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Dmitry_Shevchenko [17]
3 years ago
10

Which equation in parallel to 3x-5y=10

Mathematics
1 answer:
Vaselesa [24]3 years ago
3 0

3x-5y=n

3x-5y=1

----------------------------

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How do you solve this problem?
jekas [21]
Very nice problem. You should look up the history of this question. It has a very long one having to do with mirrors made between 50 BC and 50 AD.

Step One
Find AB, BC, AC
Before beginning this problem, I'm going to arbitrarily name 
c = AB
a = BC
b = AC It just makes the calculations easier.

AB = radius of the large circle - radius of the medium circle = 20.62 - 8.04 = 12.58
BC = Radii of the two smaller circles added together = 8.04 + 7.35 = 15.39
AC = Radius of the large circle - Radius of the small circle = 20.62 - 7.35 = 13.27

So
a = 15.39
b = 13.27
c = 12.58

Step Two
Find Angle A or <BAC
a^2 = b^2 + c^2 - 2*b*c * Cos(A)
15.39^2 = 12.58^2 + 13.27^2 - 2 * 12.58 * 13.27 * Cos(A)
236.852 = 158.26 + 176.1 -  333.87 * Cos(A)
236.852 = 334.4 - 333.87*Cos(A)
-97.55 = - 333.87 *  Cos(A) 
-97.55 / -333.87 = Cos(A)
0.2922 = cos(A)
A = cos-1(0.2922)
A = 73.01 degrees

Step Three
Just to see if you understand what was done, I'll give you the givens for finding c, and the answer and you can work through the calculations to see if your answer agrees with mine. If it doesn't PM me.
c = 12.58
b = 13.27
a = 15.39

12.58^2 = 13.27^2 + 15.39^2 - 2*13.27*15.39*Cos(C)
C = 51.42

Step Four
Find <B
Every triangle has 180 degrees so
B = 180 - <A - C
B = 180 - 51.42 - 74.01
B = <54.57. 
I have found a moderator who opened the question up so that I can show you why the Cos law is the only way to do this. If the circles are very disproportionate as in this diagram, then no simple assumption can be made. The cos law is all that will work. I would have posted this earlier, but I didn't think anyone would find another method. It's ingenious but not possible for the situation below.

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3 years ago
What is the remainder for the synthetic division problem below?
Luden [163]

7 |1 -8 10
X. 7. -7
1 -1 3

A remainder is 3
7 0
2 years ago
Simplify the following question:
Anna71 [15]
The answer is 26x squared/9 plus 13x minus four.

4 0
2 years ago
How to find angles in a triangle
motikmotik
Well when you add up all three angles of a triangle you should get  180 degrees.
7 0
3 years ago
Read 2 more answers
The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 8 
julsineya [31]
Good afternoon, 

First side= 8cm 
Third side= x
Second side= 2x-4

We know that the sume of the lenghts of any two sides must be greater than the third side, so:

Second \,\,\,\,side+Third\,\,\,\,side>First\,\,\,\,side \\ 2x-4 + x >8 \\ 3x>12 \\ x>4&#10;

<span>Answer: Third side= x                        ;         where: x>4 or (4,+infinity)
                Second side= 2x-4              ;        </span><span> where: x>4 or (4,+infinity)</span>
3 0
3 years ago
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