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OLEGan [10]
3 years ago
10

Is 12x + 24 equation to 3(4x+8

Mathematics
1 answer:
s344n2d4d5 [400]3 years ago
3 0
Yes, because 3×(4x)= 12x (3 times 4 is 12. add the "x" and you have 12x) and 3×8=24 . If you put the two together, you get 12x+24 as the expression. ^_^
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the area A, of a square whose side has length s is given by A=s^2. calculate the length, s, of the side of a square as the posit
Romashka [77]

Given that the area of this square is 361 ft^2, the side length is √(361 ft^2), or 19 ft.

8 0
3 years ago
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
Nadia plans to paint her jewelry box. The box is shaped like a rectangular prism with the dimensions
Pachacha [2.7K]

Answer:

132\ in^{2} is closest to the total surface area of the box

Step-by-step explanation:

we know that

The surface area of the box is equal to

SA=2B+PH

where

B is the area of the base

P is the perimeter of the base

H is the height of the box

we have

L=7\frac{3}{4}\ in=\frac{7*4+3}{4}=\frac{31}{4}\ in

W=3\frac{1}{4}\ in=\frac{3*4+1}{4}=\frac{13}{4}\ in

H=3\frac{7}{8}\ in=\frac{3*8+7}{8}=\frac{31}{8}\ in

<em>Find the area of the base B</em>

B=LW

B=(\frac{31}{4})(\frac{13}{4})=\frac{403}{16}\ in^{2}

<em>Find the perimeter of the base P</em>

P=2(L+W)

P=2(\frac{31}{4}+\frac{13}{4}))

P=2(\frac{44}{4})=22\ in

<em>Find the surface area</em>

SA=2(\frac{403}{16})+22(\frac{31}{8})

SA=(\frac{403}{8})+(\frac{682}{8})

SA=\frac{1,085}{8}=135.625\ in^{2}

6 0
3 years ago
Pablo mixes three units white paint and one unit of black paint to make gray paint. What two equations show the relationship bet
svet-max [94.6K]
It’s b and when you put w to egbert
8 0
3 years ago
Anyone mind helping me ?
storchak [24]

Answer:

<GOJ

Step-by-step explanation:

O is the center of the circle

So central angle is <GOJ

3 0
3 years ago
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