There are two types of special right triangles: 45-45-90 and 30-60-90. The legs on a 45-45-90 triangle are 1 and 1 and the hypotenuse is the square root of 2. The legs on a 30-60-90 triangle are 1 and the square root of 3 and the hypotenuse is 2. If you were to take the three trigonometric functions of either 45 degree angle, you would get the (square root of 2)/2 for both cosine (x) and sine (y) and 1 for tangent (y/x). If you were to take the three trigonometric functions of the 30 degree angle, you would get the (square root of 3)/2 for cosine, ½ for sine and the (square root of 3)/3 for tangent.
AB is the diameter of a circle. A is (1, 3) and B is (7, -1). i) Find the coordinates of the centre C of the circle. [2] ii) Find the radius of the circle. [2] iii) Find the equation of the circle.
MA1310 – Week 3 Lab Answer the following questions to complete this lab: 1. State in a few words, what is an exponential function? * Functions whose equations contain a variable in the exponent. 2. What is the natural exponential function?
Write assignment statements that perform the following operations with the variables a,b,c A. set b=a+2 B. set a=b*2 C. set b=a/3.14 D. set a=b-8 4. Assume the variables result, w,x,y, and z are all integers and that w=5, x=4, y=8, and z=2. What value will be stored in result in each in of the following statements? A. Set result = 4+8 B.
On comparing this equation with standard equation of ellipse with centre (h,k) which is given by x-h2a2+y-k2b2=1 , we have , h = 3 and k = -5. Therefore, coordinates of centre of ellipse = (3, -5). b) Given equation of ellipse. On comparing this equation with standard equation of ellipse with major axis 2a and minor axis 2b which is given by x-h2a2+y-k2b2=1 , we have, a2=64=>a=8 And b2=100=>b=10 Therefore, length of major axis = 2a = 2*8 = 16. And length of minor axis = 2b = 2*10 = 20. c) From part a) and b), we have a = 8 and b = 10 and h=3,k=-5 So, c2=b2-a2=102-82=100-64=36 =>c=sqrt36= 6.
GEOMETRY MIDTERM REVIEW 1. Use the diagram to name all points that are collinear to points P and Q. Use the diagram to find where MQ= 30, MN = 5, MN=NO, and OP=PQ. 2. Find the length of OQ .
Discuss (generally) some of the contributions of Greek/Hellenic scientists such as Galen, Ptolemy, Euclid, Pythagoras, and Archimedes. Or, focus on the discoveries and contributions of one or two of the
e) Set the left side of the equation equal to the positive square root of the number on the right side and solve for x. f) Set the left side of the equation equal to the negative square root of the number on the right side of the equation and solve for x. A) x² - 2x – 13 = 0 x² - 2x = 13 4x² - 8x = 52 4x² - 8x + 4 = 56 (2x – 2) ± 56 2x – 2 = 56 2x – 2 = 56 2x = 56+2 2x = 56+2 x = 56+2/2 x = 56+2/2 Project 2 C) x² + 12x – 64 = 0 -x² + 12x = 64 4x² + 48x = 256 4x² + 48 + 144 = 400 2x + 12 = ±20 2x +12 = 20 2x + 12 = -20 2x = 8 2x = -32 x = 4 x = -16 The method selected was the method shown in our text. I do not think I will ever have a chance to use this knowledge in a real-world situation. Algebra and Geometry are the hardest subjects for me, and I do not retain the teaching very well, so I am sure I will never use this formula. References Bluman, A.
In the 12th century, the Indian mathematician, Bhāskara II, developed an early derivative representing infinitesimal change, and he described an early form of "Rolle's theorem". [5] Also in the 12th century, the Persian mathematician Sharaf al-Dīn al-Tūsī discovered the derivative of cubic polynomials, an important result in differential calculus. [6] In the 14th century, Madhava of Sangamagrama, along with other
n mathematics, the Pythagorean theorem—or Pythagoras' theorem—is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of thehypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:[1] where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. The Pythagorean theorem is named after the Greek mathematician Pythagoras (ca. 570 BC—ca.