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kolezko [41]
3 years ago
11

Question 2 (1 point) Solve 2d - 7= 8-34. O a d- 5 Oь d = -15 Ос d=-1 5 Od Submit​

Mathematics
1 answer:
harkovskaia [24]3 years ago
8 0

Answer: D= -9.5 or -19/2

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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
Which shows a graph of a linear equation in standard form Ax + By = C, where A = 0, B is positive, and C is negative? A coordina
IrinaK [193]

Answer:

A coordinate plane with a horizontal line passing through (negative 4, negative 3), (0, negative 3) and (4, negative 3).

Step-by-step explanation:

Ax + By = C, where A = 0, B is positive, and C is negative

By= C or y= C/B which is negative

Since A is zero and C is negative, the line is parallel to x- axis and has negative value for y, so it is a horizontal line below zero

---------------

A coordinate plane with a vertical line passing through (1, negative 4), (1, 0) and (1, 4).

  • no, the line is horizontal

A coordinate plane with a vertical line passing through (negative 2, negative 4), (negative 2, 0) and (negative 2, 4).

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A coordinate plane with a horizontal line passing through (negative 4, 4), (0, 4) and (negative 4, 4).

  • no, the y-values should be negative

A coordinate plane with a horizontal line passing through (negative 4, negative 3), (0, negative 3) and (4, negative 3).

  • yes, this is horizontal line below zero
8 0
3 years ago
Read 2 more answers
Perez’s Ski Shop made a profit of $32,000 last year. This year, the profits are 250 percent of last year’s profits. How much of
Tanzania [10]

Answer:

$80,000 I think is right

3 0
3 years ago
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Slove system of equation.<br><br> 2x - 6y = 8<br> -3x + 9y = 12
Bond [772]
Answers:

2x - 6y = 8 -> x = 4 + 3y

-3x + 9y = 12 -> x = -4 + 3y
7 0
2 years ago
A pitcher holds 3/4 gallons of kool-aid. Martin wants to pour equal amounts of kool- aid into 6 smaller cotainers. How much kool
statuscvo [17]

Answer:

\dfrac{1}{8}\ gallons

Step-by-step explanation:

Amount of kool - aid that the pitcher can hold = \frac{3}4 gallons

There are 6 smaller containers in which this kool - aid is to be adjusted.

Also, the volume of the smaller containers is equal to each other i.e. the containers are identical to each other in terms of volume.

To find:

The amount of kool - aid that each container can hold?

Solution:

Volume of all the smaller containers combined = Volume of the kool - aid available

Let the volume of one smaller container = V

V + V + V + V + V + V = \dfrac{3}{4}\ gallons

\Rightarrow 6V = \dfrac{3}{4}\ gallons\\\Rightarrow V = \dfrac{3}{4\times 6 }\ gallons\\\Rightarrow V=\bold{\dfrac{1}{8}\ gallons}

\frac{1}{8}\ gallons of kool - aid is the amount that each smaller can hold.

8 0
3 years ago
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