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Rom4ik [11]
3 years ago
7

9.

Mathematics
1 answer:
Svet_ta [14]3 years ago
3 0

Answer:

√234

Step-by-step explanation:

Drawing it out will help you

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7 / 336 in long divi​
Alexus [3.1K]

Answer: 48 r0

Step-by-step explanation:  JUST IMAGINE THE LINES

  7 ÷3 3 6

− 0    

 3 3  

− 2 8  

   5 6

 − 5 6

     0

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3 years ago
What is the constant of variation, k,
ValentinkaMS [17]
The K-constant variation is the factor of the increase-decrease relationship between the x-variable and y-variable which can be stated as y=k*x or x=y/k<span>. For example, if y variable equal 5 and the x variable equal 2 then the k-constant variation equal 2 (calculation y=k*x --> 5=2*2.5). This constant shows the relationship between the variables.</span>
6 0
3 years ago
Read 2 more answers
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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The train travels at a constant speed. What is its speed? please hurry
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Answer:

300 km in hour are the answers

4 0
3 years ago
Lucia has 3.5 hours left in her workday as a car mechanic. Lucia needs 1/2 of an hour to complete one oil change.
MatroZZZ [7]

Answer: So Lucía has 3.5 hours left, and need 1/2 of an hour (or 0.5 hours) to do one oil change.

a) If you divide the total time she has by the time she needs for each oil change, then you got the total number of oil changes that she can do in that time; this is:

3.5/0.5 = 7

So she can do 7 oil changes in 3.5 hours.

b) If she can complete two car inspections in the same amount of time it takes her to complete one oil change, then she can do two car inspections in 0.5 hours.

2*car inspections = 0.5 hours

car inspection = (0.5/2) hours

then one car inspection will take 0.5/2 = 0.25 hours.

c) Two ways to solve this:

1) Do the same that we did in a), this is: 3.5/0.25 = 14

she can do 14 car inspections.

2) If in 3.5 hours, she can do 7 oil changes, and in the time she does an oil change, she can do two car inspections, then in 3.5 hours she can do 7*2 car inspections, and 7*2 = 14

5 0
3 years ago
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