home

__Mast Notes Chapter 4__ __4.1:__ __Right angle-a 90 degree triangle__ __Straight angle-a 180 degree triangle__ __Acute angle-less than 90 degree triangle__ __Obtuse angle-greater than 90 degree triangle__ __Complementary angles-angle a + angle b = 90 degrees__ __Supplementary angles- angle a + angle b = 180 degrees__ __Area of sector of circle-__ A=(1/2)r^2(radians) __Arc Length-__ s=r (radian)

4.2: Trigonometry stems from the Greek work trigonon, which means triangle, and metrein, which means to measure. Simple triangle- all angles measure the same. Right triangle- Has one 90 degree angle. Since one angle is 90 degrees the other two angles must be complementary. a^2+b^2=c^2 sin(angle)= opposite/hypotenuse cos(angle)= adjacent/hypotenuse tan=opposite/adjacent cse(angle)=1/sin(angle) sec(angle)=1/cos(angle) cot(angle)=1/tan(angle)

__ Master Notes Chapter 2.1 __ Polynomial function Quadratic function- ax^2+bx+c standard form of quadratic f(x)= a(x-h)^2 + k graphing a quadratic-

step 1: find the vertex (-b/2a,f(-b/2a)) step 2: determine whether the parabola opens up or down step 3: find additional points near the vertex step 4: sketch the graph with a parabolic curve

__ Master Notes __ Hudson Tillett

· A relation is a function when there isn’t a repeating x-value in the set of numbers. · {(-3,4),(2,4),(3,5),(6,4)} this is a function because each x-value is different · {(-3,4),(2,4),(3,5),(2,2)} is not a function because there is a repeated x-value of 2 · To tell if a equation represents a functions you graph it and see if there are multiple x-values using the vertical line test · Function notation is a good way to check if it is a function or not. If you can make a function notation then it is a function. · To find a value of a function you just plug in a number into the x-value to find the y-value · To find a value of a function you just plug in a number into the y-value to find the x-value · The domain is a set of numbers and the range corresponds to the domain. · All functions are relations but not all relations are functions

__ Collaborative project for Pre-calculus __


 * Problem: ** For this assignment, Harry, Hudson, and I (Olivia), were given the task of calculating the surface area and volume of the gym. In order to do so, we needed to find the dimensions of gym; the height, the width, and the length. We needed to use the formulas for both surface area and volume and account for every part and or side of the gym. After we decided to convert our measurements from feet to meters. Here are our steps and results.

-ruler -paper
 * Materials ** : -pen

Volume: 247,464 feet ³
 * Estimation: ** Area: 38,480 feet²


 * Procedure: **

Step 1: First we measured the length and width of each individual brick.

Step 2: Then, we determined the amount of bricks there was from one side of the gym to the other side by simply counting them. (We did this for each individual side in order to calculate the length.)

Step 3: We then determined the width using the same technique. (Counting the bricks of each individual side.)

Step 4: We also used the same technique of counting to determine the height of the rectangular section of the gym. (Not including the triangular portion that makes up the roof.)

Step 5: In order to calculate the surface area of the rectangular portion of the gym (of the front & back), we used the area formula (length x width) using the dimensions we determined for length and width.

Step 6: Next, we measured the height from the top of the entrance to the very top of the roof. (This will provide the height of the triangle in the front & back.)

Step 7: In order to find the length of the triangular portion of the gym (in the front & back), we divided the total length of the gym by two.

Step 8: To calculate the hypotenuse of the triangle, we used the Pythagorean theorem. (a² + b² = c²)

Step 9: Once we determined the dimensions of the triangular portion of the gym, we determine the surface area using the Area formula for a triangle. (length x width divided by two)

Step 10: Then, we calculated the surface area (length x width) of the roof multiplying the hypotenuse of the triangle and the length of the gym by two.

Step 11: To determine the surface area of the two sides of the gym, we multiplied the width of the gym and the height of the gym by two.

Step 12: to determine the total surface area of the gym we added all of the sections together. (The surface area of the front, the back, both sides, and the roof)

Step 13: We first broke the building into three parts to determine the volume; the entrance, the roof, and the rectangular shape of the gym. The formula for volume is length multiplied by the width multiplied by the height. We used this formula to find the volume of the entrance, the roof, and the rectangular shape of the gym. (Using the pre-determined dimensions; height, length and width.)

Step 14: To calculate the total volume of the gym, we added the volume of the three parts.


 * Data: **

Surface Area of the front = 4440 feet²

Surface Area of the back = 4440 feet²

Surface Area of the roof = 23,310 feet²

Surface Area of both sides = 6290 feet²

(Add all of these together)

Total Surface Area = 38,480 feet²

Volume of the entrance = 3264

Volume of the roof (triangular portion) = 222,000

Volume of the rectangular portion = 22,200

(Add all of these together)

Total Volume = 247,464

Conversions:

1 feet =12 inch = 30cm Surface Area: 20*30=600cm 60*30=18m 18m*2=3600 (600 * 3600) / 2=10800m² 52*30*2=3120cm 16*30=480cm 17*30=510cm (480+3120)*510=18360m² 1080000+1836000=29160m² Volume: 185*30=5550cm 510*3120*5550=101898000 ³    5550*3120=8670cm 8670*600=52020m ³ 101898000m ³ +52020m ³ =10195002cm ³


 * Conclusion: **

Our estimation of wasn’t even close because the size of the building made it very difficult to guess the exact surface area, even harder to guess the volume. With a big building as the gym being off by a couple feet would change drasticly the surface area and volume so estimating is extremely difficult. Y=3x y=feet x=meter. We learned that teamwork is very much needed to complete a big task as this in an effective amount of time.