533/25 as a decimal

∫∫(x+y)dxdy ,d là miền giới hạn bởi x²+y²=1

igor_vitrenko [27]

It looks like you want to compute the double integral

$\displaystyle \iint_D (x+y) \,\mathrm dx\,\mathrm dy$

over the region D with the unit circle x ² + y ² = 1 as its boundary.

Convert to polar coordinates, in which D is given by the set

D = {(r, θ) : 0 ≤ r ≤ 1 and 0 ≤ θ ≤ 2π}

and

x = r cos(θ)

y = r sin(θ)

dx dy = r dr dθ

Then the integral is

$\displaystyle \iint_D (x+y)\,\mathrm dx\,\mathrm dy = \iint_D r^2(\cos(\theta)+\sin(\theta))\,\mathrm dr\,\mathrm d\theta \\\\ = \int_0^{2\pi} \int_0^1 r^2(\cos(\theta)+\sin(\theta))\,\mathrm dr\,\mathrm d\theta \\\\ = \underbrace{\left( \int_0^{2\pi}(\cos(\theta)+\sin(\theta))\,\mathrm d\theta \right)}_{\int = 0} \left( \int_0^1 r^2\,\mathrm dr \right) = \boxed{0}$

3 0

3 years ago

6. We want to build the smallest cube possible using bricks with dimensions 8 cm - 12 cm 20 cm. How many bricks do we need?

Georgia [21]

Answer:

1200

Step-by-step explanation:

We’ll need a number that is evenly dividable by all three values: 8,12 & 15. We can develop the generic common multiple by multiplying all three numbers and get 1440. But is that the smallest common multiple? The quick and dirty way to factor the number is to divide it by it’s various elements and see what works. In this case 1440/12=120 which is the smallest common multiple of the three numbers. The smallest length is therefore 120.

In order to find how many bricks just divide (120x120x120)/(8x12x15)=1200 bricks

7 0

2 years ago

Dennis is cutting construction paper into rectangles for a project he needs to cut one rectangle that is 12 inches times 15 1/4

Nataly_w [17]

Answer:

Dennis need 288.91 square inches of construction paper for his project.

Step-by-step explanation:

Dennis is cutting construction paper into rectangles for a project.

He needs to cut one rectangle that is 12 inches times 15 1/4 inches

First convert the mixed fraction to improper fraction

$15\frac{1}{4} = \frac{(15\times4) + 1}{4} = \frac{61}{4}$

So the area of 1st rectangle is

$A_1 = 12\times \frac{61}{4} = 183 \: in^{2}$

He needs to cut another rectangle that is 10 1/3"" x 10 1/4""

The symbol " means inches

First convert the mixed fraction to improper fraction

$10\frac{1}{3} = \frac{(10\times3) + 1}{3} = \frac{31}{3}$

$10\frac{1}{4} = \frac{(10\times4) + 1}{4} = \frac{41}{4}$

So the area of 2nd rectangle is

$A_2 = \frac{31}{3}\times \frac{41}{4} = 105.91 \: in^{2}$

The total construction paper needed for this project is

$A = A_1 + A_2\\\\A = 183 + 105.91\\\\A = 288.91 \: in^{2}$

Therefore, Dennis need 288.91 square inches of construction paper for his project.

6 0

3 years ago

Write each improper fraction as a mixed number. 9/4. 8/3. 23/6. 11/2. 17/5. 15/8. 33/10. 29/12.

yanalaym [24]

Aloha~! My name is Zalgo and I am here to provide a bit more knowledge to you today. The following Improper Fractions have been changed into Mixed Numbers (and also into decimals because I like Math :3):

9/4 - 2.25 - 2 4/1
8/3 - 2.67 - 2 2/3
23/6 - 3.83 - 3 5/6
11/2 - 5.5 - 5 1/2
17/5 - 3.4 - 3 2/5
15/8 - 1.875 - 1 7/8
33/10 - 3.3 - 3 3/10
29/12 - 2.416 - 2 5/12

I hope that this info helps! :D

"Stay Brainly and stay proud!" - Zalgo

(By the way, can you mark me as Brainliest? I'd greatly appreciate it! Mahalo~! XP)

7 0

3 years ago

Read 2 more answers

It’s number 1. I’ll give brainliest

tamaranim1 [39]

Answer:

D, The last one

Step-by-step explanation:

Hope this Helps!

5 0

3 years ago