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.
Interpret. From the scatter plot it is evident that the slope of the ‘best fit’ line is positive, which indicates that Credit Balance varies directly with Size. As Size increases, Credit Balance increases and vice versa. MINITAB OUTPUT: Regression Analysis: Credit Balance ($) versus Size The regression equation is Credit Balance ($) = 2582 + 404 Size Predictor Coef SE Coef T P Constant 2581.9 195.3 13.22 0.000 Size 404.13 51.00 7.92 0.000 S = 620.793 R-Sq = 56.7% R-Sq (adj) = 55.8% Analysis of Variance Source DF SS MS F P Regression 1 24200717 24200717 62.80 0.000 Residual Error 48 18498431 385384 Total 49 42699149 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 4602.6 119.2 (4363.0, 4842.2) (3331.6, 5873.6) Values of Predictors for New Observations New Obs Size 1 5.00 2. Determine the equation of the ‘best fit’ line, which describes the relationship between CREDIT BALANCE and SIZE.
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.
I collected 2 olive leaves from the north side which are exposed to low sunlight density and 2 olive leaves from the south side which are exposed to high sunlight density. I placed the north side leaves in a Ziploc bag labeled north and the south side leaves on another Ziploc bag labeled south in order to avoid getting them confused. I then traced each leaf from the low sunlight environment onto a paper, cut around the outline, weighed the leaves and made sure to keep track of their weight. I also repeated these steps with the leaves from the high sunlight environment. In order to calculate the leaves’ surface area, I used the conversion factor of a 100mm x 100mm paper which is (Mass/Surface Area = .000122mm^2).
Stevens uses the same technique to commence his poem, saying, “There it was, word for word,/ The poem that took the place of a mountain” (1-2). The language used here is reminiscent of the Genesis passage before it. In both cases, the creation of the thing in question is simply spoken into being, and is then observed. During the process of creation, both works appear to pay close attention to the details of their world. In Genesis, it is said, “And God said, Behold, I have given you every herb bearing seed, which is upon the face of all the earth, and every tree, in the which is the fruit of a tree yielding seed; to you it shall be for meat.
You can find the volume of a rectangular prism using the same formula given above (V= l × w × h.) Another way to say it is to multiply the area of the base times the height. 1. 2. 3. Find the area of the base for the rectangular prism pictured above.
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.
The Hall of Supreme Harmony, the Hall of Central Harmony, and the Hall of Preserving Harmony in the outer court together with Palace of Heavenly Purity, Hall of Union, and the Palace of Earthly Tranquility in the inner court were constructed on the central axis. Other palaces are in parallel with the central axis. All the palaces were constructed based on 'The book of change' and Chinese traditional Confucian culture. “The union of human being and the nature” is the main idea in the Book of Change. In the names of the Palace of Heavenly Purity and the Palace of Earthly Tranquility, union of the heaven and the earth can be reflected.
The Golden Mean, also known as the golden ratio, golden section or even the divine proportion, is an irrational number that is represented by the Greek sign for Phi. ( ) The number for the Golden Mean is 1.61803398875. The Golden Mean is represented in more than just math, it is seen in architecture, geometry, art, nature and even in the human body. For example, we can see it in the middle of a flower, or in a sea shell. The Golden Mean is the moderate position between two extremes.
Traditionally associated with Christmas, red and green offer an array of options to embellish our homes for the holiday season. Actually, their use as Christmas colors dates back to paganism and early Christianity. Symbolizing respectively life, nature, revival, and eternity on the one hand, and on the other – birth and death, as well as Christ’s sacrifice, green and red are definitely universally accepted Christmas colors. As trends come and go, sometimes even retro orange, pink, and purple are used to add a fresh, unique look to Christmas décor. However, usually complemented by white and gold/yellow and sometimes blue, with some creativity and imagination, with red and green we all can go far beyond mundane seasonal décor and add some