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3 years ago

If the area of a square is multiplied by 16, the area becomes 25 square inches. Find the length x of a side of the square.

1 answer:

8 0

1.25 is the length x of a side of the square. Think about it like this. Divide 25 by 16 and you get 1.5625. Then, you do that number squared. So, √1.5625. That gives you 1.25. Hope that helps! Good luck!

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Real answers only pls! no links either!

MaRussiya [10]

Answer:

A. 4/8 + 2/4 =1 B.5/8 + 1/4 =0.875

C.6/8 + 3/4 =1.5 D.7/8 + 2/4 =1.375

3 0

2 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

kifflom [539]

Looks like we have

$\vec F(x,y,z)=z^2x\,\vec\imath+\left(\dfrac{y^3}3+\sin z\right)\,\vec\jmath+(x^2z+y^2)\,\vec k$

which has divergence

$\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(z^2x)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial z}=z^2+y^2+x^2$

By the divergence theorem, the integral of $\vec F$ across $S$ is equal to the integral of $\nabla\cdot\vec F$ over $R$ , where $R$ is the region enclosed by $S$ . Of course, $S$ is not a closed surface, but we can make it so by closing off the hemisphere $S$ by attaching it to the disk $x^2+y^2\le1$ (call it $D$ ) so that $R$ has boundary $S\cup D$ .

Then by the divergence theorem,

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(x^2+y^2+z^2)\,\mathrm dV$

Compute the integral in spherical coordinates, setting

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

so that the integral is

$\displaystyle\iiint_R(x^2+y^2+z^2)\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^1\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{2\pi}5$

The integral of $\vec F$ across $S\cup D$ is equal to the integral of $\vec F$ across $S$ plus the integral across $D$ (without outward orientation, so that

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\iint_D\vec F\cdot\mathrm d\vec S$

Parameterize $D$ by

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

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to $D$ to be

$\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}=-u\,\vec k$

Then we have

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^1\left(\frac{u^3}3\sin^3v\,\vec\jmath+u^2\sin^2v\,\vec k\right)\times(-u\,\vec k)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{2\pi}\int_0^1u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac\pi4$

Finally,

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\left(-\frac\pi4\right)=\boxed{\frac{13\pi}{20}}$

6 0

4 years ago

write the equation of the perpendicular bisector that goes through the line segment with end points of A -1,-2 and B -2,-8

Dennis_Churaev [7]

Answer:

2x +12y = -63 . . . in standard form

y = -1/6x -21/4 . . . in slope-intercept form

Step-by-step explanation:

It is useful to find the midpoint of the segment. That is the average of the end points:

M = ((-1, -2) +(-2, -8))/2 = ((-1-2)/2, (-2-8)/2) = (-3/2, -5)

It is also useful to find the changes in coordinates from B to A:

Δ = A-B = (-1-(-2), -2-(-8)) = (1, 6)

From here, there are a couple of ways you can write the equation of the perpendicular line.

One way is to use the Δ values to compute the slope of the segment. The perpendicular line will have a slope that is the negative reciprocal of that.

Δy/Δx = 6/1 = 6

m = -1/6 . . . . . slope of the perpendicular line

Now we have a point and a slope for the desired line, so we can use a point-slope form of the equation for a line:

y = m(x -h) +k

y = (-1/6)(x -(-3/2)) +(-5)

y = (-1/6)x -21/4 . . . . . . . . eliminate parentheses; point-slope form

Another way to write the perpendicular line is to use the Δ values directly as coefficients in the standard form equation:

Δx(x -h) +Δy(y -k) = 0

1(x -(-3/2)) + 6(y -(-5)) = 0 . . . substitute values

x +6y +31.5 = 0 . . . . . . . . . . .collect terms

2x +12y = -63 . . . . . . . . . . . . multiply by 2, put in standard form

7 0

3 years ago

The gas tank of Tyrell's truck holds 19.8 gallons. When the tank is empty, tyrell fills it with gas that costs 3.65 per gallon.

Dima020 [189]

3.65x19.8=$72.07 hit that thanks button and 5 star rating plz thankyou!!!!

7 0

3 years ago

Please come help me With four really easy math problems

Eva8 [605]

The answers checked for #1, #2, #4, and #5 are correct.

In #3, the constant factor is -3 . So the absolute value of
each term is 3 times the absolute value of the previous one,
AND the signs alternate.

7 0

4 years ago