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3 years ago

2+2 is 4 minus 1 that’s 3 quick maths

Mathematics

2 answers:

mr_godi [17]3 years ago

4 0

Answer:

love that meme

Step-by-step explanation:

Masja [62]3 years ago

3 0

Answer:

Very quick math

Step-by-step explanation:

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Snow Dome Ski Resort has 65 inches of snow. It is currently snowing there at a rate of 1 inch per hour. Mt. Winterpark Ski Resor

34kurt

Answer:

a) Equation for Snow Dome Ski Resort:

$I_s = 65+t$

Equation for Mt. Winterpark Ski Resort:

$I_m = 74+\frac{t}{2}$

b) After 19 hours, Snow dome will have more snow.

Step-by-step explanation:

Given that:

Initial snow at Snow Dome Ski Resort = 65 inches

Snowing rate at Snow Dome Ski Resort = 1 inch per hour

Initial snow at Mt. Winterpark Ski Resort = 74 inches

Initial snow at Mt. Winterpark Ski Resort = $\frac{1}{2}$ inch per hour

a) To write equations that show amount of snow at each resort.

Let the time in hours be represented by $t$ .

Snow increased in $t$ hours by snowing at Snow Dome Ski Resort = $1\times t = t$ inches per hour

Snow increased in $t$ hours by snowing at Mt. Winterpark Ski Resort = $\frac{1}{2}\times t = \frac{t}{2}$ inches per hour

Equation for Snow Dome Ski Resort:

$I_s = 65+t$

Equation for Mt. Winterpark Ski Resort:

$I_m = 74+\frac{t}{2}$

b) Time at which Snow Dome has more snow.

Using the above equations, we can write the following inequality:

$65+t>74+\dfrac{t}{2}\\\Rightarrow t-\dfrac{t}{2}>74-65\\\Rightarrow \dfrac{t}{2}>9\\\Rightarrow t>18\ hours$

After 18 hours have passed, they will have equal amount of snow.

After 19 hours, Snow dome will have more snow.

7 0

2 years ago

Evaluate the surface integral. (give your answer correct to at least three decimal places.) s is the boundary of the region encl

telo118 [61]

Split up the surface $S$ into three main components $S_1,S_2,S_3$ , where

$S_1$ is the region in the plane $y=0$ bounded by $x^2+z^2=1$ ;

$S_2$ is the piece of the cylinder bounded between the two planes $y=0$ and $x+y=2$ ;

and $S_3$ is the part of the plane $x+y=2$ bounded by the cylinder $x^2+z^2=1$ .

These surfaces can be parameterized respectively by

$S_1:~\mathbf s_1(u,v)=\langle u\cos v,0,u\sin v\rangle$
where $0\le u\le1$ and $0\le v\le2\pi$ ,

$S_2:~\mathbf s_2(u,v)=\langle\cos v,u,\sin v\rangle$
where $0\le u\le2-\cos v$ and $0\le v\le2\pi$ ,

$S_3:~\mathbf s_3(u,v)=\langle u\cos v,2-u\cos v,u\sin v\rangle$
where $0\le u\le1$ and $0\le v\le2\pi$ .

The surface integral of a function $f(x,y,z)$ along a surface $R$ parameterized by $\mathbf r(u,v)$ is given to be

$\displaystyle\iint_Sf(x,y,z)\,\mathrm dS=\iint_Sf(\mathbf r(u,v))\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times\frac{\partial\mathbf r(u,v)}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

Assuming we're just finding the area of the total surface $S$ , we take $f(x,y,z)=1$ , and split up the total surface integral into integrals along each component surface. We have

$\displaystyle\iint_{S_1}\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}u\,\mathrm dv\,\mathrm du$
$\displaystyle\iint_{S_1}\mathrm dS=\pi$

$\displaystyle\iint_{S_2}\mathrm dS=\int_{v=0}^{v=2\pi}\int_{u=0}^{u=2-u\cos v}\mathrm du\,\mathrm dv$
$\displaystyle\iint_{S_2}\mathrm dS=4\pi$

$\displaystyle\iint_{S_3}\mathrm dS=\int_{u=0}^{u=1}\int_{v=0}^{v=2\pi}\sqrt2u\,\mathrm dv\,\mathrm du$
$\displaystyle\iint_{S_3}\mathrm dS=\sqrt2\pi$

Therefore

$\displaystyle\iint_S\mathrm dS=\left\{\iint_{S_1}+\iint_{S_2}+\iint_{S_3}\right\}\mathrm dS=(5+\sqrt2)\pi\approx20.151$