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fomenos
3 years ago
5

Choose the best answer.

Mathematics
2 answers:
tekilochka [14]3 years ago
8 0
I believe its D, 7.5% But check it with other sources because IM not 100% positive! 
aliya0001 [1]3 years ago
4 0
The answer is b. 6.5% hope this helps!
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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
On a number line what is the distance between -3/2 and 6?
sesenic [268]

Answer:

  • 7.5 units

Step-by-step explanation:

The distance is always positive and is same as the absolute value of subtraction of the two numbers on the line.

<u>This can be shown as:</u>

  • |-3/2 - 6| =
  • |-1.5 - 6| =
  • |-7.5| =
  • 7.5

or

  • | 6 - (-3/2)| =
  • |6 + 1.5| =
  • |7.5| =
  • 7.5
6 0
3 years ago
Read 2 more answers
What is 9999 times 886 + 234
barxatty [35]

9999*886+234

(9999*886)+234

= 8859114+234

+ 8859348


I hope that's help !

7 0
3 years ago
Read 2 more answers
What is the median for the set of data shown below?
JulsSmile [24]
42. This is because you cross out the numbers left from right until theres a number inbetween.
8 0
3 years ago
Read 2 more answers
How long qouod it take a person traveling 10 miles per hour to trsvel 80 miles?
Bas_tet [7]

Answer:

if youre traveling 10 miles per hour then 8 hours would multiply 8 · 10 = 80 thus telling us that it would take us 8 hours to travel 80 miles. its basic math tbh...

Step-by-step explanation:


8 0
3 years ago
Read 2 more answers
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