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3 years ago

A _______ represents the idea of "if and only if." Its symbol is a double arrow, left right arrow↔.

Mathematics

1 answer:

Bond [772]3 years ago

4 0

Answer:

A bi-conditional statement represents the idea of "if and only if." Its symbol is a $\leftrightarrow$ .

Step-by-step explanation:

We have been given an incomplete sentence. We are supposed to fill in the given blank.

A _______ represents the idea of "if and only if." Its symbol is a $\leftrightarrow$ .

We know that "if and only if" stands for bi-conditional statement, which represents either both statements are true or both are false.

The symbol $\leftrightarrow$ represent a bi-conditional statement.

Therefore, our complete statement would be: A bi-conditional statement represents the idea of "if and only if." Its symbol is a $\leftrightarrow$ .

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Write a polynomial that represents the length of the rectangle help please !!

disa [49]

Answer:

$\textsf{Length}=0.8x^2-0.7x+0.7\quad \sf units$

Step-by-step explanation:

Area of a rectangle = width × length

Therefore, to find the length of the rectangle, we need to divide the area by the width.

Using long division:

$\large\begin{array}{r}0.8x^2-0.7x+0.7\phantom{)} \\x+0.5{\overline{\smash{\big)}\,0.8x^3-0.3x^2+0.35x+0.35\phantom{)}}}\\-~\phantom{(}\underline{(0.8x^3+0.4x^2)\phantom{-b))))))))))))))}}\\0-0.7x^2+0.35x+0.35\phantom{)}\\ \underline{-~\phantom{()}(-0.7x^2-0.35x)\phantom{-b)))))}}\\ 0.7x+0.35\phantom{)}\\\underline{-~\phantom{()}(0.7x-0.35)}\\ 0\phantom{)}\end{array}$

Therefore, the length of the rectangle is:

$0.8x^2-0.7x+0.7$

5 0

2 years ago

Ask questions slove for x 5(x-3)=15

Pavel [41]

Answer:

Step-by-step explanation:

Your answer is 6

4 0

3 years ago

Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of

GenaCL600 [577]

Close off the hemisphere $S$ by attaching to it the disk $D$ of radius 3 centered at the origin in the plane $z=0$ . By the divergence theorem, we have

$\displaystyle\iint_{S\cup D}\vec F(x,y,z)\cdot\mathrm d\vec S=\iiint_R\mathrm{div}\vec F(x,y,z)\,\mathrm dV$

where $R$ is the interior of the joined surfaces $S\cup D$ .

Compute the divergence of $\vec F$ :

$\mathrm{div}\vec F(x,y,z)=\dfrac{\partial(xz^2)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial k}=z^2+y^2+x^2$

Compute the integral of the divergence over $R$ . Easily done by converting to cylindrical or spherical coordinates. I'll do the latter:

$\begin{cases}x(\rho,\theta,\varphi)=\rho\cos\theta\sin\varphi\\y(\rho,\theta,\varphi)=\rho\sin\theta\sin\varphi\\z(\rho,\theta,\varphi)=\rho\cos\varphi\end{cases}\implies\begin{cases}x^2+y^2+z^2=\rho^2\\\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi\end{cases}$

So the volume integral is

$\displaystyle\iiint_Rx^2+y^2+z^2\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^3\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{486\pi}5$