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2 years ago

What is the center? (X-0.5)^2+(y-3.5)^2=16

Mathematics

2 answers:

pantera1 [17]2 years ago

5 0

Answer:

(.5,3.5) is the center and 4 is the radius

Step-by-step explanation:

(X-0.5)^2+(y-3.5)^2=16

This is written in the form

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

where (h,k) is the center and r is the radius

(X-0.5)^2+(y-3.5)^2=4^2

(.5,3.5) is the center and 4 is the radius

Aleks [24]2 years ago

3 0

Answer:

center = (0.5, 3.5)

Step-by-step explanation:

An equation of a circle is given by the general equation;

(x-a)² + (y-b)² = r²

Where (a, b) is the center of the circle and r is the radius of the circle.

Relating the general equation with the equation given;

(x- 0.5)² + (y- 3.5)² =16 with(x-a)² + (y-b)² = r²

then, a= 0.5, b = 3.5 and r = 4 units

Thus, the center is (0.5, 3.5)

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Step-by-step explanation:

Let x represent width of the original rectangle.

We have been given that a rectangle has a length 6 more than it's width. S the length of the original rectangle would be $x+6$ .

We have been given that when the width is decreased by 2 and the length decreased by 4 the resulting has an area of 21 square units.

The width of new rectangle would be $x-2$ .

The length of new rectangle would be $x+6-4=x+2$ .

The area of new rectangle would be $(x+2)(x-2)$ .

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Therefore, the length of original rectangle is 11 units.

$\text{Area of original rectangle}=5\times 11$

$\text{Area of original rectangle}=55$

Therefore, area of the original rectangle is 55 square units.

Now we will find ratio of the original rectangle area to the new rectangle area as:

$\frac{\text{Area of original rectangle}}{\text{Area of new rectangle}}=\frac{55}{21}$

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