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daser333 [38]
3 years ago
13

F ind the volume under the paraboloid z=9(x2+y2) above the triangle on xy-plane enclosed by the lines x=0, y=2, y=x

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
4 0

Answer:

The answer is 48 units³

Step-by-step explanation:

If we simply draw out the region on the x-y plane enclosed between these lines we realize that,if we evaluate the integral the limits all in all cannot be constants since one side of the triangular region is slanted whose equation is given by y=x. So the one of the limit of one of the integrals in the double integral we need to evaluate must be a variable. We choose x part of the integral to have a variable limit, we could well have chosen y's limits as non constant, but it wouldn't make any difference. So the double integral we need to evaluate is given by,

V=\int\limits^2_0 {} \, \int\limits^{x=y}_0 {z} \, dx dy\\V=\int\limits^2_0 {} \, \int\limits^{x=y}_0 {9(x^{2}+y^{2})} \, dx dy

Please note that the order of integration is very important here.We cannot evaluate an integral with variable limit last, we have to evaluate it first.after performing the elementary x integral we get,

V=9\int\limits^2_0 {4y^{3}/3} \, dy

After performing the elementary y integral we obtain the desired volume as below,

V= 48 units^{3}

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The answer would be C, oxygen because there was not a sufficient amount.
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leonid [27]

Answer:

The price of the admission is 15.

Step-by-step explanation:

From the information given, you can write the following equations:

a+3e=45 (1)

a+5e=65 (2), where:

a is the admission cost

e is the exhibition cost

First, you can solve for a in (1):

a=45-3e (3)

Second, you can replace (3) in (2):

45-3e+5e=65

45+2e=65

2e=65-45

2e=20

e=20/2

e=10

Finally, you can replace the value of e in (3):

a=45-3e

a=45-3(10)

a=45-30

a=15

According to this, the price of the admission is 15.

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3 years ago
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2 years ago
Thomas drew a line of best fit for the scatter plot as shown. Enter an equation for the line of best fit in slope-intercept form
juin [17]

Answer:

Equation of line best fits the scatter plot is y = -\frac{30}{7} x + 108

Step-by-step explanation:

Let the equation of line be y = mx + c

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from the graph intercept on y-axis is 108

and the slope of line is given by m = \frac{y_2 - y_1}{x_2 - x_1} where (x_2,y_2) and (x_1,y_1) is the points on line

let, points be (4,96) and (18,36)

on calculating this m = \frac{y_2 - y_1}{x_2 - x_1} = -\frac{30}{7}

Therefore equation of line best fits the scatter plot is y = -\frac{30}{7} x + 108

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