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2 years ago

What are four kinds of parabolas

1 answer:

3 0

Solutions

A right handed parabola: $y^2=4ax$ 

A left handed parabola: $y^2=-4ax$ 

An up facing parabola: $x^2=4ay$ 

A down facing parabola: $x^2=-4ay$

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How many 1/6 are in 2/3?

mel-nik [20]

Answer:

It takes 4 one-sixth sized pieces to make the two-thirds. and we can see that there 1 \times 6 = 6 sixths in a whole.

Step-by-step explanation:

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2 years ago

Read 2 more answers

A sphere of radius r is cut by a plane h units above the equator, where

Anika [276]

Consider the top half of a sphere centered at the origin with radius $r$ , which can be described by the equation

$z=\sqrt{r^2-x^2-y^2}$

and consider a plane

$z=h$

with $0$ . Call the region between the two surfaces $R$ . The volume of $R$ is given by the triple integral

$\displaystyle\iiint_R\mathrm dV=\int_{-\sqrt{r^2-h^2}}^{\sqrt{r^2-h^2}}\int_{-\sqrt{r^2-h^2-x^2}}^{\sqrt{r^2-h^2-x^2}}\int_h^{\sqrt{r^2-x^2-y^2}}\mathrm dz\,\mathrm dy\,\mathrm dx$

Converting to polar coordinates will help make this computation easier. Set

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

Now, the volume can be computed with the integral

$\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_0^{\arctan\frac{\sqrt{r^2-h^2}}h}\int_{h\sec\varphi}^r\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta$

You should get

$\dfrac{2\pi}3\left(r^3\arctan\dfrac{\sqrt{r^2-h^2}}h-\dfrac{h^3}2\left(\dfrac{r\sqrt{r^2-h^2}}{h^2}+\ln\dfrac{r+\sqrt{r^2-h^2}}h\right)\right)$

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3 years ago

H(x)=4/x-5 What is the domain of h?

Inga [223]

Answer:

domain: (-∞, 5)∪(5, ∞)

domain in interval form: {x|x ≠ 5}

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2 years ago

What are the coordinates of Y(-35, 5) is reflected across the x-axis

puteri [66]

Answer:

(- 35, - 5 )

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ), hence

(- 35, 5 ) → (- 35, - 5 )

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2 years ago

New Oats cereal is packged in a cardboard cylinder. The packaging is 10 inches tall with a diameter of 3 inches. What is the vol

Otrada [13]

30 is the answer thanks

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