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3 years ago

A number decreased by half of the number is four. What is the number?

Mathematics

2 answers:

Goshia [24]3 years ago

6 0

Answer:

It should be a number between 12 and 14

Step-by-step explanation:

Start with given compound inequality, Add 4 to all sides ,combine terms on the left side ,combine terms on the right side, multiply all by 2, multiply ,so the number is between 12 and 14 which makes it possible to be 12,13,or 14

MrRa [10]3 years ago

4 0

Answer:

four is the right answer i think

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3 years ago

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2 years ago

Evaluate the surface integral. s y ds, s is the helicoid with vector equation r(u, v) = u cos(v), u sin(v), v , 0 ≤ u ≤ 6, 0 ≤ v

Juliette [100K]

Compute the surface element:

$\mathrm dS=\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv$

$\vec r(u,v)=(u\cos v,u\sin v,v)\implies\begin{cases}\vec r_u=(\cos v,\sin v,0)\\\vec r_v=(-u\sin v,u\cos v,1)\end{cases}$

$\|\vec r_u\times\vec r_v\|=\sqrt{\sin^2v+(-\cos v)^2+u^2}=\sqrt{1+u^2}$

So the integral is

$\displaystyle\iint_Sy\,\mathrm dS=\int_0^\pi\int_0^6u\sin v\sqrt{1+u^2}\,\mathrm du\,\mathrm dv$

$=\displaystyle\left(\int_0^\pi\sin v\,\mathrm dv\right)\left(\int_0^6u\sqrt{1+u^2}\,\mathrm du\right)$

$=\dfrac23(37^{3/2}-1)$

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3 years ago