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grandymaker [24]
3 years ago
8

Plz help math #5 questions

Mathematics
1 answer:
vekshin13 years ago
5 0
Okay , wheres the questions at tho...?


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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
You need $3,000 to buy a new stereo for your car. If you have $1,200 to invest at
DiKsa [7]

Answer:

15 years and 8 months

Step-by-step explanation:

I used the formula for compound interest as shown below and solved for the unknown, time.

Since our interest is compounded annually (So once a year) our m value is 1.

3 0
2 years ago
X+2y=-2 3x+4y=6 ????
Korvikt [17]

Answer:

X+2y=-23x+4y=6

=(x,y)= (6/25, 72/25)

6 0
3 years ago
Read 2 more answers
What is the equation for a line passing through (-2,3) and perpendicular to y= -1/2+1 ?
nata0808 [166]

Answer:

y=2x+7

Step-by-step explanation:

<u><em>The correct question is</em></u>

what is the equation for a line passing through (-2,3) and perpendicular to y= -1/2<em>x</em>+1 ?

Remember

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes are equal to -1)

The slope of the given line is m=-1/2

so

the opposite reciprocal is m=2

<em>Find the equation of the line in point slope form</em>

y-y1=m(x-x1)

we have

m=2\\point\ (-2,3)

substitute

y-3=2(x+2)

<em>Convert to slope intercept form</em>

y=mx+b

isolate the variable y

y-3=2x+4

y=2x+4+3

y=2x+7

3 0
3 years ago
The vertex of the parabola below is at the point (1, 5), and the point (2, 8) is on the parabola. What is the equation of the pa
N76 [4]

Answer: B

Step-by-step explanation:

the parabola having (1,5) as vertex have as equation:

y=k*(x-1)²+5

It is passing through (2,8)

8=k*(2-1)²+5 ==> k+5=8 ==> k=3

equation is  y=3(x-1)²+5

Answer B

6 0
2 years ago
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