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Ymorist [56]
2 years ago
12

By finding the radius of each circle and the distance between their centers, show that the circles x²+y²=4 and x²-4x+y²-4y+4=0 i

ntersect. Illustrate graphically.

Mathematics
1 answer:
Contact [7]2 years ago
6 0

Answer:

The circles do intersect.

Step-by-step explanation:

A circle is of the form

(x-h)^2+(y-k)^2=r^2

where,

h = Point on x axis of the circle center

k = Point on y axis of the circle center

x^2+y^2=4\\\Rightarrow (x-0)^2+(y-0)^2=2^2

So, the center of the circle is at (0,0) and radius is 2 units

x^2-4x+y^2-4y+4=0\\\Rightarrow (x^2-4x)+(y^2-4y)=-4\\\Rightarrow (x-2)^2+(y-4)^2=-4\\\Rightarrow (x^2+4-4x)+(y^2+4-2y)=-4\\\Rightarrow (x-2)^2+(y-2)^2=-4+4+4\\\Rightarrow (x-2)^2+(y-2)^2=4\\\Rightarrow (x-2)^2+(y-2)^2=2^2

The circle center is at the point (2,2) and radius is 2 units.

Hence, the circles do intersect.

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Answer:

-1

Step-by-step explanation:

-2-3-(-4)=-2-3+4=-5+4=-1

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3 years ago
Write a quadratic function f(x) for the area of a rectangle length x+5 width 3x-7
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A box contains 20 miniature golf putt-putt balls; 10 are
stellarik [79]

Answer: The answer is provided below

Step-by-step explanation:

From the question, a box contains 20 miniature golf putt-putt balls out of which 10 are yellow, 6 are red, and the remaining 4 are pink.

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2 years ago
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Find the value of x such that the data set 31.7, 42.8, 26.4, and x has a mean of 35.
Travka [436]

Answer:

x = 39.1

Step-by-step explanation:

To find the mean, add up all the data points and then divide by the number of data points

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(31.7+ 42.8+ 26.4+ x)/4*4 = 35*4

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3 years ago
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