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Georgia [21]
3 years ago
6

Find the volume of a sphere with a radius of 2 meters. Round your answer to the nearest tenth.

Mathematics
2 answers:
Arturiano [62]3 years ago
8 0

Answer:

Volume = 33.51 m^3

Step-by-step explanation:

<u>Formula for a Sphere:  V = 4 /3 * π * r^3</u>

<u />

<u>Step 1:  Plug in</u>

V = 4 /3 * π * (2)^3

V = 4/3 * π * 8

V = c

<em>V = 33.51</em>

<em />

Answer:  Volume = 33.51 m^3

Lubov Fominskaja [6]3 years ago
3 0

Answer:

33. 5 meters cubed.

\frac{4}{3} multiplied by 3.14 and by 8. Divide it by 5. This gives you approximately 33.5.

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Prove the formula that:
azamat

Step-by-step explanation:

Given: [∀x(L(x) → A(x))] →

[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

To prove, we shall follow a proof by contradiction. We shall include the negation of the conclusion for

arguments. Since with just premise, deriving the conclusion is not possible, we have chosen this proof

technique.

Consider ∀x(L(x) → A(x)) ∧ ¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

We need to show that the above expression is unsatisfiable (False).

¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]

∃x¬((L(x) ∧ ∃y(L(y) ∧ H(x, y))) → ∃y(A(y) ∧ H(x, y)))

∃x((L(x) ∧ ∃y(L(y) ∧ H(x, y))) ∧ ¬(∃y(A(y) ∧ H(x, y))))

E.I with respect to x,

(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ ¬(∃y(A(y) ∧ H(a, y))), for some a

(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ (∀y(¬A(y) ∧ ¬H(a, y)))

E.I with respect to y,

(L(a) ∧ (L(b) ∧ H(a, b))) ∧ (∀y(¬A(y) ∧ ¬H(a, y))), for some b

U.I with respect to y,

(L(a) ∧ (L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b

Since P ∧ Q is P, drop L(a) from the above expression.

(L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b

Apply distribution

(L(b) ∧ H(a, b) ∧ ¬A(b)) ∨ (L(b) ∧ H(a, b) ∧ ¬H(a, b))

Note: P ∧ ¬P is false. P ∧ f alse is P. Therefore, the above expression is simplified to

(L(b) ∧ H(a, b) ∧ ¬A(b))

U.I of ∀x(L(x) → A(x)) gives L(b) → A(b). The contrapositive of this is ¬A(b) → ¬L(b). Replace

¬A(b) in the above expression with ¬L(b). Thus, we get,

(L(b) ∧ H(a, b) ∧ ¬L(b)), this is again false.

This shows that our assumption that the conclusion is false is wrong. Therefore, the conclusion follows

from the premise.

15

5 0
2 years ago
If 140 students want to go on the Coronado Island field trip and are ALL riding together, how many cars will they need if each c
Kryger [21]

Answer:

24

Step-by-step explanation

bruh...

1. Divide 140 by 6 and you get 23.3 repeating

2. When you multiply 23 times 6 you get 138. (not enough seats)

3. So, you would need to have at least 24 cars in order for everyone to go on the trip. (24 x 6 = 144 seats)

3 0
3 years ago
8. A rain barrel collected 75 gallons of water. Water leaked
Mnenie [13.5K]

Answer:

30 days (do correct me if I'm wrong haha)

Step-by-step explanation:

5 gallons = 2 days

75 gallons = 30 days

75÷5=15 15×2=30

7 0
2 years ago
Given: BD is a diameter<br> m 1= 100°<br> m BC = 30°<br> m CD =<br> 100<br> 150<br> 330
sertanlavr [38]

Answer:

150

Step-by-step explanation:

330 is to big because the diameter is 180

100 is angle 1 and CD is bigger

so it would be 150

hope i helped

4 0
2 years ago
Let f(x) = (x − 3)−2. Find all values of c in (1, 7) such that f(7) − f(1) = f '(c)(7 − 1). (Enter your answers as a comma-separ
Sidana [21]

Answer:

This contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) (7 − 1) , but f is not continuous at x = 3

Step-by-step explanation:

The given function is

f(x)=(x-3)^{-2}

When we differentiate this function with respect to x, we get;

f'(x)=-\frac{2}{(x-3)^3}

We want to find all values of c in (1,7) such that f(7) − f(1) = f '(c)(7 − 1)

This implies that;

0.06-0.25=-\frac{2}{(c-3)^3} (6)

-0.19=-\frac{12}{(c-3)^3}

(c-3)^3=\frac{-12}{-0.19}

(c-3)^3=63.15789

c-3=\sqrt[3]{63.15789}

c=3+\sqrt[3]{63.15789}

c=6.98

If this function satisfies the Mean Value Theorem, then f must be continuous on  [1,7] and differentiable on (1,7).

But f is not continuous at x=3, hence this hypothesis of the Mean Value Theorem is contradicted.

 

3 0
3 years ago
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