implies \frac{2}{3}\pi r h=\lambda (\pi \sqrt{r^2+h^2}+\frac{\pi r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}r h= \lambda (\sqrt{r^2+h^2}+\frac{ r^2}{\sqrt{r^2+h^2}})\hfill (2)$

And,

$f_h=\lambda g_h$

$\implies \frac{1}{3}\pi r^2=\lambda \frac{\pi rh}{\sqrt{r^2+h^2}}$

$\implies \lambda=\frac{r\sqrt{r^2+h^2}}{3h}\hfill (3)$

Substitute (3) in (2) we get,

$\frac{2}{3}rh=\frac{r\sqrt{R^2+h^2}}{3h}(\sqrt{R^2+h^2+}+\frac{r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}rh=\frac{r}{3h}(2r^2+h^2)$

$\implies h^2=2r^2$

Substitute this value in (1) we get,

$\pi r\sqrt{h^2+r^2}=8$

$\implies \pi r \sqrt{2r^2+r^2}=8$

$\implies r=\sqrt{\frac{8}{\pi\sqrt{3}}}\equiv 1.21252$

Then,

$h=\sqrt{2}(1.21252)\equiv 1.71476$

Hence largest volume,

$V=\frac{1}{3}\times \pi \times\frac{\pi}{8\sqrt{3}}\times 1.71476=0.407114$

3 0

3 years ago

What is the value of y in the solution to the system of equations?

Yuliya22 [10]

Answer: y = 8

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Keirra’s mother gave her $7.50 to buy 8 spiral notebooks. With tax, the cost of each notebook is $1.05. Does Keirra have enough

GuDViN [60]

Answer:

No

Step-by-step explanation:

each notebook is $1.05 and the is $7.50

there is only enough for seven notebooks not eight.

7 0

3 years ago

A car manufacturer wants to analyze the safety features of 7 different car models by comparing each model with every other model

klio [65]

Answer:

28,000

Step-by-step explanation:

multiply 7 cars with 4,000

8 0

3 years ago