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Oliga [24]
2 years ago
7

Find the surface area of the prism.

Mathematics
1 answer:
tatyana61 [14]2 years ago
6 0

Answer:

Whats the question?

Step-by-step explanation:

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Consider a sphere of radius R > 0. Take two antipodal points A and B on the sphere, and another point C on the sphere. Check
aleksklad [387]

Answer:

To this question; we want to show that if two antipodal points on a sphere were A and B, for any random point C on the sphere, AC is perpendicular to BC?

Step-by-step explanation:

I would proceed by imagining the sphere in a three dimensional Cartesian coordinate system. For example, use a sphere of diameter 2 and let it sit at the origin. Then (0, 0, 1) and (0, 0, -1) are the vector locations of the “north and south poles” of the sphere.

Now choose the vector location of any point on the surface of the sphere. It will have a vector location - we’ll call it (x, y, z). Now the vectors from your point to the two poles are (-x, -y, 1-z) and (-x, -y, -1-z).

Now just form the dot product of those two vectors:

(-x, -y, 1-z) . (-x, -y, -1-z) = x^2 +y^2 + (1-z)*(-1-z)

Now the truth of your claim will be embodied in that dot product being zero:

x^2 + y^2 - (1+z)(1-z) = 0

x^2 + y^2 - (1-z^2) = 0

x^2 + y^2 + z^2 = 1

But that last line is just the definition of points on the surface of a sphere of radius 1, so the claim is proven.

Since R>0 and AC is perpendicular to BC, the <ACB is at right angle.

Please, find attached a simple image to show antipodal points (Two points that makes a diameter) and a point C on the sphere.

5 0
3 years ago
Doug drove 253 ½ miles in 4 ½ hours. How many miles did ,he average <br> per hour
nasty-shy [4]

Answer:

56.33 is the average of miles per hour.

Step-by-step explanation:

5 0
2 years ago
What is the binomial expansion of (m + 2)4?
ankoles [38]

Answer:

m+2

Step-by-step explanation:

use the binomial expansion theorem to find and simplify each term  

4 0
3 years ago
1325\1500X 100\1<br><br><br><br>guys help​
Schach [20]

Answer:

Exact Form:

265/3

Decimal Form:

88.3 (with a line over the 3)

Mixed Number Form:

88 1/3

4 0
2 years ago
I need to know the opposite of 8 1/4
masya89 [10]

Well Hello!


I believe the answer to your question would be -8 1/4

4 0
2 years ago
Read 2 more answers
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