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2 years ago

Use algebra tiles to find the difference. Let one yellow tile equal +1 and one red tile equal –1. 8 – (–6)

Mathematics

2 answers:

valentina_108 [34]2 years ago

8 0

There is 10 white tiles, and shade 9 of them.

One of the tiles are NOT shaded.

SO, your answer will be.

Sauron [17]2 years ago

4 0

We draw 10 white tiles.

Then we shade in 9 of them.

We count the remaining tiles to get the answer, which is 1.

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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:

Step 1:-

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)

Step( ii):

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)

Step (iii):-

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

y = 1

substitute y =1 in x = 9y

x = 9

substitute y =1 in 4z =9y

z = 9 /4

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

Conclusion:-

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

Solve the inequality x+2 1/2 >-1/2.graph the solution set on a number line. Show your work.

Ainat [17]

Answer:

x > -11

Step-by-step explanation:

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4 0

2 years ago

A set of cards includes 20 yellow cards, 16 green cards, and 24 blue cards. What is the probability that a blue card is chosen a

baherus [9]

Answer:

Blue cards

Step-by-step explanation:

Because that is the highest amount so it is most likely youll get that one.

7 0

3 years ago

Help me please !! Tell me the algebraic expression to 1 please !!!

Anuta_ua [19.1K]

You need to distribute the 4 to both the n and the positive 5 so you’re answer would be 4n + 20.

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3 years ago

Which expression is not equivalent to

Romashka [77]

Answer:

B: 2x + 2 + x

Step-by-step explanation:

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2 years ago

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