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antoniya [11.8K]
2 years ago
12

2.75 metres of cloth are required to sew a trouser. how many metres of cloth are required to sew 4 such trousers ?

Mathematics
1 answer:
const2013 [10]2 years ago
5 0

Answer:

11 meters of cloth

Step-by-step explanation:

2.75 x 4 = 11 meters of cloth

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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

=

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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 cone-shaped tent has a diameter of 12 ft and a height of 6 ft.
HACTEHA [7]
Volume should be 226.08 
volume of a cone= 1/3 pi radius squared multiplied by height 
6x6=36 multiply by height 36x6=216  divide by 3=72 now multiply by pi =226.08 
your answer is 226.08
7 0
3 years ago
Read 2 more answers
Hannah can paint a room in 20 hours. Destiny can paint the same room in 16 hours. How long does it take for both Hannah and Dest
UNO [17]
Amount of room hannah can paint in an hour = 1/20
amount of room destiny can paint in an hour = 1/16
number of hours = x

1/20x + 1/16x = 1
the reason why this formula is true is, the amount of the room painted in the end should be 1 (the whole room)

4/80x + 5/80x = 1
9/80x = 1
9x = 80
x = 80/9 hours
x = 8.89 hours

8 0
3 years ago
The radius of a sphere is 12 units. Find the volume of the sphere. Write your answer in terms of pi.
stiv31 [10]

Answer:

V = 2304π units³

Step-by-step explanation:

The volume (V) of a sphere is calculated as

V = \frac{4}{3}πr³ ( where r is the radius ) , then

V = \frac{4}{3}π × 12³

   = \frac{4}{3} π × 1728

   = 4π × 576

   = 2304π units³

5 0
2 years ago
Solve for the variable x - 9 = 11
Strike441 [17]

Answer:

20

Step-by-step explanation:

x - 9 = 11

+9         +9

x = 20

3 0
2 years ago
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