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3 years ago

HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP

Mathematics

2 answers:

Helen [10]3 years ago

3 0

Answer:

7 seconds

Step-by-step explanation:

Hello There!

I had created a graph to make it easier to understand

So when y = 0 is when the ball is at the ground

when y = 0 x = 7 so it took about 7 seconds for the ball to hit the ground

Lady bird [3.3K]3 years ago

3 0

Answer:

Step-by-step explanation:

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3 years ago

Find the center and radius of the circle with the given equation. Then select the correct

8_murik_8 [283]

Answer:

The center of the circle is $(-4, 7)$ .

Its radius is $5$ .

Step-by-step explanation:

Let $(a,\, b)$ represent the center of the circle, and let $r$ represent the radius of this circle. The equation for the circle would be:

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

Expand the left-hand side of this equation using the binomial expansion:

$\left(x^2 - 2\, a\,x + a^2\right) + \left(y^2 - 2\, b\, y + b^2\right) = r^2$ .

$x^2 + (- 2\,a)\, x + y^2 + (-2\, b)\, y + \left(a^2 + b^2 - r^2\right)= 0$ .

Compare this equation with the one given in the question:

$x^2 + 8x + y^2 - 14\, y + 40 = 0$ .

These two equations should represent the same circle. For that to happen, the coefficients should match. That gives a few equations about $a$ , $b$ , and $r$ .

The coefficients for $x$ should match: $(-2\,a ) =8 \implies a = -4$ .
The coefficients for $y$ should match: $(-2\, b) = -14 \implies b = 7$ .
The constant terms should match: $a^2 + b^2 - r^2 = 40$ .

However, it is already determined that $a = -4$ and $b = 7$ . That means $a^2 + b^2 - r^2 = (-4)^2 + 7^2 - r^2 = 65 - r^2$ .

$65 - r^2 = 40 \implies r^2 = 25 \implies r = 5$ .

Hence, the radius of this circle is $r = 5$ . Also, its center is at $(a,\, b) = (-4,\, 7)$ .

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