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Tamiku [17]
2 years ago
9

A piece of wire 13 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria

ngle. (a) How much wire should be used for the square in order to maximize the total area? (b) How much wire should be used for the square in order to minimize the total area?
Mathematics
1 answer:
Rom4ik [11]2 years ago
5 0

The function you seek to minimize is

()=3‾√4(3)2+(13−4)2

f

(

x

)

=

3

4

(

x

3

)

2

+

(

13

−

x

4

)

2

Then

′()=3‾√18−13−8=(3‾√18+18)−138

f

′

(

x

)

=

3

x

18

−

13

−

x

8

=

(

3

18

+

1

8

)

x

−

13

8

Note that ″()>0

f

″

(

x

)

>

0

so that the critical point at ′()=0

f

′

(

x

)

=

0

will be a minimum. The critical point is at

=1179+43‾√≈7.345m

x

=

117

9

+

4

3

≈

7.345

m

So that the amount used for the square will be 13−

13

−

x

, or

13−=524+33‾√≈5.655m

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In a triangle the first angle is 10 degrees more than the second angle. The third angle is equal to the sum of first 2 angles .
timurjin [86]
First angle= x+10
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Third angle = x+x+10 or 2x+10

X+10+x+2x +10=180
4x+20=180
Subtract 20 from both sides
4x=160
Divide both sides by 4
X=40
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Step-by-step explanation:

x^2 + 17x + 60

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8 0
2 years ago
Help ill give brainliest 9 − 3z + 4 + 6z − 2 = ______
Lyrx [107]

Answer:

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3 0
2 years ago
Read 2 more answers
John has decided to prepare an old field for his son's new horse. the length of the field is 10 meters less than 4 times its wid
tatuchka [14]

Answer: The total money invested in the field will be $1,623.80

Step-by-step explanation:

step 1

Find the dimensions of the field

Let

x -----> the length of the field

y -----> the width of the field

p=2(x+y)

p(4.80)=1,584

p=330m

we know that

The perimeter of the field is equal to

so

330=2(x+y)----> equation A

x=4y-10 ------> equation B

substitute equation B in equation A and solve for y

330=2(4y-10+y)

165=(5y-10)

5y=165+10

y+35

Find the value of x

x=4(35)-10+130

therefore

The length of the field is 130 meters and the width of the field is 35 meters

step 2

Find the area of the field

The area of the field is

A=xy

substitute

A=(130)(35)=4,550m2

step 3

Find the number of bags of seed

Divide the area by 460

4,550/460=9.89 bags

Round up to the nearest whole number

9.89 bags=10 bags

step 4

Find the cost of the seed

(10 )(3.98)=$19.8

step 5

Find the total money invested in the field

1,584+$39.8=$1,623.80

7 0
2 years ago
Read 2 more answers
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