Look at the figure below:

Mathematics

2 answers:

aleksley [76]3 years ago

7 0

Answer:

Answer is option 1)

Answer is given below with explanations.

Step-by-step explanation:

$triangle \: ABD \: and \: triangle \:ECD \: are \: congruent \\ length \: of \: BD \: = \: length \: of \: CD \\ \: and \: also \\ length \: of \: AD = length \: of \: ED \\ angle \: BDA \: = \: angle \: CDE \\ by \: \: side \: - angle - side \: postulate \\ triangle \: ABD \: and \: triangle \:ECD \: are \: congruent.$

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mr Goodwill [35]3 years ago

6 0

Answer: A) ΔABD ≡ ΔECD

Step-by-step explanation:

Match up the letters of the congruent sides.

AD = ED and BD = CD

A D B D → ABD

E D C D → ECD

This can be written in any order as long as the letters are matched properly. A & E, D & D, B & C

ADB or BDA or ...

EDC CDE

The only correct option provided is option A.

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Use spherical coordinates. evaluate xyz dv e , where e lies between the spheres ρ = 4 and ρ = 6 and above the cone ϕ = π/3.

sergey [27]

Set

$x=\rho\cos\theta\sin\varphi$

$y=\rho\sin\theta\sin\varphi$

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so that the volume element is

$\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

The integral is then

$\displaystyle\iiint_Exyz\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi/3}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=4}^{\rho=6}\rho^5\cos\theta\sin\theta\sin^3\varphi\cos\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\rho$

$=\displaystyle\left(\int_0^{\pi/3}\sin^3\varphi\cos\varphi\,\mathrm d\varphi\right)\underbrace{\left(\int_0^{2\pi}\cos\theta\sin\theta\,\mathrm d\theta\right)}_0\left(\int_4^6\rho^5\,\mathrm d\rho\right)$