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goldenfox [79]
3 years ago
15

ABCD is a trapezium with AB parallel to DC.

Mathematics
1 answer:
Julli [10]3 years ago
4 0

Answer:

Step-by-step explanation:a or b ?

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Set up, but do not evaluate, the integral that represents the length of the curve given by x = 1 + 3t^2, y = 4 + 2t^3 over the i
kherson [118]

L

=

∫

t

f

t

i

√

(

d

x

d

t

)

2

+

(

d

y

d

t

)

2

d

t

. Since  

x

and  

y

are perpendicular, it's not difficult to see why this computes the arclength.

It isn't very different from the arclength of a regular function:  

L

=

∫

b

a

√

1

+

(

d

y

d

x

)

2

d

x

. If you need the derivation of the parametric formula, please ask it as a separate question.

We find the 2 derivatives:

d

x

d

t

=

3

−

3

t

2

d

y

d

t

=

6

t

And we substitute these into the integral:

L

=

∫

√

3

0

√

(

3

−

3

t

2

)

2

+

(

6

t

)

2

d

t

And solve:

=

∫

√

3

0

√

9

−

18

t

2

+

9

t

4

+

36

t

2

d

t

=

∫

√

3

0

√

9

+

18

t

2

+

9

t

4

d

t

=

∫

√

3

0

√

(

3

+

3

t

2

)

2

d

t

=

∫

√

3

0

(

3

+

3

t

2

)

d

t

=

3

t

+

t

3

∣

∣

√

3

0

=

3

√

3

+

3

√

3

=6The arclength of a parametric curve can be found using the formula:  

L

=

∫

t

f

t

i

√

(

d

x

d

t

)

2

+

(

d

y

d

t

)

2

d

t

. Since  

x

and  

y

are perpendicular, it's not difficult to see why this computes the arclength.

It isn't very different from the arclength of a regular function:  

L

=

∫

b

a

√

1

+

(

d

y

d

x

)

2

d

x

. If you need the derivation of the parametric formula, please ask it as a separate question.

We find the 2 derivatives:

d

x

d

t

=

3

−

3

t

2

d

y

d

t

=

6

t

And we substitute these into the integral:

L

=

∫

√

3

0

√

(

3

−

3

t

2

)

2

+

(

6

t

)

2

d

t

And solve:

=

∫

√

3

0

√

9

−

18

t

2

+

9

t

4

+

36

t

2

d

t

=

∫

√

3

0

√

9

+

18

t

2

+

9

t

4

d

t

=

∫

√

3

0

√

(

3

+

3

t

2

)

2

d

t

=

∫

√

3

0

(

3

+

3

t

2

)

d

t

=

3

t

+

t

3

∣

∣

√

3

0

=

3

√

3

+

3

√

3

=

6

√

3

Be aware that arclength usually has a difficult function to integrate. Most integrable functions look like the above where a binomial is squared and adding the two terms will flip the sign of the binomial.    

Be aware that arclength usually has a difficult function to integrate. Most integrable functions look like the above where a binomial is squared and adding the two terms will flip the sign of the binomial.

8 0
3 years ago
A probability experiment is conducted in which the sample space of the experiment is Sequals=StartSet 9 comma 10 comma 11 comma
White raven [17]

Answer:

From both approaches P(F or G)=0.667

Step-by-step explanation:

P(F or G)=?

F={9, 10, 11, 12, 13}​

G={13,14,15,16}

Finding P(F or G) by counting outcomes in F or G

F or G={9, 10, 11, 12, 13}or {13,14,15,16}

F or G={9, 10, 11, 12,13,14,15,16}

number of outcomes in F or G=n(F or G)=8

S={9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}​

number of outcomes in S=n(S)=12

P(F or G)=n(F or G)/n(S)

P(F or G)=8/12

P(F or G)=0.667

Finding P(F or G) by addition rule

P(F or G)=P(F)+P(G)-P(F and G)

F={9, 10, 11, 12, 13}​

number of outcomes in F=n(F)=5

P(F)=n(F)/n(S)

P(F)=5/12

P(F)=0.417

G={13,14,15,16}

number of outcomes in G=n(G)=4

P(G)=n(G)/n(S)

P(G)=4/12

P(G)=0.333

F and G={9, 10, 11, 12, 13}and {13,14,15,16}

F and G={13}

number of outcomes in F and G=n(F and G)=1

P(F and G)=n(F and G)/n(S)

P(F and G)=1/12

P(F and G)=0.083

P(F or G)=P(F)+P(G)-P(F and G)

P(F or G)=0.417+0.333-0.083

P(F or G)=0.667

8 0
3 years ago
Read 2 more answers
the length of a rectangle is 4 times its width. The rectangles perimeter is 68 feet what is the rectangles length and width ??
kodGreya [7K]

Answer:

Length = 27.2

Width = 6.8

Step-by-step explanation:

P = L+L+W+W

68 = 4(L+L)+W+W

68 = 4(x+x)+x+x

68 = 4x+4x+x+x

68 = 10x

x = 6.8

L = 4x

L = 27.2

W = x

W = 6.8

68 = 27.2+27.2+6.8+6.8

68 = 68

7 0
3 years ago
PLEASE! Is this correct?
Paladinen [302]
I believe it’s correct, but i’m not smart
6 0
3 years ago
Need help kinda quick
Fed [463]

Answer:

A;-6

B;-8

C;-2

D;-14

E;-1

F;2

G;5

H;0

4 0
2 years ago
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