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ratelena [41]
3 years ago
8

Im confused is 3a the same as 5a squared or 4b to 4b squared​

Mathematics
1 answer:
NeX [460]3 years ago
6 0

Step-by-step explanation:

In order to be like terms, the variables and exponents must be the same.

3a can be combined with 14a and 4a.

4b can be combined with 3b and 16b.

a² cannot be combined with any of the terms.

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Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinat
tensa zangetsu [6.8K]

Answer:

The volume of the largest rectangular box (V) = 81/4

Step-by-step explanation:

<u>Step 1</u>:-

Given volume of the largest rectangular box in the first octant

V = l b h

let (x ,y, z) be the one vertex in the given plane

V = f(x, y, z) = x y z

given plane.   Ф (x, y, z) = x + 9y + 4z = 27 ........(1)

<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

27y -27 =0

<u> y = 1</u>

substitute y =1 in x = 9y

<u>x = 9</u>

substitute y =1 in 4z =9y

<u>z = 9 /4</u>

therefore the dimensions are x =9 , y=1 and z = 9 /4

<u>Conclusion</u>:-

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

substitute x =9 , y=1 and z = 9 /4

V = 9(1)(9/4) =81/4

The largest volume of the rectangular box (V) = 81/4

Verification :-

Given plane x + 9y + 4z = 27

substitute x =9 , y=1 and z = 9 /4

              9 + 9 + 4(9/4) = 27

           27 =27

so satisfied equation

     

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Convert 4/6 into a fraction with a denominator of 24
deff fn [24]
The correct answer would be 16/24. You would need to multiply both the denominator and numerator by 4.
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Worldwide, the proportion of babies who are boys is about 0.51 . Let the random variable X represent the number of boys in five
solmaris [256]

Answer:

mean = 2.55

Standard deviation = 1.118

Step-by-step explanation:

Probability of babies who are boys

P = 0.51

Then we have q = 1-p

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= 0.49

We have n = 5

We calculate the mean as:

np

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Therefore mean = 2.55

The standard deviation

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Answer:

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Step-by-step explanation:

-60, -120, -154

because

from 6 to get to 36, it is multiplied by itself.

from 36 to get to 2, it is subtracted by 34.

the pattern continues.

Can I get brainliest please? Thanks! Hope this helps!

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3 years ago
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Which Greek mathematician is known as the father of geometry
erastova [34]

Answer:

Euclid was a great mathematician and often called the father of geometry.

Step-by-step explanation:

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