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HACTEHA [7]
3 years ago
5

Taylor is building doghouses to sell. Each doghouse requires 3 full sheets of plywood which Taylor cuts into new shapes. The ply

wood is shipped in bundles of 14 full sheets. How many doghouses can Taylor make from 12 bundles of plywood?
Mathematics
1 answer:
lapo4ka [179]3 years ago
8 0

Answer:

Step-by-step explanation:

taylor is building doghouses to sell. each doghouse requires 3 full sheets of plywood which taylor cuts into new shapes. the plywood is shipped in bundles of 14 full sheets. how many doghouses can taylor make from 12 bundles of plywood?

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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
tresset_1 [31]

Because I've gone ahead with trying to parameterize S directly and learned the hard way that the resulting integral is large and annoying to work with, I'll propose a less direct approach.

Rather than compute the surface integral over S straight away, let's close off the hemisphere with the disk D of radius 9 centered at the origin and coincident with the plane y=0. Then by the divergence theorem, since the region S\cup D is closed, we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV

where R is the interior of S\cup D. \vec F has divergence

\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(xz)}{\partial x}+\dfrac{\partial(x)}{\partial y}+\dfrac{\partial(y)}{\partial z}=z

so the flux over the closed region is

\displaystyle\iiint_Rz\,\mathrm dV=\int_0^\pi\int_0^\pi\int_0^9\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=0

The total flux over the closed surface is equal to the flux over its component surfaces, so we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iint_S\vec F\cdot\mathrm d\vec S+\iint_D\vec F\cdot\mathrm d\vec S=0

\implies\boxed{\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=-\iint_D\vec F\cdot\mathrm d\vec S}

Parameterize D by

\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec k

with 0\le u\le9 and 0\le v\le2\pi. Take the normal vector to D to be

\vec s_u\times\vec s_v=-u\,\vec\jmath

Then the flux of \vec F across S is

\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_u\times\vec s_v)\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_0^9(u^2\cos v\sin v\,\vec\imath+u\cos v\,\vec\jmath)\cdot(-u\,\vec\jmath)\,\mathrm du\,\mathrm dv

=\displaystyle-\int_0^{2\pi}\int_0^9u^2\cos v\,\mathrm du\,\mathrm dv=0

\implies\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\boxed{0}

8 0
3 years ago
Write a multiplication sentence using zero as the property
gtnhenbr [62]
The "Property<span> of </span>Zero" of Multiplication <span>shows that the product of </span>zero<span> and any number is </span>zero<span>.
</span>
Here is one example:
___________________________
5 x 0 = 0 .
______________________________
{"Five times zero equals zero."}.
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___________________________________
4 0
3 years ago
Anyone know this answer?
damaskus [11]
La of sine:

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6 0
3 years ago
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Flauer [41]

Answer:

She spent $160 total

Step-by-step explanation:

(5 × 20) + (3 × 20)          Multiply in the parentheses first

100 + 60                        Add

$160 total

If this answer is correct, please make me Brainliest!

6 0
3 years ago
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Sally Lauren is the external auditor for Modus Industries, a public company that manufactures disk drives. As she analyzes the n
ololo11 [35]

Answer:

Fictitious account receivable

Step-by-step explanation:

Fictitious account receivables involves creating fake accounts or fake sales for the purpose of having the company appear to be in a better financial condition. This can be by creating fake invoices for fake customers.

These malicious activities are carried out by employees for the purpose of having an increase in sales commission.

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