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diamong [38]
2 years ago
8

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)
3 0
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.
6 0
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:

Given,

For first 30 miles, her speed is 30 miles per hour,

Let x be her speed in miles per hour for another 30 miles,

Since, here the distance are equal in each interval,

So, the average speed of the entire journey

=\frac{\text{Average speed for first 30 miles + Average speed for another 30 miles}}{2}

=\frac{30+x}{2}

According to the question,

\frac{30+x}{2}=60

30+x=120

\implies x = 90

Hence, she needs to go 90 miles per hour for remaining 30 miles.

7 0
3 years ago
Find the solution to x2=28
bekas [8.4K]

x² = 28

x = √28

Factoring 28

28 | 2

14 | 2

7 | 7

1

28 = 2.2.7 = 2².7

x = √2².7

x = 2√7

7 0
3 years ago
Read 2 more answers
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