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Ines-noelly T.
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French
TutorMe
Question:

Combine les deux propositions avec un pronom relatif afin d’éviter la répétition: La fille m'a l'air sympathique. La fille marche avec mon frère.

Ines-noelly T.
Answer:

La fille qui marche avec mon frère m'a l'air sympathique.

Geometry
TutorMe
Question:

Circle C' has radius 3 Triangle ABC is inscribed in the circle such that BC=6 The angle ACB is such that Cos(ACB)= 4/5 Find Cos(ABC)

Ines-noelly T.
Answer:

ABC is inscribed in the circle such that length BC corresponds with the diameter of the circle so ABC has a right angle in A, hence ABC and ACB are complementary angles. If 2 angles are complementary, the sine of one is the cosine of the other, therefore Sin(ABC)=4/5 We know that sin^2+cos^2=1 so we get Cos(ABC)= +/- 3/5 Given that we are dealing with a geometric angle and that angle is less than 180, we conclude that Cos(ABC)= +3/5

Calculus
TutorMe
Question:

Find the volume of the solid obtained by rotating the region bounded by y=x^2, y=0 and x=2 about the x-axis.

Ines-noelly T.
Answer:

<a href="http://www.codecogs.com/eqnedit.php?latex=V=\int&space;Adx" target="_blank"><img src="http://latex.codecogs.com/gif.latex?V=\int&space;Adx" title="V=\int Adx" /></a> Given our configuration, A=pi*r^2 with r=y=x^2 (a graph helps so much for these problems) Therefore: <a href="http://www.codecogs.com/eqnedit.php?latex=V=\int_{0}^{2}\pi&space;x^{4}dx=\left&space;[&space;\frac{\pi&space;}{5}x^{5}&space;\right&space;]=\frac{\pi&space;}{5}\left&space;(&space;2^{5}&space;-0^{5}\right&space;)=\frac{32\pi&space;}{5}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?V=\int_{0}^{2}\pi&space;x^{4}dx=\left&space;[&space;\frac{\pi&space;}{5}x^{5}&space;\right&space;]=\frac{\pi&space;}{5}\left&space;(&space;2^{5}&space;-0^{5}\right&space;)=\frac{32\pi&space;}{5}" title="V=\int_{0}^{2}\pi x^{4}dx=\left [ \frac{\pi }{5}x^{5} \right ]=\frac{\pi }{5}\left ( 2^{5} -0^{5}\right )=\frac{32\pi }{5}" /></a>

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