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2 years ago

Jada & Zeke compare their monthly text message plans. Jada's plan costs $5 plus an additional $0.05 per text.

Mathematics

1 answer:

Nata [24]2 years ago

8 0

Answer:

t=100

Step-by-step explanation:

The easiest way is to graph them—otherwise, set each equation equal to each other:

.1x=.05x +5

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Please help I have no idea

marin [14]

The answer would be the top left one, and the correct answer would be 17/8 or 2 1/8.

4 0

2 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

2 years ago

If you have 256 data points, how many classes (bins) would sturges' rule suggest

MArishka [77]

<span>Since Sturge's Rule states that the optimal number of bins is equal to the 1 plus 3.3 log(n), where n is the number of data points, the estimated solution (since you can only have whole bins) is to provide 6 bins, each storing 42 to 43 data points.</span>

8 0

2 years ago

What are the solutions to the equation 0 = x2 – x –6? Select two options

KatRina [158]

Answer:

$x=3$ or $x=-2$

Step-by-step explanation:

This is factorable.

The leading coefficient is 1.

Since this is a quadratic all we have to do is find two numbers that multiply to be c and add up to be b to factor the expression that is to the left of the equal sign.

By the way a quadratic expression looks like $ax^2+bx+c$ .