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3 years ago

Which expression is equivalent to 3x+10-x+12

Mathematics

1 answer:

Blababa [14]3 years ago

3 0

2(x+11) is equivalent to 3x+10x+12

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Find the average value of f over the region D. f(x, y) = 3xy, D is the triangle with vertices (0, 0), (1, 0), and (1, 9)

MakcuM [25]

The average value of f over the region D is 243/4

To answer the question, we need to know what the average value of a function is

<h3>What is the average value of a function?</h3>

The average value of a function f(x) over an interval [a,b] is given by

$\frac{1}{b - a} \int\limits^b_a {f(x)} \, dx$

Now, given that we require the average value of f(x,y) = 3xy over the region D where D is the triangle with vertices (0, 0), (1, 0), and (1, 9).

x is intergrated from x = 0 to 1 and the interval is [0,1] and y is integrated from y = 0 to y = 9

So, $\frac{1}{b - a} \int\limits^b_a {f(x,y)} \, dA = \frac{1}{1 - 0} \int\limits^1_0 \int\limits^9_0 {3xy} \, dxdy \\= \frac{3}{1} \int\limits^1_0 {x} \,dx\int\limits^9_0 {y} \,dy\\ = \frac{3}{1} [\frac{x^{2} }{2} ]^{1}_{0}[\frac{y^{2} }{2} ]^{9}_{0} \\= 3[\frac{1^{2} }{2} - \frac{0^{2}}{2} ] [\frac{9^{2} }{2} - \frac{0^{2}}{2} ] \\= 3[\frac{1}{2} - 0 ][\frac{81}{2} - 0 ]\\= \frac{81}{2} X3 X \frac{1}{2} \\= \frac{243}{4}$

So, the average value of f over the region D is 243/4

Learn more about average value of a function here:

brainly.com/question/15870615

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8 0

2 years ago

Mary can paint a house in 12 hours.it takes them 2hours.without help,how long would it take Nancy to complete the same job?

frez [133]

It Takes Nancy 10 Hours.

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4 years ago

Which situation could best be represented by the integer 120

ASHA 777 [7]

Which situation could best be represented by the integer 120?

1. could be negative but the likely of losing 120 pounds is very low

2. this number would be positive

3. could be between -1 to - infinity

answer: 3. the number of feet below a surface

8 0

3 years ago

I need some help on this math

olga55 [171]

Answer:

Step-by-step explanation:

2n^2/3pq^4-(-3)

7 0

3 years ago

Jocelyn was asked to draw a square with an area of 20 cm2. Which could be the side length of the square? I. 20 cm II. 5 cm III.

Paladinen [302]

Answer:

The correct option is III: 4.5 cm.

Step-by-step explanation:

The area of a square is the following:

$A = b^{2}$ (1)

Where:

A: is the area

b: is the side of the square

We have that the area is 20 cm², hence by solving equation (1) for <em>b</em> we can find the side:

$b = \sqrt{A} = \sqrt{20 cm^{2}} = 4.5 cm$

Therefore, the correct option is III: 4.5 cm.

I hope it helps you!

5 0

3 years ago