Sarah+B's+page

Sarah B

Phase One

  ~ Yang Hui ~

Yang Hui lived during the Song Dynasty, which was from 960 to 1279 AD. His courtesy name was Qianguang. He mainly worked with magic circles, magic squares, and the binomial theorem. Yang's teacher Qin Jiushao. He was influenced by Jia Xian, who had created Pascal's Triangle. Yang also made a triangle, but acknowledged that the original triangle was created by Jia Xian. He published his first mathematical book in 1275 AD.

He attributed all these:
 * He attributed magic circles, which "is the arrangement of natural numbers on circles where the sum of the numbers on each circle and the sum of numbers on diameter are identical."


 * The binomial theorem "is an important formula giving the expansion of powers and sums"


 * Magic squares were "a square containing integers arranged in an equal number of rows and columns so that the sum of the integers in any row, column, or diagonal is the same"

~Brahmagupta ~

He was born in 598 CE in Rajasthan (India). His father's name was Jisnugupta. He was an Indian astronomer and mathematician. He wrote many important works on astronomy and mathematics. He was the head of the astronomical observatory in Ujjain. During his career, he wrote four texts on mathematics and astronomy. Even though he had his own theories and ways of doing things, he had an excess of criticism toward other astronomers.

Brahmugupta's most famous practice in mathematics was Indian Mathematics. In his book, //Brahmasphutasiddhanta,// he gave the solution of the linear equation. There were many different styles of mathematics he worked with, such as: Algebra, Arithmetic, Diophantine Analysis, Geometry, Trigonometry, and Astronomy. He had his own theorem and way of solving every problem. He put all of this information down in his book.

 Phase Two

Part one

1. Suppose a farmer has 2500 yards of fencing to enclose a rectangular field. What is the largest area that the farmer can enclose? 390,625



 2. The owner of a ranch decides to enclose a rectangular region with 280 feet of fencing. To help the fencing cover more land, he plans to use one side of his barn as part of the enclosed region. What is the maximum area the rancher can enclose? 9,800





3. A farmer wishes to enclose a rectangular region bordering a river using 2100 feet of fencing. He wants to divide the region into two equal parts using some of the fence material. What is the maximum area that can be enclosed with the fencing? 367,500





<span style="display: block; font-size: 140%; font-family: Impact, Charcoal, sans-serif; text-align: left; color: rgb(128, 0, 128);">Part Two

<span style="display: block; font-size: 21px; font-family: arial; text-align: left; color: rgb(128, 0, 128); line-height: 32px;">s(t) = –gt2 + v0t + h0....... <span style="display: block; font-size: 21px; font-family: arial; text-align: left; color: rgb(0, 0, 0); line-height: 32px;">g= acceleration due to gravity t= time in seconds after the item is released v= initial velocity h= initial height from which the item is released <span style="display: block; font-size: 21px; font-family: 'Comic Sans MS', cursive; text-align: left; color: rgb(0, 0, 0); line-height: 32px;"> 1. Some fireworks are fired vertically into the air from the ground at an initial velocity 68 feet per second. Find the highest point reached by the projectile just as it explodes. <span style="color: rgb(0, 128, 0);">72.25





2. A ball is thrown vertically upward with an initial velocity of 69 feet per second. If the ball started from a height of 10 feet off the ground, determine the time it will take for the ball to hit the ground. <span style="color: rgb(0, 128, 0);">4.45





<span style="display: block; font-size: 21px; font-family: 'Comic Sans MS', cursive; text-align: center; color: rgb(0, 128, 0); line-height: 32px;"> <span style="display: block; font-size: 21px; font-family: 'Comic Sans MS', cursive; text-align: center; color: rgb(0, 128, 0); line-height: 31px;">Phase Three

<span style="font-size: 120%; font-family: Impact, Charcoal, sans-serif; color: rgb(128, 0, 128);">x^2 - 14x - 72 = 0<span style="font-family: Impact, Charcoal, sans-serif; font-size: 110%;">

1. You need to explain what it means to say “ solve by graphing”. Once you have this written on your wiki you will solve the quadratic by graphing.

<span style="font-size: 144%; font-family: 'Comic Sans MS', cursive;"> )( <span style="font-size: 120%; font-family: 'Comic Sans MS', cursive; color: rgb(0, 128, 128);"> <span style="font-size: 144%; font-family: 'Comic Sans MS', cursive; color: rgb(0, 128, 128);">Basically, since solutions to "ax^2+bx+c=0" are the x-intercepts "y=ax^2+bx+c", <span style="font-size: 144%; font-family: 'Comic Sans MS', cursive; color: rgb(0, 128, 128);">you can look at the <span style="font-size: 120%; font-family: 'Comic Sans MS', cursive; color: rgb(0, 128, 128);">  //<span style="font-size: 120%; font-family: 'Comic Sans MS', cursive; color: rgb(0, 128, 128);">x // <span style="font-size: 144%; font-family: 'Comic Sans MS', cursive; color: rgb(0, 128, 128);">-intercepts of the graph to find the solutions to the equation.

x= __-b__ 2a

x= __-(-14)__ 2(1)

x= __14__ 2

x= 7



2. You need to explain what it means to say “solve the quadratic by factoring.” Once you have this written on your wiki, you will then solve the same equation by factoring. What do the solutions represent after factoring a quadratic?

3. Last you need to explain what it means to say “solve the equation using the quadratic formula.” Put your explanation on your wiki, then take your equation and use the quadratic formula to solve it. Show the step-by-step process in solving this, on your wiki.

<span style="font-family: 'Comic Sans MS', cursive; font-size: 20.8px; line-height: normal; color: rgb(0, 128, 128);">The simplest way to solve ax^2+bx+c=0 for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor.

<span style="color: rgb(0, 128, 0); font-family: 'Comic Sans MS'; font-size: 23px; line-height: 27px;">x= 18, -4



<span style="font-family: 'Comic Sans MS', cursive; font-size: 160%; color: rgb(0, 128, 0); text-align: center; display: block;"> Phase Four

<span style="font-size: 160%; color: rgb(0, 128, 0); text-align: center; display: block; font-family: 'Comic Sans MS', cursive;"> <span style="font-family: Impact, Charcoal, sans-serif; font-size: 130%; color: rgb(128, 0, 128);">Here is my video...

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