the equation of the tangent line must be passed on a point A (a,b) and perpendicular to the radius of the circle. 
I will take an example for a clear explanation:
let x² + y² = 4 is the equation of the circle, its center is C(0,0). And we assume that the tangent line passes to the point A(2.3).

since the tangent passes to the A(2,3), the line must be perpendicular to the radius of the circle.

Let's find the equation of the line parallel to the radius.

The line passes to the A(2,3) and C (0,0). y= ax+b is the standard form of the equation. AC(-2, -3) is a vector parallel to CM(x, y).

det(AC, CM)= -2y +3x =0, is the equation of the line // to the radius.

let's find the equation of the line perpendicular to this previous line.

let M a point which lies on the line. so MA.AC=0 (scalar product),

it is (2-x, 3-y) . (-2, -3)= -4+4x + -9+3y=4x +3y -13=0 is the equation of tangent

7 0

4 years ago

A 57 kg skier starts from rest at a height of H = 27 m above the end of the ski-jump ramp. As the skier leaves the ramp, his vel

Hatshy [7]

Answer:

(a) $h=5.95m$

(b) h is the same

Explanation:

According to the law of conservation of energy:

$E_i=E_f\\U_i+K_i=U_f+K_f$

The skier starts from rest, so $K_i=0$ and we choose the zero point of potential energy in the end of the ramp, so $U_f=0$ . We calculate the final speed, that is, the speed when the skier leaves the ramp:

$mgH=\frac{mv^2}{2}\\v=\sqrt{2gH}\\v=\sqrt{2(9.8\frac{m}{s^2})(27m)}\\v=23\frac{m}{s}$

Finally, we calculate the maximum height h above the end of the ramp:

$v_f^2=v_i^2-2gh\\$

The initial vertical speed is given by:

$v_i=vsin\theta$

and the final speed is zero, solving for h:

$h=\frac{v_i^2}{2g}\\h=\frac{((23\frac{m}{s})sin(28^\circ))^2}{2(9.8\frac{m}{s^2})}\\h=5.95m$

(b) We can observe that the height reached does not depend on the mass of the skier

3 0

4 years ago

Explain how the graphic organizer helped you formulate your decision and participate in the discussion.

nekit [7.7K]

Answer:

The graphic organizers help to keep track of the details. They are a visual representation of knowledge that rescue the important aspects of a concept using labels within a scheme. They also present information in a concise manner, highlighting the organization and the relationship of the concepts. Graphic organizers help students organize their thinking process and their writing.

Explanation:

6 0

3 years ago