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4 years ago

Simplify (-3ab^2)^3

Mathematics

2 answers:

koban [17]4 years ago

7 0

(-3ab^2)^3

(-3)^3 a^3 (b^2)^3

-27 a^3 b^(2*3)

-27 a^3 b^6

pogonyaev4 years ago

3 0

Answer:

(-3ab^2)^3

(-3)^3 a^3 (b^2)^3

-27 a^3 b^(2*3)

-27 a^3 b^6Step-by-step explanation:

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Elise built a large rectangular vegetable garden that is 9 meters long and has an area of 72 square meters.

taurus [48]

Answer: 34 meters.

Step-by-step explanation;

Step One. Find the value of the width. Use an equation with w representing the width and the two values you already have. 9 meters x w = 72 square meters.

Step Two. Solve for width. This is w = 8.

Step Three. Use the value for width in a perimeter formula to calculate the perimeter; 9(2) + 8(2). <em>This is 34 meters for perimeter</em>.

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3 years ago

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A computer went on a 15% off sale. The sale price is given as $510. What was the original price of the computer?

cricket20 [7]

The original price of the computer is $600

During the sale, the computer is 15% cheaper. This means that the computer is selling at 85% (100 - 15%) of its original price.

In order to determine the answer to the question, the following information would be needed :

Sales price of the computer = $510
The percentage of the original price the computer is being sold for during the sales = 85%

The formula that can be used to determine the original price of the computer is : sales price / percentage of the original price

$510 / 85%

$510 / 0.85

= $600

A similar question was solved here: brainly.com/question/24457716?referrer=searchResults

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2 years ago

Which of the following has 5.1012 in written form?

Pani-rosa [81]

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3 years ago

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Express GHD80.00 as a percentage of GHD320.00

lara [203]

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If using a calculator, you can calculate one number as a percentage of another by dividing the numbers and multiplying by 100.

Step-by-step explanation:

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2 years ago

Surface integrals using an explicit description. Evaluate the surface integral \iint_{S}^{}f(x,y,z)dS using an explicit represen

Jobisdone [24]

Parameterize $S$ by the vector function

$\vec r(x,y)=x\,\vec\imath+y\,\vec\jmath+f(x,y)\,\vec k$

so that the normal vector to $S$ is given by

$\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=\left(\vec\imath+\dfrac{\partial f}{\partial x}\,\vec k\right)\times\left(\vec\jmath+\dfrac{\partial f}{\partial y}\,\vec k\right)=-\dfrac{\partial f}{\partial x}\vec\imath-\dfrac{\partial f}{\partial y}\vec\jmath+\vec k$

with magnitude

$\left\|\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}\right\|=\sqrt{\left(\dfrac{\partial f}{\partial x}\right)^2+\left(\dfrac{\partial f}{\partial y}\right)^2+1}$

In this case, the normal vector is

$\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=-\dfrac{\partial(8-x-2y)}{\partial x}\,\vec\imath-\dfrac{\partial(8-x-2y)}{\partial y}\,\vec\jmath+\vec k=\vec\imath+2\,\vec\jmath+\vec k$

with magnitude $\sqrt{1^2+2^2+1^2}=\sqrt6$ . The integral of $f(x,y,z)=e^z$ over $S$ is then

$\displaystyle\iint_Se^z\,\mathrm d\Sigma=\sqrt6\iint_Te^{8-x-2y}\,\mathrm dy\,\mathrm dx$

where $T$ is the region in the $x,y$ plane over which $S$ is defined. In this case, it's the triangle in the plane $z=0$ which we can capture with $0\le x\le8$ and $0\le y\le\frac{8-x}2$ , so that we have

$\displaystyle\sqrt6\iint_Te^{8-x-2y}\,\mathrm dx\,\mathrm dy=\sqrt6\int_0^8\int_0^{(8-x)/2}e^{8-x-2y}\,\mathrm dy\,\mathrm dx=\boxed{\sqrt{\frac32}(e^8-9)}$

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3 years ago