b. Find the length of the transverse and conjugate axes. c. Find the slopes of the asymptotes. d. Find the coordinates of the foci. e. Graph the hyperbola.
Find the perimeter and area of the shaded sections of these shapes. (i) [7] (ii) [7] Total 60 marks Geometry and trigonometry Solutions to Topic assessment 1. The curve is a circle, centre O and radius 2. [2] 2. Substituting [pic] into [pic] gives [pic] Since the equation has a repeated root, the line meets the circle just once, and so the line is a tangent to the circle.
For most purposes Newton's laws of gravity apply, with minor modifications to take the general theory of relativity into account. 2. Inertia - A property of matter by which it continues in its existing state of rest or uniform motion in a straight line, unless that state is changed by an external force. 3. Potential Energy - Is the energy stored in an object due to its position in a force field or in a system due to its configuration.
1.explain what a radian measure represents using the unit circle as a reference. -A radian measure on a unit circle is the measure of the length of the arc at certain points on the unit circle. 2.how do special right triangles directly relate to a unit circle. -On the unit circle the radius of the circle is also the hypotenuse. therefore if you set the hypotenuse to be a value such as 1. the side (x,y) of the triangle will be the sine and cosine values on the unit circle.
A circumscribed circle touches each vertex of the triangle. There are also things called the incenter and the circumcenter. The incenter is the center of the inscribed circle and the circumcenter is the center of a circumscribed circle. The relation between a circle and a triangle is that
Science Physics Core science questions and answers- Topic 1- The solar system- 1. What is a geocentric model? It is a model with the earth at the centre. 2. Describe two differences between ptolemy’s and Copernicus’s models- What is at the centre of the model and the way in which the planets followed smaller circles in their orbits in ptolemy’s model.
So the radian is the measure of how close a degree is to a complete circle. * How do special right triangles directly relate to the unit circle? There are two types of special right triangle, 90, 60, 30 and 45, 45, 90. With both triangles, the angles of degrees are directly related to the x and y values on the unit circle. With the case of 90, 60, 30 and 90, 45, 45, the angles are relative to the sin of its value on the unit circle.
G. TRUE or FALSE: The acceleration of a particle following a space curve lies in the normal plane. 2) Sketch the curve with the given vector equation, starting at t=0 . Indicate with an arrow the direction in which t increases. Be sure to include a few points to justify your graph. 8pts r(t) = cos t, sin t, sin
Explain what a radian measure represents using the Unit Circle as a reference. A radian measure represents the distance of a radius on the unit circle from the positive x-axis. Radians are mostly associated with pi. 2) How do special right triangles directly relate to the circle? There are two types of special right triangles: 45-45-90 and 30-60-90.
G. Compare the values of the measured angles with the average computed values and determine their difference. 2. Determination of the sides of a right triangle when the hypotenuse and one angle are measured: A. Create a new triangle by taping the bottom of the string to a different position on the floor or table, as in Procedure 1. B.