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3 years ago

Julie bought 12

Mathematics

1 answer:

Drupady [299]3 years ago

5 0

She would have 12 seeds left from her planting of all packs

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Find an equation of the sphere that passes through the origin and whose center is (-2, 2, 3). Be sure that your formula is monic

Andrei [34K]

Answer:

$\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

Step-by-step explanation:

Given the center of sphere is: (-2, 2, 3)

Passes through the origin i.e. (0, 0, 0)

To find:

The equation of the sphere ?

Solution:

First of all, let us have a look at the equation of a sphere:

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

Where ( $x,y,z$ ) are the points on sphere.

$(a, b, c)$ is the center of the sphere and

$r$ is the radius of the sphere.

Radius of the sphere is nothing but the distance between any point on the sphere and the center.

We are given both the points, so we can use distance formula to find the radius of the given sphere:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

Here,

$x_1 =0 \\y_1 =0 \\z_1 =0 \\x_2 =-2 \\y_2 =2 \\z_2 =3$

So, Radius is:

$r = \sqrt{(-2-0)^2+(2-0)^2+(3-0)^2}\\\Rightarrow r = \sqrt{4+4+9} = \sqrt{17}$

Therefore the equation of the sphere is:

$(x-(-2))^2+(y-2)^2+(z-2)^2=(\sqrt{17})^2\\\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

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3 years ago

Which property is illustrated by the following equation? - 10 + 8 = 8 + ( - 10 )

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I believe it is commutative property cause the numbers didn't change instead they just switched places in the equation.

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3 years ago

I need help with number 13

nikklg [1K]

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept → (0, b)

We have the point (0, 5). Therefore b = 5.

We have: y = mx + 5

Other point (3, 2). Substitute the coordinates of the point to the equation of the line:

$2=3m+5$ subtract 5 from both sides

$-3=3m$ divide both sides by 3

$-1=m\to m=-1$

<h3>Answer: f(x) = -1x + 5 = -x + 5</h3>

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3 years ago

The science club is raising money for a trip to the museum. Tickets to the museum cost $8. Five students already have a membersh

mrs_skeptik [129]

Answer: 42

Step-by-step explanation:

8/296 + 5 = S

296 divided by 8 plus 5 (the free student) equals 42

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A triangle has angles measuring 30 degrees and 90 degrees the length of the included side is 6cm. tell whether the conditions fo

Alexxx [7]

Angle 1 = 30°
Angle 2 = 90°
⇒ Angle 3 = 60°
So, it's right triangle. We can set the length of one side and get all other sides.
So, we have 1 triangle. If there are 2 or more triangles with the same data, all the triangles will be congruent because of : Two triangles are congruent if "ASA: Two interior angles and the included side in a triangle have the same measure and length, respectively, as those in the other triangle."

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3 years ago