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PolarNik [594]
3 years ago
6

20 points

Mathematics
2 answers:
BlackZzzverrR [31]3 years ago
7 0
Answer: 2+0.15(x-15)\le 7 which is choice C

============================================================

Explanation:

x = total number of minutes spent using the vacuum

If x is larger than 15, then x-15 represents the amount of time spent past the first 15 minutes. The machine will charge 15 cents per minute at this point. The machine will charge 0.15 dollars for (x-15) minutes. So 0.15*(x-15) dollars is charged on top of the $2 already spent for those first 15 minutes.

In total, the cost for Caroline is
T = 2+0.15(x-15)

This total must not be larger than $7. The total T can be equal to 7 or smaller than 7

So,
T \le 7
2+0.15(x-15)\le 7

blsea [12.9K]3 years ago
6 0
The answer I think is 2+7+0.15x_>15
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3 0
3 years ago
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1. Solve the shape equation puzzle:<br> = 8<br> =<br> = 15
Vesnalui [34]
Star = 5
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3 years ago
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the part of the paraboloid z = 9 − x2 −
Korolek [52]

The vector field

\vec F(x,y,z)=x^2\sin z\,\vec\imath+y^2\,\vec\jmath+xy\,\vec k

has curl

\nabla\times\vec F(x,y,z)=x\,\vec\imath+(x^2\cos z-y)\,\vec\jmath

Parameterize S by

\vec s(u,v)=x(u,v)\,\vec\imath+y(u,v)\,\vec\jmath+z(u,v)\,\vec k

where

\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=(9-u^2)\end{cases}

with 0\le u\le3 and 0\le v\le2\pi.

Take the normal vector to S to be

\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}=2u^2\cos v\,\vec\imath+2u^2\sin v\,\vec\jmath+u\,\vec k

Then by Stokes' theorem we have

\displaystyle\int_{\partial S}\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S

=\displaystyle\int_0^{2\pi}\int_0^3(\nabla\times\vec F)(\vec s(u,v))\cdot\left(\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right)\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_0^3u^3(2u\cos^3v\sin(u^2-9)+\cos^3v\sin v+2u\sin^3v+\cos v\sin^3v)\,\mathrm du\,\mathrm dv

which has a value of 0, since each component integral is 0:

\displaystyle\int_0^{2\pi}\cos^3v\,\mathrm dv=0

\displaystyle\int_0^{2\pi}\sin v\cos^3v\,\mathrm dv=0

\displaystyle\int_0^{2\pi}\sin^3v\,\mathrm dv=0

\displaystyle\int_0^{2\pi}\cos v\sin^3v\,\mathrm dv=0

4 0
3 years ago
A farmer has 450 eggs . egg cartons hold 12 eggs who many cartons does farmer need ?​
Brilliant_brown [7]

Answer:

Step-by-step explanation:

38. 450 divided by 12 is 37.5 and you can’t have half of a carton so one carton would be half full

7 0
3 years ago
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I need the this done soon
Trava [24]
  1. pay attention in class.
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