Ocean currents transport _ to _.

1 answer:

4 0

Ocean currents transport <em>heat from the equator to the poles (C)</em>. Also once in a while to the Danes and the Swedes.

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Which statement describes a property of a magnet? A. It attracts ferrous materials. B. It could have only one pole (north or sou

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Answer:

It attracts ferrous materials

Explanation:

A magnet attracts ferrous materials A ferrous materials are metallic substances or conductors that can conduct heat and electricity. Example of this ferrous materials includes iron, metal etc. Since magnets only can attracts metallic substance to itself, then we can also conclude that they attract ferrous materials since ferrous materials. possesses properties of a metal.

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Find the work done by the force field F(x, y) = xi + (y + 6)j in moving an object along an arch of the cycloid r(t) = (t − sin(t

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Answer:

177.65

Explanation:

Work done by the force field,F along path C is given by:

$W=\int\limits_C F.dr$

Given that:

$r(t) = (t -sin(t)i + (1 -cos(t)j,\\\\\frac{dr}{dt}=(1-cos t)i+sin t\ j\\\\dr=(1-cos\ t)i +sin\ t \ j)dt\\\\F(x,y)=x\ i +(y+6)j\\\\F(r(t))=(t-sin \ t) i+((1-cos \t)+2)j\\\\\\$

$F(r(t))=(t-sin \ t)i+(3-cos \ t)j\\\\\\W=\int\limits_C F.dr\\=\int\limits^{6\pi}_0(t-sin \ t)i+(3-cos \ t)j).((1-cos \ t)i+sin \ t \ j)dt\\\\=\int\limits^{6\pi}_0(t-sin \ t)(1-cos \ t)+(3-cos \ t)sin \ t \ dt\\\\=\int\limits^{6\pi}_0t-tcos \ t+2sin\ t\ dt\\\\=\int\limits^{6\pi}_0-tcos \ t\ dt+[\frac{t^2}{2}-2cos \ t]\limits^{6\pi}_0\\\\=-I+177.65$

#Integrating I by parts:

$I=\int\limits^{6\pi}_0 tcos \ t \ dt\\\\=[\int \ tcos \ t \ dt]\limits^{6\pi}_0\\\\=[t\int cos \ t \ dt-\int (\frac{dt}{dt}\intcos \ t \ dt)dt]\limits^{6\pi}_0\\\\=[tsin\ t -\int sin\ t \ dt]\limits^{6\pi}_0\\\\=0$