Help center of circle

Mathematics

1 answer:

Lelu [443]3 years ago

7 0

Answer:

Center = (7, - 5)

Radius = 3

Step-by-step explanation:

${x}^{2} + {y}^{2} + 14x - 10y + 65 = 0 \\ {x}^{2} + 14x + {y}^{2} - 10 + 65 = 0 \\ ( {x}^{2} + 14x + {7}^{2}) - {7}^{2} + ({y}^{2} - 10y + {5}^{2}) \\- {5}^{2} + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 - 25 + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 + 40= 0 \\ (x + 7)^{2} + (y - 5)^{2} - 9= 0 \\ (x + 7)^{2} + (y - 5)^{2} = 9 \\ (x + 7)^{2} + (y - 5)^{2} = {3}^{2} \\ equating \: it \: with \: \\ (x - h)^{2} + (y - k)^{2} = {r}^{2} \\ - h = 7 \implies \: h = - 7 \\ - k = - 5 \implies \: k = 5 \\ center = ( - h, \: - k) = (7, \: \: - 5) \\ \\ radius \: r = 3$

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The graph of the function showing the path of a soccer ball thrown by a goalie in a video game, f(x) = –0.05x2 + 2.5x + 5.2, is

Tju [1.3M]

Answer:

The correct option is 4.

Step-by-step explanation:

The given function is

$f(x)=-0.05x^2+2.5x+5.2$

Where f(x) is height of the ball and x is the distance.

It is a polynomial function with degree 2. All polynomial functions are defined for all real numbers, therefore the mathematical domain of the function is all real numbers.

$-\infty$

Factorize the given function.

$f(x)=-0.05(x^2-50x-104)$

$f(x)=-0.05(x^2-52x+2x-104)$

$f(x)=-0.05(x(x-52)+2(x-52))$

$f(x) = -0.05 (x - 52) (x + 2)$

Put f(x)=0 to find the x intercepts.

$0 = -0.05 (x - 52) (x + 2)$

Equate each factor equal to 0.

$x=52,-2$

Therefore at x=52 and -2, the graph of f(x) intersects x-axis. Before x=-2 and after x=52 the values of f(x) is negative. Height cannot be negative, therefore reasonable domain is lie between -2 to 52.

Distance cannot be negative, therefore the reasonable domain must be positive.

$0\leq x\leq 52$