1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
EleoNora [17]
1 year ago
14

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)

Mathematics
1 answer:
MakcuM [25]1 year ago
8 0

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

#SPJ1

You might be interested in
Can you guys name the property please.
Setler [38]

Answer:

I think A. Reflexive Property but if I am wrong, I am so sorry

Step-by-step explanation:

because 6 + 1 is is not subtracting or multiplying

Hope this helps

3 0
3 years ago
What 2 numbers add up to 1 and multiply to -12
Vinil7 [7]
-3 and 4......................
7 0
3 years ago
Read 2 more answers
Bonita deposited $1300 into a bank account that earned 5.75% simple interest each year. She earned $299 in interest before closi
Marrrta [24]
After 4 years, the account gains $325.8, so 4 years
8 0
3 years ago
Read 2 more answers
Write a paragraph comparing the two classes' semester grades. Be sure to compare the extremes, the quartiles, the medians, and t
Gnom [1K]

Answer:

Second class have higher marks and greater spread.

Step-by-step explanation:

First box plot  represents class first. From the first box plot, we get

\text{Minimum value }= 53,Q_1=62,Median=80,Q_3=86,\text{Maximum value }= 89

Range=Maximum-Minimum=89-53=36

IQR=Q_3-Q-1=86-62=24

Second box plot  represents class second. From the second box plot, we get

\text{Minimum value }= 56,Q_1=62,Median=74,Q_3=89,\text{Maximum value }= 96

Range=Maximum-Minimum=96-56=40

IQR=Q_3-Q-1=89-62=27

First class has greater minimum value, first quartile of both classes are same, second class has greater median, first class has greater third quartile and first class has greater maximum value. It means second class have higher marks but class first have less variation.

Second class has greater range and greater inter quartile range. It means data of second class has greater spread.

Therefore, second class have higher marks and greater spread.

3 0
3 years ago
Factor 18 to prime numbers<br> 2 * 9<br> 3* 6<br> 2*3*7<br> 2*3*3
valina [46]

Answer:

Step-by-step explanation:

18 frime factorizarion is 2*3*3

because 18= 2 *9=2*3*3

5 0
3 years ago
Other questions:
  • Profit is equal to the revenue obtained from selling items minus the cost of producing those items, i.e. P(x) = R(x) – C(x) wher
    14·2 answers
  • Pleaseeeeeeeeee help me
    14·1 answer
  • Given 7cx + b = a, rearrange the equation for x, in terms of a, b, and c. A) x = 7c a + b B) x = 7c a − b C) x = a + b 7c D) x =
    6·2 answers
  • Geometry math question no Guessing and Please show work
    6·1 answer
  • which of the following best explain whether 1/2 or 1 is the better estimate of 36/40? remeber that 20/40= 1/2 and 40/40=1​
    14·1 answer
  • I need help asap. I will give 15 points to who ever helps me with The problem is down below
    8·1 answer
  • In ΔXYZ, the measure of ∠Z=90°, the measure of ∠X=65°, and ZX = 4.8 feet. Find the length of YZ to the nearest tenth of a foot.
    12·1 answer
  • If k is one of the roots of x+4k-20/x=0, determine the possible values of k.
    11·1 answer
  • 9. Find the measure of angle<br> a.<br> a<br> 36°<br> 57°
    7·1 answer
  • Show your work <br> A is the answer but you need to show your work to back this up.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!