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3 years ago

Will path 1 intercept the crocidile river

Mathematics

1 answer:

Nataly_w [17]3 years ago

4 0

Answer:

Is there a picture?

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On Tuesday it was 48 degrees

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3 years ago

Use a surface integral to ﬁnd the surface area of the portion of the sphere xUse a surface integral to ﬁnd the surface area of t

brilliants [131]

Parameterize this surface (call it $S$ ) by

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

with $0\le u\le2\pi$ and $0\le v\le\dfrac\pi4$ . The limits on $u$ should be obvious. We find the upper limit for $v$ by solving for $v$ where the sphere and cone intersect:

$\begin{cases}x^2+y^2+z^2=1\\z=\sqrt{x^2+y^2}\end{cases}\implies x^2+y^2=\dfrac12$

$\implies(\cos u\sin v)^2+(\sin u\sin v)^2=\dfrac12$

$\implies\sin^2v=\dfrac12$

$\implies\sin v=\dfrac1{\sqrt2}\implies v=\dfrac\pi4$

Take the normal vector to $S$ to be

$\vec r_u\times\vec r_v=-\cos u\sin^2v\,\vec\imath-\sin u\sin^2v\,\vec\jmath-\cos v\sin v\,\vec k$

(orientation does not matter here)

Then the area of $S$ is

$\displaystyle\iint_S\mathrm dA=\iint_S\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{\pi/4}\int_0^{2\pi}\sin v\,\mathrm du\,\mathrm dv$

$=\displaystyle2\pi\int_0^{\pi/4}\sin v\,\mathrm dv=\boxed{(2-\sqrt2)\pi}$

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3 years ago

Put the following equation of a line into slope-intercept form, simplifying all fractions.

Elena L [17]

Answer:

-2y=(-10)-2x

+2 +2

y=(-8)-2x

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3 years ago

Solve the question below

mamaluj [8]

Answer: the scale factor is 2.5

Step-by-step explanation: hope it helps :)

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Find the value of x in the isosceles triangle shown below.<br> 2<br> 2<br> 12<br> 10

Rudik [331]

Answer: x=13

Step-by-step explanation:

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3 years ago