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miss Akunina [59]
3 years ago
14

HELPPPPPPPPPpppppppppppp!!!!!!

Mathematics
1 answer:
kotykmax [81]3 years ago
4 0
The first quartile is from the first dot to first vertical line, which is 13-15.5.
The maximum is the right most dot, which is 35.
The median is the line in the box, which is 10.5.
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Let S be the solid beneath z = 12xy^2 and above z = 0, over the rectangle [0, 1] × [0, 1]. Find the value of m > 1 so that th
jonny [76]

Answer:

The answer is \sqrt{\frac{6}{5}}

Step-by-step explanation:

To calculate the volumen of the solid we solve the next double integral:

\int\limits^1_0\int\limits^1_0 {12xy^{2} } \, dxdy

Solving:

\int\limits^1_0 {12x} \, dx \int\limits^1_0 {y^{2} } \, dy

[6x^{2} ]{{1} \atop {0}} \right. * [\frac{y^{3}}{3}]{{1} \atop {0}} \right.

Replacing the limits:

6*\frac{1}{3} =2

The plane y=mx divides this volume in two equal parts. So volume of one part is 1.

Since m > 1, hence mx ≤ y ≤ 1, 0 ≤ x ≤ \frac{1}{m}

Solving the double integral with these new limits we have:

\int\limits^\frac{1}{m} _0\int\limits^{1}_{mx} {12xy^{2} } \, dxdy

This part is a little bit tricky so let's solve the integral first for dy:

\int\limits^\frac{1}{m}_0 [{12x \frac{y^{3}}{3}}]{{1} \atop {mx}} \right.\, dx =\int\limits^\frac{1}{m}_0 [{4x y^{3 }]{{1} \atop {mx}} \right.\, dx

Replacing the limits:

\int\limits^\frac{1}{m}_0 {4x(1-(mx)^{3} )\, dx =\int\limits^\frac{1}{m}_0 {4x-4x(m^{3} x^{3} )\, dx =\int\limits^\frac{1}{m}_0 ({4x-4m^{3} x^{4}) \, dx

Solving now for dx:

[{\frac{4x^{2}}{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right. = [{2x^{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right.

Replacing the limits:

\frac{2}{m^{2} }-\frac{4m^{3}\frac{1}{m^{5}}}{5} =\frac{2}{m^{2} }-\frac{4\frac{1}{m^{2}}}{5} \\ \frac{2}{m^{2} }-\frac{4}{5m^{2} }=\frac{10m^{2}-4m^{2} }{5m^{4}} \\ \frac{6m^{2} }{5m^{4}} =\frac{6}{5m^{2}}

As I mentioned before, this volume is equal to 1, hence:

\frac{6}{5m^{2}}=1\\m^{2} =\frac{6}{5} \\m=\sqrt{\frac{6}{5} }

3 0
3 years ago
How do you do this?<br> Please help x
kirill115 [55]

Answer:

Step-by-step explanation:

a). Given equation is y = 3x - 4

   Table for the input-output values is,

   x          -1           0          1            2          3

   y          -7          -4         -1           2          5

Now we can plot these points on the graph (graph attached).

b). Equation is y = -2x + 3

   Table for the input-output values will be,

  x       -1          0         1        2       3

  y       5          3         1        -1       -3

3 0
2 years ago
Mr. Cannon has a piece of land that is 3/7 of an acre. He wants to build 10 houses on his land. How much land does each house ge
sashaice [31]

Answer:

Step-by-step explanation:

3/7 divided by 10 houses= 0.042 acres per house

4 0
3 years ago
Un trabajador gano el lunes 2 y 2/3 euros y el martes 2/5, cuantos euros gano en los dos días?
babymother [125]

Answer: <em>no hablo espanol</em>

5 0
1 year ago
Read 2 more answers
Which is a solution to the equation?
stiks02 [169]
If you would like to know the solution to the equation (x - 2) * (x + 5) = 18, you can calculate this using the following steps:

(x - 2) * (x + 5<span>) = 18
</span>x^2 + 5x - 2x - 10 = 18
x^2 + 3x - 28 = 0
(x + 7) * (x - 4) = 0
1. x = - 7
2. x = 4

The correct result would be x = - 7.
3 0
3 years ago
Read 2 more answers
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