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3 years ago

a box of cereal is shaped like a rectangular prism. The box is 26cm long by 11 cm,by 36 cm high. What is the surface area?

Mathematics

1 answer:

Kobotan [32]3 years ago

7 0

Answer:

A=3236

Step-by-step explanation:

A=2(wl+hl+hw)

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Suppose that surface σ is parameterized by r(u,v)=⟨ucos(3v),usin(3v),v⟩, 0≤u≤7 and 0≤v≤2π3 and f(x,y,z)=x2+y2+z2. Set up the sur

Bad White [126]

Looks like you have most of the details already, but you're missing one crucial piece.

$\sigma$ is parameterized by

$\vec r(u,v)=\langle u\cos3v,u\sin3v,v\rangle$

for $0\le u\le7$ and $0\le v\le\frac{2\pi}3$ , and a normal vector to this surface is

$\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=\left\langle\sin3v,-\cos3v,3u\right\rangle$

with norm

$\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|=\sqrt{\sin^23v+(-\cos3v)^2+(3u)^2}=\sqrt{9u^2+1}$

So the integral of $f(x,y,z)=x^2+y^2+z^2$ is

$\displaystyle\iint_\sigma f(x,y,z)\,\mathrm dA=\boxed{\int_0^{2\pi/3}\int_0^7(u^2+v^2)\sqrt{9u^2+1}\,\mathrm du\,\mathrm dv}$

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3 years ago

What speed must you toss a ball straight up so that it takes 4 s to return to you? Show your work.

vekshin1

1) Type of motion: constant acceleration.

2) acceleration, a = 9.8 m/s^2

3) time up = time down = 4seconds / 2 = 2 seconds

4) formula = Vf = Vo - a*t^2/2

Vf = 0 => Vo = a*t^2 / 2 = 9.8m/s^2 * (2 s)^2 / 2 = 19.6 m/s

Answer: 19.6 m/s

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