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lys-0071 [83]
3 years ago
10

Find the coordinates of the circle and the radius y²+2x+x²-24y= -120

Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
3 0
We know that
the equation of a circle is
(x-h+(y-k)²=r²
where (k,k)----> is the center
and
r----> is the radius
y²+2x+x²-24y= -120

Group terms that contain the same variable
 (y²-24y)+(x²+2x)=-120

Complete the square twice. Remember to balance the equation by adding the same constants to each side
 (y²-24y+144)+(x²+2x+1)=-120+144+1

<span>Rewrite as perfect squares</span>

(y-12)²+(x+1)²=25

(x+1)²+(y-12)²=5²

the answer is
the coordinates of the center are (-1,12)
the radius is 5 units
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I need some help please
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Lim t^4 - 6 / 2t^2 - 3t + 7
Harman [31]

I think you meant to say

\displaystyle \lim_{t\to2}\frac{t^4-6}{2t^2-3t+7}

(as opposed to <em>x</em> approaching 2)

Since both the numerator and denominator are continuous at <em>t</em> = 2, the limit of the ratio is equal to a ratio of limits. In other words, the limit operator distributes over the quotient:

\displaystyle \lim_{t\to2} \frac{t^4 - 6}{2t^2 - 3t + 7} = \frac{\displaystyle \lim_{t\to2}(t^4-6)}{\displaystyle \lim_{t\to2}(2t^2-3t+7)}

Because these expressions are continuous at <em>t</em> = 2, we can compute the limits by evaluating the limands directly at 2:

\displaystyle \lim_{t\to2} \frac{t^4 - 6}{2t^2 - 3t + 7} = \frac{\displaystyle \lim_{t\to2}(t^4-6)}{\displaystyle \lim_{t\to2}(2t^2-3t+7)} = \frac{2^4-6}{2\cdot2^2-3\cdot2+7} = \boxed{\frac{10}9}

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3 years ago
A bucket holds b liters of water. But a jar holds 8 fewer liters than the bucket. How many times can the bucket hold than the ja
kykrilka [37]

Answer:

b / (b - 8)

Step-by-step explanation:

Given that :

Litres of water held by bucket = b

Jar holds 8 litres fewer than bucket; hence, litres held by jar = b - 8

The number of times bucket can hold than jar is :

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8 0
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Ummm help ig please................
AlexFokin [52]

Answer:

Cost of 500 g of standard pack = € 7.50

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Cost of 100 g of standard pack = 7.50/500 ×100

= 7.50/5

= € 1.50

Hope it helps uh dear

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3 years ago
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