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3 years ago

How do you find the circumference of a circle? Please include an example if you’d like.

Mathematics

1 answer:

crimeas [40]3 years ago

5 0

Answer:

Step-by-step explanation:

Plug the given value of the diameter into the formula and solve.[2]

Example problem: You have a circle tub with a diameter of 8 feet, and you want to build a white fence that creates a 6-foot wide space around the tub. To find the circumference of the fence that has to be created, you should first find the diameter of the tub and the fence which will be 8 feet + 6 feet + 6 feet, which will account for the entire diameter of the tub and fence. The diameter is 8 + 6 + 6, or 20 feet. Now plug it into the formula, plug π into your calculator for its numerical value, and solve for the circumference:

C = πd

C = π x 20

C = 62.8 feet

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I will mark u as brainliest if u answer this!!

lawyer [7]

i)On z, define a∗b=a−b
here aϵz
+
and bϵz
+

i.e.,a and b are positive integers
Let a=2,b=5⇒2∗5=2−5=−3
But −3 is not a positive integer
i.e., −3∈
/
z
+

hence,∗ is not a binary operation.
ii)On Q,define a∗b=ab−1
Check commutative
∗ is commutative if,a∗b=b∗a
a∗b=ab+1;a∗b=ab+1=ab+1
Since a∗b=b∗aforalla,bϵQ
∗ is commutative.
Check associative
∗ is associative if (a∗b)∗c=a∗(b∗c)
(a∗b)∗c=(ab+1)∗c=(ab+1)c+1=abc+c+1
a∗(b∗c)=a∗(bc+1)=a(bc+1)+1=abc+a+1
Since (a∗b)∗c

=a∗(b∗c)
∗ is not an associative binary operation.
iii)On Q,define a∗b=
2
ab

Check commutative
∗ is commutative is a∗b=b∗a
a∗b=
2
ab

b∗a=
2
ba

=
2
ab

a∗b=b∗a∀a,bϵQ
∗ is commutativve.
Check associative
∗ is associative if (a∗b)∗c=a∗(b∗c)
(a∗b)∗c=
2
(
2
ab

)∗c

=
4
abc

(a∗b)∗c=a∗(b∗c)=
2
a×
2
bc

=
4
abc

Since (a∗b)∗c=a∗(b∗c)∀a,b,cϵQ
∗ is an associative binary operation.
iv)On z
+
, define if a∗b=b∗a
a∗b=2
ab

b∗a=2
ba
=2
ab

Since a∗b=b∗a∀a,b,cϵz
+

∗ is commutative.
Check associative.
∗ is associative if $$
(a∗b)∗c=a∗(b∗c)
(a∗b)∗c=(2
ab
)
∗
c=2
2
ab

c
a∗(b∗c)=a∗(2
ab
)=2
a2
bc

Since (a∗b)∗c

=a∗(b∗c)
∗ is not an associative binary operation.
v)On z
+
define a∗b=a
b

a∗b=a
b
,b∗a=b
a

⇒a∗b

=b∗a
∗ is not commutative.
Check associative
∗ is associative if $$
(a∗b)∗c=a∗(b∗c)
(a∗b)∗c=(a
b
)
∗
c=(a
b
)
c

a∗(b∗c)=a∗(2
bc
)=2
a2
bc

eg:−Leta=2,b=3 and c=4
(a∗b)
∗
c=(2∗3)
∗
4=(2
3
)
∗
4=8∗4=8
4

a∗(b∗c)=2
∗
(3∗4)=2
∗
(3
4
)=2∗81=2
81

Since (a∗b)∗c

=a∗(b∗c)
∗ is not an associative binary operation.
vi)On R−{−1}, define a∗b=
b+1
a

Check commutative
∗ is commutative if a∗b=b∗a
a∗b=
b+1
a

b∗a=
a+1
b

Since a∗b

=b∗a
∗ is not commutatie.
Check associative
∗ is associative if (a∗b)∗c=a∗(b∗c)
(a∗b)∗c=(
b+1
a

)
∗
c=
c
b
a

+1

=
c(b+1)
a

a∗(b∗c)=a∗(
c+1
b

)=
c+1
b
a

=
b
a(c+1)

Since (a∗b)∗c

=a∗(b∗c)
∗ is not a associative binary operation

6 0

3 years ago

Let C(x) be the statement "x has a cat," let D(x) be the statement "x has a dog," and let F(x) be the statement "x has a ferret.

jek_recluse [69]

Answer:

$\mathbf{a)} \left( \exists x \in X\right) \; C(x) \; \wedge \; D(x) \; \wedge \; F(x)\\\mathbf{b)} \left( \forall x \in X\right) \; C(x) \; \vee \; D(x) \; \vee \; F(x)\\\mathbf{c)} \left( \exists x \in X\right) \; C(x) \; \wedge \; F(x) \; \wedge \left(\neg \; D(x) \right)\\\mathbf{d)} \left( \forall x \in X\right) \; \neg C(x) \; \vee \; \neg D(x) \; \vee \; \neg F(x)\\\mathbf{e)} \left((\exists x\in X)C(x) \right) \wedge \left((\exists x\in X) D(x) \right) \wedge \left((\exists x\in X) F(x) \right)$

Step-by-step explanation:

Let $X$ be a set of all students in your class. The set $X$ is the domain. Denote

$C(x) - ' \text{$x $ has a cat}'\\D(x) - ' \text{$x$ has a dog}'\\F(x) - ' \text{$x$ has a ferret}'$

$\mathbf{a)}$

Consider the statement 'A student in your class has a cat, a dog, and a ferret'. This means that $\exists x \in X$ so that all three statements C(x), D(x) and F(x) are true. We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as follows

$\left( \exists x \in X\right) \; C(x) \; \wedge \; D(x) \; \wedge \; F(x)$

$\mathbf{b)}$

Consider the statement 'All students in your class have a cat, a dog, or a ferret.' This means that $\forall x \in X$ at least one of the statements C(x), D(x) and F(x) is true. We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as follows

$\left( \forall x \in X\right) \; C(x) \; \vee \; D(x) \; \vee F(x)$

$\mathbf{c)}$

Consider the statement 'Some student in your class has a cat and a ferret, but not a dog.' This means that $\exists x \in X$ so that the statements C(x), F(x) are true and the negation of the statement D(x) . We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as follows

$\left( \exists x \in X\right) \; C(x) \; \wedge \; F(x) \; \wedge \left(\neg \; D(x) \right)$

$\mathbf{d)}$

Consider the statement 'No student in your class has a cat, a dog, and a ferret..' This means that $\forall x \in X$ none of the statements C(x), D(x) and F(x) are true. We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as a negation of the statement in the part a), as follows

$\neg \left( \left( \exists x \in X\right) \; C(x) \; \wedge \; D(x) \; \wedge \; F(x)\right) \iff \left( \forall x \in X\right) \; \neg C(x) \; \vee \; \neg D(x) \; \vee \; \neg F(x)$

$\mathbf{e)}$

Consider the statement ' For each of the three animals, cats, dogs, and ferrets, there is a student in your class who has this animal as a pet.'

This means that for each of the statements C, F and D there is an element from the domain $X$ so that each statement holds true.

We can express that in terms of C(x), D(x) and F(x) using quantifiers, and logical connectives as follows

$\left((\exists x\in X)C(x) \right) \wedge \left((\exists x\in X) D(x) \right) \wedge \left((\exists x\in X) F(x) \right)$

5 0

4 years ago

If the cube above has a surface area of 54cm^3, what is the volume of the cube?

Colt1911 [192]

9514 1404 393

Answer:

27 cm³

Step-by-step explanation:

The surface area of a cube is ...

SA = 6s²

Then the edge length is ...

54 cm² = 6s² . . . . . please note that cm³ is not the appropriate unit for area

9 cm² = s² . . . . . .divide by 6

3 cm = s . . . . . . . take the square root

The volume of a cube is ...

V = s³

V = (3 cm)³ = 27 cm³

The volume of the cube is 27 cm³.

3 0

3 years ago

A dslr camera increased in price from 900 to 1,200 what was the percent of increase

stiv31 [10]

Answer:

33.33%

Step-by-step explanation:

% increase : new value - old value/old value * 100%

1200 - 900/900 * 100% (to make it easier, cut the zeros the best

you can)

300/ 9

= 33.33 or 33 1/3%

5 0

3 years ago

Question 4 of 25

Yuki888 [10]

Answer:

Las Vegas

Step-by-step explanation:

4 0

3 years ago