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2 years ago

Enter a formula using k to connect the two variables.

Mathematics

2 answers:

LenKa [72]2 years ago

6 0

Answer:

Weres The Formula?

Step-by-step explanation:

Romashka-Z-Leto [24]2 years ago

6 0

Answer:

f=ka

Step-by-step explanation:

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Write the equation of the sphere in standard form. x2 + y2 + z2 + 8x − 6y + 4z + 20 = 0

Nuetrik [128]

Answer:

$(x+4)^2 + (y-3)^2 + (z+2)^2 - 3^2 = 0$

Step-by-step explanation:

You have to find a, b, c, r so that the polynomial expands to match the given equation.

$(x-a)^2 + (y-b)^2 + (z-c)^2 - r^2 =\\x^2-2ax+a^2+\\y^2-2by+b^2+\\z^2-2cz+c^2-r^2 =\\ x^2 + y^2 + z^2 + 8x - 6y + 4z + 20$

$(a^2+b^2+c^2-r^2-20)+\\x(-8-2a)+y(6-2b)+z(-4-2c)=0$

$-8-2a=0, 6-2b=0, -4-2c=0\\a=-4, b=3, c=-2$

$(-4)^2+3^2+(-2)^2-r^2-20 = 0$

$16+9+4-20=r^2$

$r^2=9$

$r=3$

$(x+4)^2 + (y-3)^2 + (z+2)^2 - 3^2 = 0$

5 0

3 years ago

Sin(x2 y2 da r , where r is the region in the first quadrant between the circles with center the origin and radii 1 and 5

Rudik [331]

I assume there's a plus sign missing above...

Convert to polar coordinates, using

$\begin{cases}x(r,\theta)=r\cos\theta\\y(r,\theta)=r\sin\theta\end{cases}$

Then the Jacobian is

$\dfrac{\partial(x,y)}{\partial(r,\theta)}=\begin{vmatrix}x_r&y_r\\x_\theta&y_\theta\end{vmatrix}=\begin{vmatrix}\cos\theta&\sin\theta\\r\sin\theta&-r\cos\theta\end{vmatrix}=-r$

Then

$\mathrm dA=\mathrm dx\,\mathrm dy=|-r|\,\mathrm dr\,\mathrm d\theta=r\,\mathrm dr\,\mathrm d\theta$

so the integral can be written as

$\displaystyle\iint_R\sin(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_1^5r\sin(r^2)\,\mathrm dr\,\mathrm d\theta$

Let $s=r^2$ , so that $\dfrac{\mathrm ds}2=r\,\mathrm dr$ .

$\displaystyle\frac12\int_0^{\pi/2}\int_1^{25}\sin s\,\mathrm ds\,\mathrm d\theta=-\frac12(\cos25-\cos1)\int_0^{\pi/2}\mathrm d\theta=\frac\pi4(\cos1-\cos25)$

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2 years ago

Select the correct answer.<br> Which equation could possibly represent the graphed function?

AnnZ [28]

I Don’t Know If Still Need The Answer But It Should Be A.

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2 years ago

Susie has planned a trip to a city 60 miles away. She wishes to have an average speed of 60 miles/hour for the trip. Due to a tr

Nutka1998 [239]

Answer:

90 mi/h

Step-by-step explanation: