Three cell phones towers can be modeled by the points X(6,0), Y(8,4), and Z(3,9). Determine the location of another cell phone tower equidistant from the other three, and write an equation for the circle.
Answers
Answer:
The location of the new cell phone tower is [tex](h,k) = (3,4)[/tex], and the equation of the circle is [tex]x^{2}+y^{2} -6\cdot x - 8\cdot y = 0[/tex].
Step-by-step explanation:
The location of the cell phone tower coincides with the location of a circunference passing through the three cell phone towers. By Analytical Geometry, the equation of the circle is represented by the following general formula:
[tex]x^{2} + y^{2}+A\cdot x + B\cdot y +C = 0[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]A[/tex], [tex]B[/tex], [tex]C[/tex] - Circunference constants.
Given the number of variable, we need the location of three distinct points:
[tex](x_{1},y_{1}) = (6,0)[/tex]
[tex]36 +6\cdot A + C = 0[/tex]
[tex](x_{2},y_{2}) = (8,4)[/tex]
[tex]80 + 8\cdot A + 4\cdot B + C = 0[/tex]
[tex](x_{3},y_{3}) = (3,9)[/tex]
[tex]90 + 3\cdot A + 9\cdot B + C = 0[/tex]
Then, we have the following system of linear equations:
[tex]6\cdot A + C = -36[/tex] (2)
[tex]8\cdot A +4\cdot B + C = -80[/tex] (3)
[tex]3\cdot A + 9\cdot B + C = -90[/tex] (4)
The solution of this system is:
[tex]A = -6[/tex], [tex]B = -8[/tex], [tex]C = 0[/tex]
By comparing the general form with the standard form of the equation of the circunference is:
[tex]A = -2\cdot h[/tex] (5)
[tex]B = -2\cdot k[/tex] (6)
[tex]C = h^{2}+k^{2}-r^{2}[/tex] (7)
Where:
[tex]h[/tex], [tex]k[/tex] - Coordinates of the center of the circle.
[tex]r[/tex] - Radius of the circle.
If we know that [tex]A = -6[/tex], [tex]B = -8[/tex] and [tex]C = 0[/tex], then coordinates of the center of the circle and its radius are, respectively:
[tex]h = -\frac{A}{2}[/tex]
[tex]k = -\frac{B}{2}[/tex]
[tex]r = \sqrt{h^{2}+k^{2}-C}[/tex]
[tex]h = 3[/tex], [tex]k = 4[/tex], [tex]r = 5[/tex]
The location of the new cell phone tower is [tex](h,k) = (3,4)[/tex], and the equation of the circle is [tex]x^{2}+y^{2} -6\cdot x - 8\cdot y = 0[/tex].
Related Questions
Jessica makes $1500 a month at her job. If she saves 20% of it each month, how much savings will she have after one year? Remember that there are 12 months in one year!
Answers
Explanation:
20% x 1500 = 300
300 x 12 = 3600
Hope it’s right
Best luck with your studying
$3,600
Step-by-step explanation:
You'd multiply 1,500 with .20 which equals 300. You'd then multiply 300 and 12 together to make $3,600.
i think i chose the wrong one
Answers
i think its right good luck im not so good at this
Answer:
ur good
Step-by-step explanation:
helpppppppppppppppppppp
Answers
When you flip a biased coin the probability of getting a tail is 0.2.
How many times would you expect to get tails if you flip the coin 240 times?
Answers
Answer:
48
Step-by-step explanation:
Multiply 0.2 × 240 = 48.
It's a very biased coin, so the outcome will be considerably less than the 120 we would expect from a fair coin.
Kiran is playing a video game. He earns 3 stars for each easy level he completes and 5 stars for each difficult level he completes. He completes more than 20 levels total and earns 80 or more stars
Answers
Answer:
10 easy levels and 10 difficult levels
Step-by-step explanation:
Given data
let the number of easy levels be x
and the number of difficult levels be y
so
x+y= 20----------1
and
3x+5y= 80------2
from 1
x=20-y
put this in 2
3(20-y)+5y= 80
60-3y+5y=80
2y=80-60
2y=20
y= 20/2
y= 10
put y= 10 in 1
x+10=20
x=20-10
x= 10
Hence Kiran played 10 easy levels and 10 difficult levels
please solve step by step.....
Answers
The picture is not clear... the Question has got cut at the sides .... please take the picture properly and the post the Question again... please
[tex]\\\\\huge\underline\mathbb\pink{ANSWER:}\\\\[/tex]
No they are not unequal... i. e. the two wires A and B are equal .
[tex]\frac{1}{3}[/tex] of A = [tex]\frac{1}{3}[/tex] of B
=> [tex]\frac{3}{3}[/tex] × A = B
=> 1 × A = B
=> A = B
:. The length of A = the length of B .
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HOPE IT HELPS
PLEASE MARK ME BRAINLIEST ☺️
What is the correct formula of the 3D shape below?
V= 4/3 π r³
V= 1/3 π r² h
V= π r² h
Answers
Answer:
V= π r² h
Step-by-step explanation:
HELP ME PLEASE ILL MARK BRAINLIEST!!!!!!!!!!!!!!!!!!
Answers
Answer:
91.7 inches to 1 decimal place
Step-by-step explanation:
We will use Pythagoras's theorem to find the height of the pyramid.
The height of the Pyramid forms a right-angled triangle with half of the base and the slant height.
We can get half the length of the base by dividing the length of one side of the base = 20.4 by 2 = 10.2in
slant height = 92.3in
Therefore height = [tex]\sqrt{92.3^{2} -10.2^2} =91.73in[/tex]
The height of the pyramid is 91.73inches to 1 decimal place
What is the coefficient of m in the sum of (23m−34)( 3 2 m− 4 3 ) and (−16m−r)(− 6 1 m−r) ?
Answers
Answer:
77r - 2077
Step-by-step explanation:
To find the the sum of (23m−34)( 3 2 m− 4 3 ) and (−16m−r)(− 6 1 m−r)
First open the bracket
23m × 32m - 23m × 43 - 34 × 32m + 34 × 43
736m^2 - 989m - 1088m + 1462
736m^2 - 2077m + 1462
Open the second bracket
16m × 61m + 16m × r + r × 61m + r × r
976m^2 + 16mr + 61mr + r^2
976m^2 + 77mr + r^2
Adding both equations together
736m^2 - 2077m + 1462 + 976m^2 + 77mr + r^2
1712m^2 + 77mr - 2077m + 1462 + r^2
1712m^2 + m( 77r - 2077 ) + 1462 + r^2
Therefore The coefficient of m is 77r - 2077
You are selling tomatoes. You have already earned $16 today. How many additional pounds of tomatoes do you need to sell to earn a total of $60
Answers
5 2/3 divided by 3/2
Answers
Answer:
3 7/9
Step-by-step explanation:
Skylar drew two triangles that share a side and labeled the two portions of the base w and x. Then he solved for w and x as shown. Are his calculations correct? Explain in full sentences. (5 points)
Answers
The two triangles he drew and also the calculations he did are missing, so i have attached them.
Answer:
His calculations are not correct
Step-by-step explanation:
From the attached image showing the triangle, we can see that for the smaller triangle with w, 5.5 and 45° angle, it is clear that;
Opposite side is 5.5
Adjacent side is w
And angle is 45°.
Hypotenuse is unknown
Thus, from trigonometric ratios;
Opposite/adjacent = tan (angle)
Thus;
5.5/w = tan 45°
In Skylar's calculation, he expressed it as; 5.5/w = sin 45°
Therefore, his calculation is wrong.
Secondly, for the bigger triangle, it is clear that;
Opposite side is 5.5
Adjacent side is w + x
And angle is 35°.
Hypotenuse is unknown
Thus;
5.5/(w + x) = tan 35°
Whereas,skylar expressed his own as;
5.5/(w + x) = sin 35°
Again his calculation is wrong.
You wanted to make the perfect banana split sundae. There are 9 items that you need and
they are locked away. In order to unlock these items, you must complete 9 tasks. The locks
could contain numbers, letters, or both. Unlocking a task will enable you to add an item to
your banana split. In order to complete the perfect banana split sundae, you must complete
all 9 tasks correctly and unlock all 9 missing items.
Answers
Answer:
25
Step-by-step explanation:
math
Help me with my maths question and you get good luck 10 years
Answers
Answer:
Step-by-step explanation:
Let all the measurements be in same unit.
200 cm = 2 m
2000 mm = 2 m
Let distance jumped by Jack = x m
Distance jumped by Jerzy = x + 2
Distance jumped by Abdullah = (x+ 2) + 2 = x + 4
Total = 12.69 m
x + x +2 +x +4 = 12.69
x +x + x + 2 + 4 = 12.69
3x + 6 = 12.69
3x = 12.69 - 6
3x = 6.69
x = 6.69/3
x = 2.23 m
distance jumped by Jack =2.23m
Distance jumped by Jerzy = 2.23 + 2 = 4.23 m
Distance jumped by Abdullah = 2.23 + 4 = 6.23 m
do the following, i mean like... its not THAT HARD
Answers
Answer:
y > - (4/3) x - 3
Step-by-step explanation:
use (y2-y1)/(x2-x1) for slope, which is negative (use two points given, (-6, 5) and (3, -7))
y intercept is -3, but you can plug in values for x and y in any of two points given: (-6, 5) and (3, -7)
Then, dashed line indicates values along line are not included in inequality relationship
since shaded region is above line, the inequality uses ">"
Out of 15,000 voters in a constituency, 60% voted. Find the percentage of voters who did not vote. Can you now find how many actually did not vote?
Answers
Answer:
40 did not vote
6000 people did not vote
Step-by-step explanation:
1 % of 15,000 = 150
150 * 40 = 40% of 15,000 = 6000
what is the value of B and C?
Answers
Step-by-step explanation:
value of b is 73 (reason : sum of triangles)
a= 34 ( reason:180-73-73=34)
Answer: 73+73=146, 180-146= 34°
Step-by-step explanation:
b is parallel to 73, b= 73°
c = 34°
Whoever answers correctly gets brainliest
Answers
Answer:
25 miles
Step-by-step explanation:
175/7 = 25 miles
The jet will fly 25 miles in one minute.
Milan bought 3 CDs that were each the same price. Including sales tax, he paid a total of $44.40. Each CD had a tax of $1.30. What was the price of each CD before tax?
Answers
Answer:
$13.5
Step-by-step explanation:
Given data
We are given that the tax per CD is $1.30
Hence for the 3 CDs the total tax = 3*1.3= $3.9
Also, the cost of the three CDs before tax = 44.4-3.9
=$40.5
Hence the cost of each CD before tax is
=40.5/3
=$13.5
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PLS ANSWER- POINTS AND BRAINLIEST
Answers
Answer:
12x-23
Step-by-step explanation:
Answer:
peen
Step-by-step explanation:
Combine like terms: c + c + c
what do you get?
A- 3c
B- c3
Answers
Answer:
A. 3c
Step-by-step explanation:
c + c + c = c × 3
c × 3 = 3c
when t is 1, 3x2t =
when t is 4, 3x2t
Answers
3 Time 2 and time 1 so number one is 6
and number 2 is 24
Step-by-step explanation:
when t is 1
3X2t=6
when t is 4
3X2t=24
find the value of X, please!
Answers
Answer:
x=42°
Step-by-step explanation:
We know that 2 of the legs are congruent, so the angles opposite them will be congruent.
The angles of a triangle add up to 180°
This can be represented by [tex]96+2x=180[/tex]
[tex]2x=84[/tex]
[tex]x=42[/tex]
Hope this helps :-)
Answer: 42 degrees
Step-by-step explanation: Since this is an isosceles triangle, your remaining two angles will be equal
There are 180 degrees in any triangle
Since you have already used 96 degrees, you must subtract to find what is remaining
180-96=84
Since your remaining two angles are equal, you can half 84 to find your answer
84/2=42
Both x and your one remaining angle should be 42
X=42
HELP ME PLEASE ASAP!
Rewrite using a single positive exponent
(6^-3)^-9
Answers
Write in simplest form: 25ab/(15b2) = _____
Answers
Answer:
5a/3b
Step-by-step explanation:
as long as b ≠ 0
Help! please ( I am stuck on these questions so please help me!!)
Answers
Answer:
4in 5in and 8in (in that order)
Step-by-step explanation:
You measure Hight at the place where it makes a right angle (for these look at the dotted line and the number labeling it)
Answer:
1. 4 inches
2. 5 inches
3. 8 inches
Step-by-step explanation:
The heights are labelled.
Two tutors each earn $30 per hour. The first tutor worked 10 hours. The second tutor worked 14 hours. What total amount did the tutors earn?
Answers
$720.00
-
-
30×10=300
and
30×14=420
(you multiply the money with the amount of hours they spent working)
300
+ 420
----------
$720
hope this helps you out
first person who answers something gets brainliest
Answers
Answer:
thanks for the points! have a wonderful day! ☺☺☺☺☺☺☺☺⭐⭐⭐⭐⭐⭐
i dont get know how to set it up someone help?
Answers
Answer:
114×10^5..............
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Calculate the area of the trapezoid, which is not drawn to scale.
Answers
Answer:
4 x 8 = 32
11 - 8 = 3
5 x 3 = 15
15 / 2
7.5
32 + 7.5 = 39.5
Step-by-step explanation:
Answer:
4 x 8 = 32
11 - 8 = 3
5 x 3 = 15
15 / 2
7.5
32 + 7.5 = 39.5