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Setler [38]
2 years ago
10

Find the equation of a circle with a center at (0, -4) and a point on the circle is (6, 0).

Mathematics
1 answer:
EastWind [94]2 years ago
8 0

Answer:

x^2 + ( y + 4)^2 = 52

Step-by-step explanation:

Equation of circle with center (a , b) and radius, r is :

(x -a)^2 + ( y -b)^2 = r^2

Given :  a = 0 , b = - 4

Step 1 : Find the radius.

       Given ( 6 , 0 ) lies on the circle. Therefore the distance between the center (0 , - 4) of the circle and ( 6 , 0 ) gives the radius of the circle.

   r = \sqrt{( 0 - 6)^2 + ( -4 - 0)^2} \\\\

     = \sqrt{ 36 + 16 } \\\\= \sqrt{52}

Step 2 : Equation of circle.

  (x - 0)^2 + (y -( - 4))^2 = (\sqrt{52})^2\\\\x^2 + ( y+ 4)^2 = 52

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What are opposites?
Scrat [10]

Answer:

Opposites are basically the negative and positive of a number.  I cannot think of something for a real world situation though.

Step-by-step explanation:

3 0
2 years ago
Element X decays radioactively with a half life of 12 minutes. If there are 200 grams of Element X, how long, to the nearest ten
Semenov [28]

Answer:

It would take 24 minutes for the element to decay to 50 grams

Step-by-step explanation:

The equation for the amount of the element present, after t minutes, is:

Q(t) = Q(0)e^{-rt}

In which Q(X) decays radioactively with a half life of 12 minutes.(0) is the initial amount and r is the rate it decreases.

Half life of 12 minutes

This means that Q(12) = 0.5Q(0)

So

Q(t) = Q(0)e^{-rt}

0.5Q(0) = Q(0)e^{-12r}

e^{-12r} = 0.5

\ln{e^{-12r}} = \ln{0.5}

-12r = \ln{0.5}

12r = -\ln{0.5}

r = -\frac{\ln{0.5}}{12}

r = 0.05776

If there are 200 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 50 grams?

This is t when Q(t) = 50. Q(0) = 200.

Q(t) = Q(0)e^{-rt}

50 = 200e^{-0.05776t}

e^{-0.05776t} = 0.25

\ln{e^{-0.05776t}} = \ln{0.25}

-0.05776t = \ln{0.25}

0.05776t = -\ln{0.25}

t = -\frac{\ln{0.25}}{0.05776}

t = 24

It would take 24 minutes for the element to decay to 50 grams

6 0
3 years ago
Which of the following is (are) the solution(s) to 9|x-1| = -45
Lesechka [4]

Answer:

no solution

Step-by-step explanation:

7 0
3 years ago
Lanette drove 248 miles in 4 hours. At the rate, how many hours will it take her to drive a additional 93miles.
LenaWriter [7]

Answer:

1.5 hours

Step-by-step explanation:

using the relationship between distance/ speed / time

distance = speed × time

speed = \frac{distance}{time} = \frac{248}{4} = 62 mph

travelling at this rate then

time = \frac{distance}{speed} = \frac{93}{62} = 1.5 hours


7 0
2 years ago
In triangles △ABC and △DEF,
wel

Answer:

  • BC = 4.8
  • ED = 1.1
  • DF = 1.6

Step-by-step explanation:

Since angles A and E correspond, as well as angles C and F, we can say ...

  ΔABC ~ ΔEDF

Then the ratio of side lengths of ΔABC to those of ΔEDF is ...

  AC/EF = 6/2 = 3

That means ...

  ED/AB = 1/3

  ED = AB·(1/3) = 3.3·(1/3) = 1.1

For the remaining sides, we have the relation

  3·DF = BC

  3·(BC -3.2) = BC

  2BC - 9.6 = 0 . . . eliminate parentheses, subtract length BC

  BC -4.8 = 0 . . . . . divide by 2

  BC = 4.8 . . . . . . . . add 4.8

  DF = BC·(1/3) = 1.6

The unknown side lengths are BC = 4.8, DE = 1.1, DF = 1.6.

7 0
3 years ago
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