# Tutor profile: Themis K.

## Questions

### Subject: Trigonometry

In a right triangle ABC with angle A equal to $$\frac{π}{2}$$ rad, find angle B and C so that sin(B) = cos(B).

So, b is the length of the side opposite angle B and c the length of the side opposite angle C and h the length of the hypotenuse. $$sin(B)$$ = $$\frac{b}{h}$$ and $$cos(B)$$ = $$\frac{c}{h}$$ $$sin(B)$$ = $$cos(B)$$ $$\Rightarrow$$ $$\frac{b}{h}$$ = $$\frac{c}{h}$$ which gives c = b The two sides are equal in length means that the triangle is isosceles and angles B and C are equal in size of $$\frac{π}{4}$$ rad

### Subject: Physics

F is the centripetal force of a sphere rotating along a circular path at speed u. The mass of the sphere is m and is at distance R from the center. What is the centripetal force of the same sphere if the speed u is doubled?

From the equation of the centripetal force Fk = $$ \frac{m u^{2}}{R} $$ we see that when the velocity is doubled, the centripetal force will increase 4 times. Fk' = $$ \frac{m (2u)^{2}}{R} $$ = 4$$ \frac{m u^{2}}{R} $$ = 4Fk

### Subject: Algebra

Find the point that line y = 4x +1 and line 2x + y = 13 intersect.

We substitute the y value in the second equation (as we already have it solved in the first one) and solve it for x. 2x + 4x +1 =13 6x=12 x=2. thus, y= 8+1 =9 So the point we are looking for, is (x,y) = (2,9)

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