5

A circle hus diameler of 20 cm. Calculate the urea of a scctor when the ungle made by the radius rudiun 14 marks]...

Question

A circle hus diameler of 20 cm. Calculate the urea of a scctor when the ungle made by the radius rudiun 14 marks]

A circle hus diameler of 20 cm. Calculate the urea of a scctor when the ungle made by the radius rudiun 14 marks]



Answers

Two circles have circumferences that add up to $12 \pi$ centimeters and areas that add up to $20 \pi$ square centimeters. Find the radius of each circle.

All right here we have a problem asking us to find the exact radius of two different circles. The information that we're given is that the sum of the two Cirque circumference is is 12 pie and some of the two areas of the circles is 25. So let me just rewrite these equations by including the actual formula for each of those things, circumference and area. So we know that that's formula for the circumference of the of a circle is two pi times the radius and for the area of a circle, it's pi times the radius squared. So we have circumference of acts. Plus circumference is why which are both radius is so we can say two pi times X plus two pi times Why is equal to 12 pie? And for the area we have pi X squared plus pi. Why squared is equal to 20 pie. One thing we can realize is that every single term and both these equations has the number high. In order to get just rid of this in for all the equation. Just to make our work a little bit simpler is by dividing the whole equation. Both of the equations by pie. So just do one over pi, and then we get two X plus. Two y is equal to 12 and X squared plus y squared is equal to 20. So here we have a non in your system of equations. The best thing to do is probably tingle with the first equation and solve for why or acts and then plug it into this bottom equation as a substitution method. So we have two X Plus two y is equal to 12. That's just all for why it's a track two X on both sides. Doing so results in a equation that says two y is equal to negative two X Plus 12 than to isolate the why were divided by two on both sides. Then we get why is equal to Negative X Plus six. That's our value for why, Then we plug that into this second equation right here. X squared plus y squared equals 20. So x squared plus negative X plus six squared equal to 20. We just plugged in the Y value in for here. So x squared, plus negative explosive six times negative ax plus six. So let me just do that in the side. Right here. Um so negative X plus six times negative X plus six negative acts. Times negative x will be positive. X squared negative X Time six is negative. Six x six times negative bucks is also a negative. Six x and six times six is 36 discusses the question X squared minus 12 X plus 36. Let me just make sure that is clear. 36. Or let me just rewrite this and here. So plus X squared minus 12 acts plus 36 is equal to 20. Then we can just add the's ads like Terms together two X squared minus 12. Ax plus 36 is equal to 20. And then, well, the one thing we can realize here is that there is a leading coefficient, and it's better to not have. Those were trying to factor and find a solution to the problem, and every single term is divisible by two. So we can just about the whole thing by two. Then get X squared minus six. X plus six is equal to plus high post six. That is incorrect. X squared minus six X costs 18 is equal to 10. We have a 10 year. Let's just subtract it on both sides. Negative. 10. Negative 10. This gives us X squared minus six. X Plus eight is equal to zero. So now we need to factor on the way to do this. Is finding what factors of eight. Adam to negative. Six. So eight we have eight and one, four and two. None of this would result in a negative six. So that's just going to negative numbers now. So let's say negative four and negative two and negative eight and negative one. Adding negative for negative two gives us negative six. So those two factors X minus four and X minus two is equal to zero. That would mean that X minus four is equal to zero and X minus two is equal to zero. That means are two values. After adding foreign both sides and adding to on both sides, our value for X is gonna be X equals four and X equals two. Of course, it could be either one of those or just one of these. So we have to keep solving and see which ones work out in order to determine which ones the correct answer or both are correct answers. All right, so let's go back again. So we had the fact that we had the values for X. We had two values for X. So we there's a huge possibility that we can have two answers. So executes foreign encircles to We just plugged these values and into the original equation again, or original one of the two original equations. Just use the top on here. Since it's simpler, let's say so to expose to wise, Is he going to 12? Was that equation so two x two X Plus two y is equal 12 when we plug in four for X, ray said two times for plus to Wise equal 12 eight plus two y is equal to 12. We subtract a on both sides, and then two y is equal to four. Would divide by two on both sides, and we get why is equal to two. So when X is equal to four, X is equal to four. So when one X is equal to four, why is equal to two? That's one of the answers and our other one who goes when excessive gold, too. So two X plus two y is equal to 12 when X is equal to two was our other options. So two times two plus two y is equal to 12. That is four. We just attract for on each side, so we have to Wise Eagle do eight and finally under divide. Eat size by two y is equal to for so and X is equal to two wives. You go to fourth physical, too. Why is he go to four? We have, technically four different answers, or for each of the

He said. We have to get rid of circumference in daily offices of the circle. In the first part, we know that circumference circum pigeons hey, leave nothing but two pi r and that would be two times off fire and aren't even visible to hurry. Even which is 3.5 centimeter. So we can add to the two times off by individually to and to buy, which is to Trent seven a vampire witches and our is 3.5, which began after the 35.2 and which 30 PowerPoint actually 10. So this will be five times canceled. And this one and this one it can seem so basically become 22. And I went to see him, actually, and next, but then comes to area Idea is anything what by our is squired. So by squired, which basically become 27 upon five into 3.5 off the square, it was basically become 30 centimeters. Esquire. Now, moving to the next part of this question again, we have to go believes the confidence and the idea. And in this time, we have given a radius logistical support, wind, six pipes and emedia so we know circumference. She goes to to buy our. So there's basically become two times off. 27 upon 22 upon seven into our, which is poor 70.6 private. And this had confidence over there was really on 29.2 centimeters number. Remember the next part which we have to calculate area so they re pie are square with its viruses goes 27 into our square egy poor 0.65 Esquire over there. So basically this part over there is he was a 67.9 sending me to the square.

So we want to find the diameter of a circle so the circle has a circumference of 14. Unified its diameter. So we know this. The conference formula is for that I am better. We can just say diameter times pot. So if replace 14 with our seats, so that's 14 equals D times pi. Then we can divide off pie on both sides. Pies on this side of cancel out We've indeed equal 14 divided by pi. So that is going to be our diameter 14 divided by pi.

The solution to the question 41 is here. The data can be written as side minus length is equals 9-1. So are of the regular pentagon can be calculated using the form life area. His calls to one by forth into this side minus they learned square into root of five and 25 plus two. Route five. So Putin. They will you you will get your answer as (145) 937 9.471 eight sq. Thank you.


Similar Solved Questions

5 answers
Which function has larger growth rate or are the rates comparable? f (x) = ex or g(x) 2* . Use limits to justify your answer:
Which function has larger growth rate or are the rates comparable? f (x) = ex or g(x) 2* . Use limits to justify your answer:...
5 answers
Ina study of 36 working adults, the mean hours of sleep they reported getting each night was 7.3 hours with a standard deviation of 1.62hoursCalculate the test statistic; for a hypothesis test of the claim that the mean hours that working adults sleep is less than 8 hours:Round your answer to 3 decimal places
Ina study of 36 working adults, the mean hours of sleep they reported getting each night was 7.3 hours with a standard deviation of 1.62hours Calculate the test statistic; for a hypothesis test of the claim that the mean hours that working adults sleep is less than 8 hours: Round your answer to 3 de...
5 answers
00 0 } 1 741 HH W [ 7 # 1 H V 1 H 1 3 1 N 1 1 1 H UV 11 9 4
00 0 } 1 741 HH W [ 7 # 1 H V 1 H 1 3 1 N 1 1 1 H U V 1 1 9 4...
5 answers
[8 points] Graph h(z) ( 3)2 (x + 1)2z(r - 5) in the space below . Clearly display the x-intercepts and end behavior.
[8 points] Graph h(z) ( 3)2 (x + 1)2z(r - 5) in the space below . Clearly display the x-intercepts and end behavior....
5 answers
6.-[The diagram below describes the sample space of a particular experiment and define events A and B. Suppose the sample points are equally likely:a): Find P(A)b): Find P(B)c): Find P(AnB)d). Find P(AUB)e): Find P(Bc)f): Find P(AUBC)g). Find P(B[A)h): Are A and B independent? Yes No
6.-[The diagram below describes the sample space of a particular experiment and define events A and B. Suppose the sample points are equally likely: a): Find P(A) b): Find P(B) c): Find P(AnB) d). Find P(AUB) e): Find P(Bc) f): Find P(AUBC) g). Find P(B[A) h): Are A and B independent? Yes No...
5 answers
Use an identity solve the equation on the interval [0,2r)sin 2xcosx + cos 2x sin x =Select the correct choice below ard, if necessary fill in the answer box comiplele your choice0 A (ype an exact answer, using 0 B There no solution,needed Use commn ?eparle answeneneeded_Type your answer in rad ans. Sinplijy YDur unswer3oseicick selecHype herespancDCLLenic=
Use an identity solve the equation on the interval [0,2r) sin 2xcosx + cos 2x sin x = Select the correct choice below ard, if necessary fill in the answer box comiplele your choice 0 A (ype an exact answer, using 0 B There no solution, needed Use commn ? eparle answene needed_Type your answer in rad...
5 answers
(b) [3 pts] A charge 5 ~5.0 HC is positioned at point A. Calculate the amount of work required to move it to point B.
(b) [3 pts] A charge 5 ~5.0 HC is positioned at point A. Calculate the amount of work required to move it to point B....
5 answers
Unit / Assessment12ol 18Soke tor (round t0 the nearest tenth)45981012 13Nex >
Unit / Assessment 12ol 18 Soke tor (round t0 the nearest tenth) 45 98 10 12 13 Nex >...
1 answers
Indicate whether the given statement is true or false. $$\mathbf{a} \in\{\mathbf{b}, \mathbf{c}, \mathbf{d}, \mathbf{a}\}$$
Indicate whether the given statement is true or false. $$\mathbf{a} \in\{\mathbf{b}, \mathbf{c}, \mathbf{d}, \mathbf{a}\}$$...
1 answers
Multiply the following expressions. $x^{6} \cdot x$
Multiply the following expressions. $x^{6} \cdot x$...
5 answers
Uomabaoateria Quince: Attempt 1Which is false about the bottle neck effect?It often results in a reduced genetic variability in a population: It has no effect on the gene pool.It will alter the frequency of alleles in a population:It may result from massive lava flow that destroys most of the organisms in on islandQuestion 8 (2 points) Which of the following is NOT a mechanism of evolution?genetic driftnatural selectionbiogeographyHio
uomabao ateria Quince: Attempt 1 Which is false about the bottle neck effect? It often results in a reduced genetic variability in a population: It has no effect on the gene pool. It will alter the frequency of alleles in a population: It may result from massive lava flow that destroys most of the ...
5 answers
Small laser used as pointer produces beam of red light mm in diameter; and has power output of 3 milliwatts. What the magnitude of the electric field in the laser beam? N/C
small laser used as pointer produces beam of red light mm in diameter; and has power output of 3 milliwatts. What the magnitude of the electric field in the laser beam? N/C...
5 answers
In Exercises $83-90$ , use a graphing utility to graph the function. Identify any symmetry with respect to the $x$ -axis, $y$ - axis, or origin. Determine the number of $x$ -intercepts of the graph. $$h(x)= rac{1}{5}(x+2)^{2}(3 x-5)^{2}$$
In Exercises $83-90$ , use a graphing utility to graph the function. Identify any symmetry with respect to the $x$ -axis, $y$ - axis, or origin. Determine the number of $x$ -intercepts of the graph. $$ h(x)=\frac{1}{5}(x+2)^{2}(3 x-5)^{2} $$...
5 answers
HzSOsDraw ycur Mechawiscoe bucra:
HzSOs Draw ycur Mechawiscoe bucra:...
5 answers
1 I227 { ! V 2 1 1 2 1 : 1 1 3 2
1 I227 { ! V 2 1 1 2 1 : 1 1 3 2...
5 answers
((4 points) Consider the competition experiments illustrated below Assume that in each case the rale such that only one of the two substrates undergoes the reaction For each example. circle the starting material that would react faster. No words are necessary Or will be considered in grading:OHOHCH;O
((4 points) Consider the competition experiments illustrated below Assume that in each case the rale such that only one of the two substrates undergoes the reaction For each example. circle the starting material that would react faster. No words are necessary Or will be considered in grading: OH OH ...

-- 0.019388--