Brainiest to whoever right

Simplify the expression. Write your answer using only positive exponents. Evaluate any numerical powers.

gtnhenbr [62]

Answer:

9x⁵

Step-by-step explanation:

Use properties of exponents:

$a^{b} a^{c} = a^{b+c}$ , $(a^{b} ^)^{c} = a^{bc}$ , $1/a^{-b} = a^{b}$

Simplify the given expression:

3⁴⋅x⋅(3/x²)⁻² =
3⁴·x·(3x⁻²)⁻² =
3⁴·x·(3⁻²)(x⁻²ˣ⁻²) =
3⁴⁻²·x¹⁺4 =
3²·x⁵ =
9x⁵

5 0

2 years ago

Every economic decision has only positive benefits. gained opportunities. unavoidable limitations. a consequence or tradeoff.

Alina [70]

Every economic decision has "a consequence or tradeoff" - this final answer choice is correct. Every time that an individual, business, or institution makes an economic decision, they always forgo an opportunity to use the same capital or resources for other endeavors. As such, there is a tradeoff incurred by not making the decision to use the resource in another manner. This is known as opportunity cost and is one of the fundamental tenets of economic theory.

3 0

3 years ago

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your school is setting up a row of 5 tables for a craft fair. each table is 72 inches long. the space between each pair of neigh

juin [17]

The total space needed is 600 feet. Because 5 tables times 72 feet is 360 and 5 tables times 48 feet a part is 249. You add them and it comes out to be 600. It should be worked out like this 5(72+48)

6 0

3 years ago

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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

While at the pumpkin farm, you also bought a taffy apple for $2.10, a pound of apples for $4.45 and a mum plant for $10.30. You

lbvjy [14]

Answer: B. $3.15

Step-by-step explanation: Hi! So first things you want to add all the things he bought together and then subtract it from the $20. I’m sorry if this isn’t right.

5 0

3 years ago

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