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lapo4ka [179]
3 years ago
14

Simplify (3x^2 y)^-3

Mathematics
2 answers:
madreJ [45]3 years ago
6 0

we are given

(3x^2 y)^{-3}

firstly , we can make exponent positive

\frac{1}{(3x^2y)^3}

now, we can distribute exponent

\frac{1}{(3x^2)^3(y)^3}

\frac{1}{(3)^3(x^2)^3(y)^3}

we can combine exponents

and we get

\frac{1}{27x^6y^3}...........Answer

nordsb [41]3 years ago
3 0

(3x^{2}y)^{-3}  =\frac{1}{(3x^{2}y)^{3}} = \frac{1}{27x^{6}y^{3}}

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If a monopolist supplies goods at a price; P = 170 - Q, with marginal cost; MC = 52. Find the quantity and price
Arada [10]

Answer:

Quantity = 59 units

Price = $111

Step-by-step explanation:

The Demand function is given by

P = 170 - Q

The Marginal cost is given by

MC = 52

We are asked to find the quantity and price of goods.

Firstly, obtain the Marginal revenue function from the demand function

The Total revenue is given by

TR = P \times Q \\\\TR = (170 - Q) \times Q \\\\TR = 170Q - Q^2

The Marginal revenue is the derivative of the Total revenue,

MR = \frac{d}{dQ} (TR) = 170Q - Q^2 \\\\MR = \frac{d}{dQ} (TR) = 170 - 2Q \\\\

Assuming that the monopolist maximizes profits,

MR = MC \\\\170 - 2Q = 52\\\\2Q = 170 - 52\\\\2Q = 118\\\\Q = 118/2\\\\Q = 59

Therefore, the quantity is 59 units.

The price of each good is

P = 170 - Q \\\\P = 170 - 59 \\\\P = 111

Therefore, the price is $111.

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4 years ago
What is 32.043 in expanded form?
SashulF [63]
30 + 2 + 0.04 + 0.003
7 0
3 years ago
PLZ HELP
belka [17]

Answer:

425261625

Step-by-step explanation:

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4 0
3 years ago
Which statement is true regarding the sides of a triangle
yulyashka [42]
The statement that is true regarding the sides of a triangle is the last one because the top and bottom have to be identical to each other and the sides have to be identical to each other.
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3 years ago
What is the longest line segment that can be drawn in a right rectangular prism that is 15 cm​ long, 11 cm​ wide, and 10 cm​ tal
sammy [17]

Answer:

  √446 ≈ 21.12 cm

Step-by-step explanation:

The longest dimension of a rectangular prism is the length of the space diagonal from one corner to the opposite corner through the center of the prism. The Pythagorean theorm tells you the square of its length is the sum of the squares of the dimensions of the prism:

  d² = (15 cm)² +(11 cm)² +(10 cm)² = (225 +121 +100) cm² = 446 cm²

  d = √446 cm ≈ 21.12 cm

The longest line segment that can be drawn in a right rectangular prism is about 21.12 cm.

_____

<em>Additional comment</em>

The square of the face diagonal is the sum of the squares of the dimensions of that face. The square of the space diagonal will be the sum of that square and the square of the remaining prism dimenaion, hence the sum of squares of all three prism dimensions.

8 0
3 years ago
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