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
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}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bb%20-%20a%7D%20%5Cint%5Climits%5Eb_a%20%7Bf%28x%2Cy%29%7D%20%5C%2C%20dA%20%3D%20%5Cfrac%7B1%7D%7B1%20-%200%7D%20%5Cint%5Climits%5E1_0%20%5Cint%5Climits%5E9_0%20%7B3xy%7D%20%5C%2C%20dxdy%20%5C%5C%3D%20%5Cfrac%7B3%7D%7B1%7D%20%5Cint%5Climits%5E1_0%20%7Bx%7D%20%5C%2Cdx%5Cint%5Climits%5E9_0%20%7By%7D%20%5C%2Cdy%5C%5C%20%3D%20%20%5Cfrac%7B3%7D%7B1%7D%20%5B%5Cfrac%7Bx%5E%7B2%7D%20%7D%7B2%7D%20%5D%5E%7B1%7D_%7B0%7D%5B%5Cfrac%7By%5E%7B2%7D%20%7D%7B2%7D%20%5D%5E%7B9%7D_%7B0%7D%20%20%5C%5C%3D%203%5B%5Cfrac%7B1%5E%7B2%7D%20%7D%7B2%7D%20-%20%5Cfrac%7B0%5E%7B2%7D%7D%7B2%7D%20%5D%20%5B%5Cfrac%7B9%5E%7B2%7D%20%7D%7B2%7D%20-%20%5Cfrac%7B0%5E%7B2%7D%7D%7B2%7D%20%5D%20%5C%5C%3D%203%5B%5Cfrac%7B1%7D%7B2%7D%20-%200%20%5D%5B%5Cfrac%7B81%7D%7B2%7D%20-%200%20%5D%5C%5C%3D%20%20%5Cfrac%7B81%7D%7B2%7D%20X3%20X%20%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%3D%20%20%5Cfrac%7B243%7D%7B4%7D)
So, the average value of f over the region D is 243/4
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First, list all the prime factors of both terms:
23x²: 1, 23, x, and x
6x: 1, 2, 3, and x
The two numbers share the prime factors 1 and x, so the GCF of 23x² and 6x is 1x, or x.
Answer:
By plus 2 points
Step-by-step explanation:
The median average is the midpoint in a list of acceding values, in this case the median is 16,18,<em>20</em>,24,28 so its 20. But after they score 30 points in their next game, the median will be 16,18,<em>20</em>,<em>24</em>,28,30. Since there is 2 midpoints we have to take the mean average of both, which is just adding up the value of all terms and then dividing by the number of terms in the list.
(20+24)/2 = 22
Our median average before the sixth game is 20 and after its 22, do the change in median is +2
Answer:
54 is the answer because jgcbgvnhdcmhdvmhffcfhdchfscvhfchyfbjf
Answer:
About 95 miles
Step-by-step explanation:
Let's set up a proportion using the following set up:
miles / gallons = miles / gallons
We know the car can travel 38 miles on 2.4 gallons of gas.
38 miles / 2.4 gallons = miles/ gallons
We don't know how far the car can travel on 6 gallons. Therefore, we can say the car travels x miles on 6 gallons of gas.
38 miles / 2.4 gallons = x miles /6 gallons
38/2.4=x/6
We want to find x (miles for 6 gallons). Therefore, we must isolate x.
x is being divided by 6. The inverse of division is multiplication. Multiply both sides by 6.
6*(38/2.4)=(x/6)*6
6*(38/2.4)=x
6*15.8333333=x
94.9999998=x
Let's round to the nearest whole number. The 9 in the tenth place tells us to round up.
95 ≈x
x ≈95 miles
The car can travel about 95 miles on 6 gallons of gas.
