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Alex787 [66]
3 years ago
9

Pela has 5 3/4 feet of string to make necklaces. She wants to make 4 necklaces that are the same length. How long should each ne

cklace be?
Mathematics
2 answers:
sergey [27]3 years ago
6 0

Answer: 1.4375

Step-by-step explanation:

Pela has 5 3/4 feet of string to make necklaces. We would convert 5 3/4 feet to improper fraction. It becomes 23/4 feet. So Pela has 23/4 feet of string to make necklaces.

She wants to make 4 necklaces that are the same length. To determine how long should each necklace be,

We would divide the total length of the string by the number of necklaces to be made. It becomes

23/4 ÷ 4 = 23/4 × 1/4 = 23/16

The length of each string is 23/16 or 1.4375 feet

antiseptic1488 [7]3 years ago
4 0
5.75/4 = 1.4375 feet a necklace
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Answer:

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Step-by-step explanation:

<u>Step 1</u>:-

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<u>Step( ii):</u>

By using  Lagrange multipliers

Suppose it is required to find the extreme for the function f(x, y, z) subject to the condition Ф (x, y, z) =0

Form Lagrange function F(x, y, z) = f(x, y, z) + λ  Ф (x, y, z) where λ is called the Lagrange multipliers

F(x, y, z) = x y z+ λ ( x + 9y + 4z - 27) ......(2)

Obtain the equations are δ F / δ x = 0

                                  δ f / δ x +λ  δ Ф  / δ x =0

                           ⇒ y z + λ ( 1) = 0

                          ⇒ y z = - λ ......(a)

Obtain the equations are δ F / δ y = 0

                            δ f / δ x +λ  δ Ф  / δ x =0

                        ⇒ x z + λ ( 9) = 0

                        ⇒ \frac{xz}{9} = - λ .......(b)

Obtain the equations are δ F / δ z = 0

                                  δ f / δ x +λ  δ Ф  / δ z =0

                                   x y + λ ( 4) = 0

                                    ⇒ \frac{xy}{4} = - λ .......(c)

<u>Step (iii):-</u>

Equating (a) and (b) equations

we get         y z = \frac{xz}{9}

cancel 'z' value we get  x = 9y  .......(d)

Equating (b) and (c) equations

we get     \frac{xy}{4}  = \frac{xz}{9}

cancel 'x' value on both sides , we get

              4z =9y  ......(e)

substitute (d) (e) values in equation (1)  we get

x + 9y + 4z -27 = 0

9y + 9y + 9y -27 =0

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substitute y =1 in x = 9y

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The largest volume of the rectangular box V = x y z

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