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agasfer [191]
3 years ago
14

Using the graph below, find the point(s) such that the sum of their coordinates is equal to 7.

Mathematics
1 answer:
gregori [183]3 years ago
7 0

Answer:

Only A, B and C are the points whose coordinates are equal to 7.

Step-by-step explanation:

Considering the point A

As the location of point A is (0, 7)

The sum of their coordinates is equal to 0 + 7 = 7

Considering the point B

As the location of point B is (2, 5)

The sum of their coordinates is equal to 2 + 5 = 7

Considering the point C

As the location of point C is (6, 1)

The sum of their coordinates is equal to 6 + 1 = 7

Considering the point D

As the location of point D is (4, -3)

The sum of their coordinates is equal to 4 + ( -3 ) = 1

Considering the point E

As the location of point E is (1, -6)

The sum of their coordinates is equal to 1 + ( -6 ) = -5

Considering the point F

As the location of point F is (-2, -4)

The sum of their coordinates is equal to -2 + ( -4 ) = -2 - 4 = -6

Considering the point G

As the location of point F is (-5, -2)

The sum of their coordinates is equal to -5 + ( -2 ) = -5 - 2 = -7

Considering the point H

As the location of point H is (-4, 3)

The sum of their coordinates is equal to -4 + ( 3 ) = -4 + 3 = -1

From the above discussion, only A, B and C are the points whose coordinates are equal to 7.

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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
Can anyone help!<br> WITH STEPS!
MissTica

Answer:

When we have something like:

\sqrt[n]{x}

It is called the n-th root of x.

Where x is called the radicand, and n is called the index.

Then the term:

\sqrt[4]{16}

is called the fourth root of 16.

And in this case, we can see that the index is 4, and the radicand is 16.

At the end, we have the question: what is the 4th root of 16?

this is:

\sqrt[4]{16} = \sqrt[4]{4*4}  = \sqrt[4]{2*2*2*2} = 2

The 4th root of 16 is equal to 2.

6 0
2 years ago
SOLVE
Sauron [17]

Answer:

approximately

1623.6

Step-by-step explanation:

16 1/2%=.165 which is approximately equal to 1/6, so we can just multiply the original number by 6.

7 0
3 years ago
Give the domain and range.
alexgriva [62]

Answer:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Step-by-step explanation:

Given:

There are three points on the graph.

Locate the x and y values of the points on the graph.

The points are (-2,-1),(0,1),\textrm{ and }(2,3)

Domain is the set of all possible x values. Here, the x values are -2, 0 and 2.

So, domain is: {-2, 0, 2}.

Range is set of all possible y values. Here, the y values are -1, 1 and 3.

So, range is: {-1, 1, 3}

7 0
2 years ago
Evaluate g/-5, when g=-5
daser333 [38]

Answer:

g/-5= 1

Step-by-step explanation:

g=-5, so -5/-5 is 1.

6 0
3 years ago
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