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kati45 [8]
3 years ago
11

A sphere has the radius of 3, is the volume 83.4? (that is the answer i got but its my first time trying to find the volume of a

sphere, i missed this lesson)
Mathematics
1 answer:
Vitek1552 [10]3 years ago
4 0
No it should be 6 because radius is half of diameter
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Hi there! Sorry to bother you, but can someone help me out with this?
Rudik [331]

Problem 6

<h3>Answer: A) Conjecture</h3>

Explanation:

We can rule out choices B through D because they are valid items to use in any proof. A definition is a statement (or set of statements) set up in a logical fashion that is very clear and unambiguous. This means there cannot be any contradiction to the definition. An example of a definition is a line is defined by 2 points (aka a line goes through 2 points).

A postulate is a term that refers to a basic concept that doesn't need much proof to see why it's true. An example would be the segment addition postulate which says we can break up a segment into smaller pieces only to glue those pieces back together and get the original segment back.

A theorem is more rigorous involving items B and C to make a chain of statements leading from a hypothesis to a conclusion. You usually would see theorems in the form "if this, then that". Where "this" and "that" are logical statements of some kind. One theorem example is the SSS congruence theorem that says "if two triangles have three pairs of congruent corresponding sides, then the triangles are congruent". Chaining previously proven/established theorems is often done to form new theorems. So math builds on itself.

A conjecture is basically a guess. You cannot just blindly guess and have it be valid in a proof. You can have a hypothesis and have it lead to a conclusion (whether true or false) but simply blindly guessing isn't going to cut it. So that's why conjectures aren't a good idea in a proof.

==========================================================

Problem 7

<h3>Answer: Choice A) A theorem does not require proof</h3>

Explanation:

As mentioned in the section above (paragraph 3), a theorem does require proof. It's like having a friend come up to you and make a claim, only to not back it up at all. Do you trust your friend? What if they might be lying? Now consider that instead of a friend, but now it's some random stranger you just met.

Of course, they may not realize they are lying but it's always a good idea to verify any claim no matter how trivial. Math tries to be as impartial as possible to have every theorem require proof. Some proofs are a few lines long (we consider these trivial) while others take up many pages, if not an entire book, depending on the complexity of the theorem.

So that's why we can rule out choice B since it's a true statement. Choices C and D sort of repeat the ideas mentioned, just phrased in different ways. As mentioned earlier, a theorem is built from fundamental building blocks of various definitions and postulates and theorems. The term "axiom" is more or less the same as "postulate" (though with slight differences).

If you wanted to go for a statement that doesn't require proof, then you'd go for an axiom or postulate. Another example of such would be something like "if two straight lines intersect, then they intersect at exactly one point".

5 0
3 years ago
2.) Is (-1, 2) a solution to this system of equations?<br> 1-x+2y = 3<br> 12x - y - 4
gizmo_the_mogwai [7]

Answer:

12x-y-4

Step-by-step explanation:

3 0
2 years ago
I need help with this problem
Kobotan [32]

Step-by-step explanation:

diameter = 3ft

radius = 3/2 ft

perimeter of semicircle= πr = π (3/2) = 3.14×3/2

= 4.71 ft

6 0
3 years ago
The square numbers can be defined by the recursive formula a1 = 1, and an = an-1 + (2n - 1), where n &gt; 1. The first five squa
liberstina [14]
<span>1, 4, 9, 16, and 25. Use the formula to get a2 = 1 + (2*2 - 1) = 4, a3 = 4 + (2*3 - 1) = 9, etc. Also notice that for all n, an = n2.</span>
4 0
3 years ago
Read 2 more answers
hudson pick 1 1/4 baskets of apple suzy pick 2 basket of apple how muck more basket apple did suzy pick than hudson.
Vinvika [58]

Answer:

3/4

Step-by-step explanation:

Hudson = 1 1/4 baskets

Suzy = 2 baskets

How much more apple Suzy picked than Hudson :

Suzy - Hudson

2 - 1 1/4

2 - 5/4

L. C. M = 4

(8 - 5) / 4

3 /4 apples

Suzy picked 3/4 more apples Than Hudson

6 0
3 years ago
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