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ollegr [7]
3 years ago
11

What is the least common denominator (LCD)

Mathematics
1 answer:
Romashka [77]3 years ago
3 0

The least common denominator is 15. The equivalent fractions would be 10/15 and 12/15.

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17+(-4)-4/5j-2/5j+6​
Snowcat [4.5K]

Answer:

19 - (6/5)j

Step-by-step explanation:

In this expression we have addition, subtraction and multiplication.

According to order of operations rules, mult. and div. must be carried out before add. or subt.

Therefore, we begin with 17+(-4), which becomes 17 - 4, or 13.

Next we see -4/5j, by which I assume you mean -4/5 * j.

Summarizing what we have so far:

13  - (4/5)j - 2/5j + 6

Combining the j terms, we get

13 - (6/5)j + 6, which collapses to 19 - (6/5)j.

7 0
3 years ago
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

     

3 0
3 years ago
P(Girl Sophomore) :<br> =[?]
marusya05 [52]

Probability helps us to know the chances of an event occurring. The probability being a Sophomore given she is a girl is 1/3.

<h3>What is Probability?</h3>

Probability helps us to know the chances of an event occurring.

\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}

The probability of being a girl and Sophomore is 9/37. While the probability of being a girl is 27/37. Therefore, the probability being a Sophomore given she is a girl is,

P(Girl l Sophomores) = P(Girl and Sophomore)/ P(Girl)

                                  = (9/37) / (27/37)

                                  = 9 / 27

                                  = 1/3

Hence, the probability being a Sophomore given she is a girl is 1/3.

Learn more about Probability:

brainly.com/question/795909

#SPJ1

3 0
1 year ago
Read 2 more answers
Raj has 40% of his weekly paycheck automatically dispositive into his savings account this week $160 is dispositive into the acc
ella [17]

Answer:

  Raj can look on his pay stub to find the total is $400

Step-by-step explanation:

The relation between the deposit and the total pay is ...

  deposit = 0.40 × total pay

  total pay = deposit / 0.40 = 160/0.40 = 400

Raj was paid $400 this week.

7 0
3 years ago
Lines a and b are parallel. What is the measure of ∠3 if ∠6 measures 84°?
Ray Of Light [21]

Answer:

it also measures 84° because 3is alternate angle to 6

4 0
3 years ago
Read 2 more answers
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