What is the distance between points (10, 7) and (2, 7) on a coordinate plane
1 answer:
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Answer:
Step-by-step explanation:
Begin with the standard form of a circle as a conic:
For a circle, A and C will be the exact same, and B will equal 0. If B is non-zero, the equation represents a rotation of a conic, which is reserved for college-level courses. Shortening this, then:
is good enough for us for this. Start with the first point on the circle, (2, 31) and fill in the equation above with x and y:
which simplifies down to:
Do the same with the next point on the circle, (-15, 14):
which simplifies down to:
Do the same with the last point, (33, 0):
which simplifies down to:
Now we will add (1) and (2) to get (4):
2D + 31E + F = -965
-15D + 14E + F = -421
Multiply the top equatio by -1 to get rid of the F terms:
-2D - 31E - F = 965
-15D + 14E + F = -421
which simplifies to
(4): -17D - 17E = 544
Now add (2) and (3) to get (5):
-15D + 14E + F = -421
33D + F = -1089
Multiply the bottom equation by -1 to get rid of the F terms:
-15D + 14E + F = -421
-33D - F = 1089
which simplifies to
(5): -48D + 14E = 668
Now add (4) and (5) together and eliminate the E terms:
-17D - 17E = 544
-48D + 14E = 668
In order to eliminate the E terms, multiply the top equation by 14 and the bottom equation by 17 to solve for D:
-238D - 238E = 7616
-816D + 238E = 11356
Which gives you that
D = -18
Now plug the value for D into (4) to find E:
-17(-18) - 17E = 544 and
306 - 17E = 544 and
-17E = 238 so
E = -14
Now plug the values for both D and E into (1) to find F:
2(-18) + 31(-14) + F = -965 and
-36 - 434 + F = -965 and
-470 + F = -965 so
F = -495
Now we can fill in the standard form of the conic:
but we're not done til we complete the square on both the x terms and the y terms (and I am assuming you know how to complete the square):
which simplifies to
The second choice down matches that equation, but the center they have there is not correct. The center of that circle is (9, 7) and they have it as being (7, 10) with a radius of 5. The radius is 25. The center is wrong in the equation that represents the circle as is the radius. Maybe let someone know that...
Answer:
The solutions for your four question problem are:
a) t = D^-1(x) = (1/57)*x -(13/57)
b) t = D^-1(x) = 1 h
c) D^-1(x) represents time.
d) The number of hours of driving needed for Sarah to be x km from Tempe. (option (c))
Step-by-step explanation:
a) Determine a formula in terms of x for: t = D^-1(x)
The distance in km from Tempe after t hours of driving is given by
x = D(t) = 13 + 57t.
We just need to find the value t function of x
x = 13 + 57*t
x -13 = 57*t
57*t = x -13
t = (1/57)*x -(13/57)
We can see the plots of both equation in the picture below.
b) Compute D^-1(70)
Once we find the expression for D^-1(x)
We substitute for x = 70 km
t = D^-1(x) = (1/57)*x -(13/57)
t = D^-1(x) = (1/57)*(70) -(13/57)
t = D^-1(x) = (70/57) -(13/57)
t = D^-1(x) = (1.228) -(0.228)
t = D^-1(x) = 1 h
c) In the expression D^-1(x) : what quantity (distance or time) does the x represent? what quantity (distance or time) does the entire D^-1(x) represent?
x represents Distance in both equations (D(t), and D^-1(x))
t represents Time in both equations (D(t), and D^-1(x))
Since t = D^-1(x),
D^-1(x) represents time.
d) Which of the following statements best describes D^-1(x)?
The number of hours of driving needed for Sarah to be x km from Tempe.
Since, t = D^-1(x), and t represents the amount of time elapsed since Sarah, parted from Tempe, the correct answer is option (c)
The expression for D^-1(x) can be found in the previous answers
t = D^-1(x) = (1/57)*x -(13/57)
The input is x (distance) and the output is t (time)
