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Juli2301 [7.4K]
2 years ago
8

Grace paid $54.40 for 8 outdoor pathway lights. Travis paid $40.25 for 5 of the same lights at a different store.who paid less p

er light.
Mathematics
2 answers:
Sergio039 [100]2 years ago
6 0

Answer:

Answer:  Travis paid $8.05 per light and grace paid $6.8 per light so its grac

Step-by-step explanation:

makkiz [27]2 years ago
5 0

Answer:  Travis paid $8.05 per light and grace paid $6.8 per light so its grace

Step-by-step explanation:

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Use spherical coordinates to find the volume of the region that lies outside the cone z = p x 2 + y 2 but inside the sphere x 2
Harman [31]

I assume the cone has equation z=\sqrt{x^2+y^2} (i.e. the upper half of the infinite cone given by z^2=x^2+y^2). Take

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

The volume of the described region (call it R) is

\displaystyle\iiint_R\mathrm dx\,\mathrm dy\,\mathrm dz=\int_0^{2\pi}\int_0^{\sqrt2}\int_{\pi/4}^\pi\rho^2\sin\varphi\,\mathrm d\varphi\,\mathrm d\rho\,\mathrm d\theta

The limits on \theta and \rho should be obvious. The lower limit on \varphi is obtained by first determining the intersection of the cone and sphere lies in the cylinder x^2+y^2=1. The distance between the central axis of the cone and this intersection is 1. The sphere has radius \sqrt2. Then \varphi satisfies

\sin\varphi=\dfrac1{\sqrt2}\implies\varphi=\dfrac\pi4

(I've added a picture to better demonstrate this)

Computing the integral is trivial. We have

\displaystyle2\pi\left(\int_0^{\sqrt2}\rho^2\,\mathrm d\rho\right)\left(\int_{\pi/4}^\pi\sin\varphi\,\mathrm d\varphi\right)=\boxed{\frac43(1+\sqrt2)\pi}

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2 years ago
What is the answer to this question ​
Gre4nikov [31]
4x^2 -2x +3
mark me as brainliest if i’m right !
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3 years ago
If i'm a size 9 in womens what size am i in men's
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I am a size 12 in women and I wear a size 26 in men but I still have a little room. You should try a size 22 maybe?
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If (x + y) +(2(x + y) + 3) = 9, what is x + yı?
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Answer:

i got b but truly i dont know the answer im just tryna get some points u heard

7 0
2 years ago
The container that holds the water for the football team is 23 full. After pouring out 2 gallons of water, it is 12 full. How ma
Mama L [17]
Let full be f and gallons be g
23f-2g=12f
2g=23f-12f
2g=11f
g=5.5f
note 23f is when it is full and x is the number of gallons the container can hold.
g=5.5f
xg=23f
x=46÷11
∴x approximately is 4.9

6 0
3 years ago
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