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3 years ago

Write the equation in standard form for the circle with center (5,0) passing through (-1, 9/2)

Mathematics

1 answer:

andreev551 [17]3 years ago

3 0

Answer:

(x - 5)^2 + y^2 = 225/4,

or you could write it as (x - 5)^2 + y^2 = 56.25.

Step-by-step explanation:

The factor form is

(x - h)^2 + (y - k)^2 = r^2 where the center is (h, k) and r = the radius.

So we have:

(x - 5)^2 + (y - 0)^2 = r^2

As the point (-1, 9/2) is on the line:

(-1 - 5)^2 + (9/2)^2 = r^2

r^2 = 36 + 81/4

r^2 = 225/4.

So substituting for r^2:

(x - 5)^2 + (y - 0)^2 = 225/4

(x - 5)^2 + y^2 = 225/4 is the standard form.

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What is the approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth?

LuckyWell [14K]

Answer:

The length of the pendulum is 14.13 meters.

Step-by-step explanation:

The length of a pendulum is given by the formula, $T = 2\pi \sqrt{\frac{L}{g} }$ , where T is the times period and L is the length of the pendulum.

Now, given that T = 2.4π seconds.

So, from the above equation, we get,

$2.4\pi = 2\pi \sqrt{\frac{L}{g} }$

⇒ $\sqrt{\frac{L}{g}} = 1.2$

⇒ $\frac{L}{g} = 1.44$ {We have the value of g as 9.81 m/sec²}

⇒ L = 1.44 × 9.81 = 14.13 meters. (Approx.)

Therefore, the length of the pendulum is 14.13 meters. (Answer)

3 0

3 years ago

Which statements describe the graph of y = Negative RootIndex 3 StartRoot x minus 1 EndRoot + 2? Select three options.

SOVA2 [1]

Answer:

The graph has a domain of all real numbers.

The graph has a y-intercept at $(0,1)$ .

The graph has an x-intercept at $(-7,0)$ .

Step-by-step explanation:

Given: The graph is $y=\sqrt[3]{x-1}+2$

The domain of a function is a set of input values for which the function is real and defined.

Thus, the graph has a domain of $(-\infty, \infty)$ .

To find the y-intercept: To find the y-intercept, substitute $x=0$ in $y=\sqrt[3]{x-1}+2$ .

$\begin{aligned}y &=\sqrt[3]{x-1}+2 \\&=\sqrt[3]{0-1}+2 \\&=-1+2 \\&=1\end{aligned}$

Thus, the y-intercept is $(0,1)$

To find the x-intercept: To find the x-intercept, substitute $y=0$ in $y=\sqrt[3]{x-1}+2$ .

$\begin{aligned}y &=\sqrt[3]{x-1}+2 \\0 &=\sqrt[3]{x-1}+2 \\-2 &=\sqrt[3]{x-1} \\(-2)^{3} &=(\sqrt[3]{x-1})^{3} \\-8 &=x-1 \\-7 &=x\end{aligned}$

Thus, the x-intercept is $(-7,0)$

8 0

2 years ago

Read 2 more answers

I need help finding the answer to this:

anygoal [31]

Answer:

He will earn $6 in interest in 9 months.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

$E = P*I*t$

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

$T = E + P$