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3 years ago

Write the equation of this circle in standard form. please give answer?

Mathematics

1 answer:

Law Incorporation [45]3 years ago

3 0

Given the center $(x_0,y_0)$ and the radius $r$ of a circle, its equation is

$(x-x_0)^2+(y-y_0)^2=r^2$

In your case, the center is (-4,0), and the radius is 2. Plug these values into the generic formula and you'll get the equation.

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Can you help me write this in standard form <br><img src="https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B2%7D%20x%20-%20%

Karo-lina-s [1.5K]

I think it’s 15x-10y=2

3 0

2 years ago

Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

$(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14$ .

(Expand to obtain an equivalent expression for the sphere: $x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between $\left(x_1, \, y_1, \, z_1\right)$ and $\left(x_2, \, y_2, \, z_2\right)$ would be:

$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .

The equation for a sphere of radius $r$ and center $\left(x_0,\, y_0,\, z_0\right)$ would be:

$\left(x - x_0\right)^2 + \left(y - y_0\right)^2 + \left(z - z_0\right)^2 = r^2$ .

In this case, the equation would be:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z - (-6)\right)^2 = \left(\sqrt{56}\right)^2$ .

Simplify to obtain:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z + 6\right)^2 = 56$ .

Expand the squares and simplify to obtain:

$x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ .

8 0

2 years ago

What does it mean to square a negative number

Andrej [43]

Answer:

This is because to square a number just means to multiply it by itself. For example, (-2) squared is (-2)(-2) = 4. Note that this is positive because when you multiply two negative numbers you get a positive result.

5 0

3 years ago

Read 2 more answers

Help me pls, im stuck!!!! :))

timofeeve [1]

Answer:

y=8x

Step-by-step explanation:

The graph starts at the origin so there won't be a y intercept and the slope its 8 because every book costs 8 dollars. Therefore, the equation will be y=8x. Hope this helped

7 0

2 years ago

Read 2 more answers

The value of a jewel in 2015 was $17500. The jewel was purchased in 2008, and its value appreciated 2.5%

ArbitrLikvidat [17]

Answer:

$14722.14

Step-by-step explanation:

We are given that

In 2015

The value of jewel=$17500

Rate of appreciation, r=2.5%