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EleoNora [17]
2 years 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]2 years 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

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Answer:

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Step-by-step explanation:

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Mathematical Answer: 2cups*3/4 = 1 and 1/2 cups or 1.5 cups.

How to do it while cooking:

  1. Get out a container large enough to hold at least 4 cups sauce
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And there you go you have 3/4 of 2 cups of sauce.

<em>Hoped this helped!</em>

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Vlad1618 [11]
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2 years ago
I need help with these 2
Slav-nsk [51]

Answer:

Step-by-step explanation: Hey for the second one I got y = -3/4x -0.5 I'm not sure if its correct though sorry if not
ill try my best to explain my solution though
1. From the parallel equation (3x + 4y = 12) all we need to do is find the slope

So the easiest way to do so is to put the said equation in <u>y-intercept </u>form

y=mx +b
m= slope

b= y intercept

so 1. 3x + 4y = 12

=

4y = 12-3x

divide that by 4 to get only y

y=3-3/4x

-3/4 is our slope

y=-3/4x+b

than we have a point -2, -2

if we put -2 for y

-2=-3/4x+b

and then we put our -2 for x
-2 = -3/4 * -2 + b

=

-2  = -1.5 +b
b=-0.5

Answer : y=-3/4x-0.5

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attashe74 [19]

Answer:

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Step-by-step explanation:

shipping and handling cost = percentage of shipping and handling x price

30% x $31

0.3 x $31 = $9.30

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