The volume of a Cylinder can be determined by using the formula V=pi r^2h.  Then, multiply the area of the base by the height of the cylinder to find the volume.The formula states that in order to determine the volume of the cylinder we must multiply pi by the radius of the cylinder, square it and then finally multiply by the height. The surface area of a cylinder can be determined by using the formula 2pirh+2pir^2. For example if the height of the cylinder is 18 and the radius of it is 14 that tells us that r=14 and h=18. Next we insert the variables into our formula to make 2 x pi x(14)(18)+2pi 14^2. The first thing to do is to solve the problem in the parenthesis. Which gives us 2 x pi (252)+2 x pi(196). Then after we solve and remove the parenthesis we multiply the two to both sides of the equation which gives us SA=504pi +392pi. Next we add our two numbers together which should give us 896pi. Finally we multiply our remaining n8umber by pi which gives us our final answer of 2814.867.

Angles of a polygon are found by using the formula (n-2) x 180. T N= the number of sides of a polygon. as an example a octagon has 8 sides so we use the formula (n-2) x 180 and insert or number of sides into the formula which gives us (8-2) x 180. So to solve the rest of the problem we must subtract or (N-2) which in this case is (8-2) which gives us 6. So now we have 6 x 180. Which would gives us our answer after we multiply 6 x 180 which gives us our answer of 1080. This number tells us that the total degrees of a octagon is 1080.

For finding the measure of each interior angle of a polygon we have to use our formula of Angle A + Angle B + Angle C + Angle D=360. So as an example angle S +angle T + angle R+ angle U=360. So we insert our problem into the formula so it looks like 11x + 4+ 5x+ 11x + 4 + 5x =360. The first step to solving the problem is to combine all of the like terms or the numbers with the same variables on one side. So this makes the problem            32x +8=360. Next we subtract 8 to both sides, which will cancel out the eight and cause 360 to be subtracted by 8. So the new problem should look like 32x=352.  Our next step is to divide both sides by 32 to simply the problem. Which should gives us an answer of x=11, but this is not our final answer we have to insert the answer into the other sides of the problem. angle S=11 x 11+4=125, angle T=5x 11=55, angle R=11 x 11 + 4=125, and finally angle U=5x 11+55.

Over the spring break last week nothing much happened. I mostly spent the entire time of the week just playing video games. I went to the nearest Gamestop to stock up on the latest releases. I practiced my driving skills so that I can get my license. On Friday I was able to go to Rock in Jump with my family. It was extremely boring and I will probably never go their again. I went to Best Buy to buy some movies like Thor Ragnarok. I am mostly just making up things so that I am able to finish this assignment by making up different activities that sound fun that I never did to begin with. In conclusion, my spring break mostly consider of me just playing video games all day 24/7.

A secant is a line that intersects a circle twice.  A special secant can be separated by three types (For intersecting chords inside the circle, intersecting secants outside the circle, intersecting secant and tangent outside the circle.) A secant segment is a segment of a secant line that has exactly one endpoint on the circle. For solving intersecting chords inside of the circle we use the formula a x b=c x d. For intersecting secants outside of the circle. a(a+b)=c(c+d). Finally for intersecting secant and tangent outside the circle. A special segment can be solved by after using the formula subtract by both sides twice to isolate the variable. and divide the variable by the remaining number to receive the answer.

 

 

To solve the first problem we first need to label the circle we can label the circle by first seeing the small square on m MN which tells us that the angle is a right angle which tells us that it is 90 degrees. Now we can move on to the next part since m KN is a straight line that goes right through the center of the circle we can determine that it is 180 degrees on both sides of the circle. Next we can determine that the m KM is 90 degrees since it is adjacent to m MN. And we can subtract 90-67=23 which means that m KL is equal to 23 and since m ON is adjacent to m KL it is also 23. Finally we can see that m KO can be determined by subtracting 180-23 which should give the answer of 157. But we are only done with labeling the circle. Now we are able to determine that the m KL is equal to 23, m LON is 180, m OM can be determined by adding 23 and 90 together. m KNL can be determined by subtracting 360-23 which gives us the answer of 337, and finally m NL can be determined by adding 90+67=157.

To solve the second problem we first need to see the total length of our arc we can determine this by subtracting the semicircle by our given arc which gives us that the small chunk is 52 degrees. Now we need to determine the size of m SR we can do this by subtracting 90-31 because it is a part of a right angle which gives us the answer of 51. Next we need to know the full length of the arc by adding it all together which gives our total arc to be 211 degrees. Now we can use our arc length formula l=/360 x D times pi. And we also already know that line QT is 19 feet, so when we use inset everything into our formula we should have l=211/360 x 19 x pi. Which gives us our arc length of 4, 534, 072. 181

 

Finally to solve for the third problem we need to find the circumference of circle R which in order to do we need to fist find the value of our diameter. To determine our diameter we need to use pythagorean theorem a^2 + b^2= c^2. So we have to solve for 7^2 +24^2 =c^2. So after we square all of our numbers our equation should look like 49 + 576 =c^2. Next we need to add 49+576 which gives our equation 625=c^2. But since we are not looking for c^2 we are looking for c we now need to find the square root of 625 which is 25. Now that we know that our diameter is 25.02 we are able to use our circumference formula of C= pi x D. So when we multiply D times pi we get our answer of 78

 

Tangents are lines in the same plane as a circle that intersects the circle in one point. The point that the tangents intersects is called the point of tangency. A tangent line can be anything from a line, ray or segment. A circle can have one or more tangents and therefor can have more than one point of tangency. The shortest distance between a tangent and circle is the radius drawn to the point of tangency. You can determine if a line is tangent to the circle by using the pythagorean theorem. A^2 + B^2 =C^2, First fill in the formula with the points and instead of dividing you use i to determine if the numbers are equal and if they are equal they are tangent. For example if 26=27 it is not tangent but, if 100=100 they are tangent.

An arc is a curve that travels around a circle between two endpoints. There are two different types of arcs Major Arcs and Minor Arcs. An arc will always connect two endpoints on a circle. The measure of a minor arc will always equal less than 180 degrees and a major arc will always equal more than 180 degrees. The formula for an arc length formula is 1/ 2 times pi times the radius = x / 360.  Alternately could be l=x/360 x 2 times pi times the radius. If an arc is equal to 180 degrees it is a semicircle. To change the arc to an angle the formula is angle=1/2 arc. The formula for changing the angle to an arc is arc=2angle.

For the first problem the first thing that is necessary is to find the measure of each angle. Since we know that line LO is our diameter we can determine that half of the circle is 180 degrees. Now we have to find the rest of the circle, since we know that the side of the circle is 180 degrees and since MPN is a right angle we know that it is 90 degrees. Now that we know what MPN is we can solve for the rest of the side of the circle. Since we know that LPM is 67 degrees we are then able to solve for the last piece of the half of the circle by subtracting 180-90-67=23, which means that our angle is 23 degrees and since the other angle across from it is adjacent to it, it is also 23 degrees. We are now able to solve for the other side of the circle. We are able to solve for the last piece of the circle by subtracting 180-23=157, which means that our last angle is 157 degrees. And now that our circle is labeled we can solve all of our questions. mKL can be solved by looking at our KL angle which gives us our answer 23 degrees. mLON can be solved by adding 180+23=203 which means that our answer is 203 degrees. mOM can be solves by adding 90+23=113 which gives our answer of 113 degrees. mKNL can be determined by subtracting 360-23=337  which means that our answer is 337 degrees. Our last problem for the first part mNL can be solved by adding 90+67=157 which gives our final answer of  157 degrees.

 

For the Second problem the problem is asking for us to find the arc length PQS if QT is 19 feet. For this problem we are required to use the arc length formula of l=x/360 x 2 pie r. Next we are going to need to insert the equation into the formula so the equation should look like l=128/360 x 2 x pie x 9.5 . The first thing that we need to do is to divide 128 by 360 which should change our formula to 3.555 x 2 x pie x 9.5. Next we are going to need to multiply everything together. Which gives us our answer of 212.2.

For our Final problem we are going to have to find the circumference of circle R. The first thing that we are going need to do is that because their is a right triangle inside of the circle we are going to need to use the pythgorean theorm A^2+B^2=C^2. So we are going to need to solve for 7^2+24^2=C^2. Next we re going to need to square all of the numbers into our problem 49+576=C^2. Then we add 49+576=625. After finding our answer we are going to need to find the square root if it (square root of)625= 25.593 which means that R=25.593. We are now able to solve for the circumference of the circle since R is our diameter. We now use our circumference formula C=D x pie. We insert our problem C=25.593 x pie which gives us our answer of 80.403.

Cental angles are angles that have its vertex on the center of the circle and its sides ends on the circle which creates an arc. The formula for central arc angles is arc=the angle. The sum of the measure of a cental angle of a circle will always be 360 degrees no matter what and can be checked with the formula measure of angle 1 + the measure of angle 2 + the measure 3 = 360 degrees. The circumference of a circle is the measure of the outside of a circle. The circumference of a circle can be determined with the formula c=2 times pi times the radius. The diameter is a chord that pases through the center of a circle and has both ends on the circle. The diameter can be determined by multiplying the radius times 2.

During Christmas break my family and I went down to my grandmother’s house like we do every year. When we got down their we had unpacked the car and got to speak to all of our other family members in Mobile. We decided to stay until New Years so that we had so time to chat and have fun with our family. I didn’t get much for Christmas just a video game a gift card and $175 cash. For New Years my family don’t really tell each other their resolutions so I am just going to tell you mine ” My New Years resolution is to start being more social towards others (as long as they don’t already bug me a lot everyday then they are an acceptation. When I got back from Mobile I did not do much except play video games until 1 0′ oclock in the morning for a straight week which really messed up my sleep patterns and are going to take some time back to adjust too. In Conclusion, my Christmas break was spent with family and playing video games and I am perfectly happy just like that.