What is the sum of 2xy and 17xy?

A candle in the shape of a circular cone has a base of radius r and a height of h that is the same length as the radius. which e

ladessa [460]

Answer:

$\frac{r(1-\sqrt{2})}{-3}$

Step-by-step explanation:

Volume of cone = $\frac{1}{3} \pi r^{2} h$

Since we are given that a circular cone has a base of radius r and a height of h that is the same length as the radius

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

= $\frac{1}{3} \pi r^{3}$

Surface area of cone including 1 base = $\pi r^{2} +\pi\times r \times \sqrt{r^2+h^2}$

Since r = h

So, area = $\pi r^{2} +\pi\times r \times \sqrt{r^2+r^2}$

= $\pi r^{2} +\pi\times r \times \sqrt{2r^2}$

= $\pi r^{2} +\pi\times r^2 \times \sqrt{2}$

Ratio of volume of cone to its surface area including base :

$\frac{\frac{1}{3} \pi r^{3}}{\pi r^{2} +\pi\times r^2 \times \sqrt{2}}$

$\frac{\frac{1}{3}r}{1+\sqrt{2}}$

$\frac{r}{3(1+\sqrt{2})}$

Rationalizing

$\frac{r}{3(1+\sqrt{2})} \times \frac{1-\sqrt{2}}{1-\sqrt{2}}$

$\frac{r(1-\sqrt{2})}{-3}$

Hence the ratio the ratio of the volume of the candle to its surface area(including the base) is $\frac{r(1-\sqrt{2})}{-3}$

8 0

3 years ago

Read 2 more answers

One number is times a first number. A third number is 100 more than the first number. If the sum of the three numbers

icang [17]

When a number is 3 times a first number. A third number is 100 more than the first number and the sum of the three numbers is 450, the numbers are 70, 170 and 210.

<h3>How to calculate the numbers?</h3>

Let the first number = x

Second number = 3x

Third number = x + 100

Sum = 450

The numbers will be:

x + 3x + x + 100 = 450

5x + 100 = 450

5x = 450 - 100

5x = 350

Divide

x = 350 / 5

x = 70

First number = 70

Second number = 3x = 3 × 70 = 210

Third number = x + 100 = 70 + 100 = 170

Therefore, the numbers are 70, 170 and 210.

Learn more about numbers on:

brainly.com/question/24644930

#SPJ1

One number is 3 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 450 , find the numbers.

8 0

1 year ago

Which ratio forms a proportiona with 5:15? A: 10:20 B: 75:5 C: 3:1 D: 1:3

Nata [24]

Answer:

C

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Log 10(x + 3) – log 10(x-3) = 1

nadezda [96]

Answer:33/9

Step-by-step explanation:

Log10(x+3)-Log10(x-3)=1

Log10((x+3)/(x-3))=1

(x+3)/(x-3)=10^1

(x+3)/(x-3)=10

Cross multiply

x+3=10(x-3)

Open brackets

x+3=10x-30

Collect like terms

10x-x=30+3

9x=33

Divide both sides by 9

9x/9=33/9

x=33/9

4 0

3 years ago

Doug took 180 photos during his vacation. He took 2/3 of photos during

pogonyaev

Answer:

66 pictures

Step-by-step explanation:

180 ÷ 3 = 60 60 x 2 = 120

120 = 2/3. He took 120 pictures on the first day of his vacation.

120 ÷ 4 = 30 30 x 1 = 30

30 = 1/4. He took 30 pictures of landscapes

120 ÷ 10 = 12 12 x 3 = 36

0.3 = 36. He took 36 pictures of people.

36 + 30 = 66 pictures.

He took 66 pictures of landscapes and people.

Hopefully this helps :3 sorry if wrong :( plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3

-Bee~

7 0

2 years ago