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3 years ago

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A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is units. The point (-7,

) lies on this circle

2 answers:

yKpoI14uk [10]3 years ago

3 0

The answer is (-7,4). that is the right answer

kow [346]3 years ago

3 0

Answer:

radius 5. (-7,-1) is on the circle

%100 correct on PLATO

Step-by-step explanation:

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A mechanic had a bolt with a diameter of 2/9 inch. Will the bolt fit into a hole with a diameter of 0.2 inch.

Naddik [55]

Answer:

No, the bolt won't fit into the hole

Step-by-step explanation:

We need to convert the diameter of the bolt into decimal by dividing:

2/9 = 0.222...

The hole has diameter of 0.2

<em>Hence, 0.222 is larger than 0.2, so the bolt won't fit.</em>

3 0

3 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

3 years ago

Solve Please <br> 4+8/2(6-3)

Aleksandr-060686 [28]

Answer:

16

Step-by-step explanation:

4 + 8/2 x 3

4+4 x 3

4+12

16

Hope this helped

Brainliest is appreciated.

7 0

3 years ago

Read 2 more answers

PLZ PLZ PLZ PLZ PLZ HELP, I HAVE TWO MORE QUESTIONS IF YOU WANT MORE POINTS

12345 [234]

B/5 > 30

we’re going to simplify by multiplying by 5 on both sides.

b > 150 should be the answer!

8 0

3 years ago

Find dy/dx for (y^2/x) = 18 by implicit differentiation

Natasha2012 [34]

9514 1404 393

Answer:

dy/dx = y/(2x)

Step-by-step explanation:

The product formula can be used, along with the power rule.

d(uv) = du·v +u·dv

__

d(y^2/x) = d(18)

2y·dy/x -y^2/x^2·dx = 0

2x·dy -y·dx = 0 . . . . . . . . multiply by x^2/y

dy/dx = y/(2x) . . . . . . . . add y·dx, divide by 2x·dx

6 0

3 years ago