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True [87]
1 year ago
12

(for 50 points) Choose an expression that is equivalent to negative two raised to the fourth power divided by negative two raise

d to the second power .
negative two divided by negative two raised to the fifth power

negative two raised to the second power divided by negative two raised to the fourth power

negative two raised to the fifth power divided by negative two

negative two raised to the sixth power divided by negative two raised to the fourth power
Mathematics
1 answer:
svp [43]1 year ago
5 0

The mathematical expression that is equivalent to negative two raised to the fourth power divided by negative two raised to the second power is negative two raised to the sixth power divided by negative two raised to the fourth power; option D.

<h3>What is a mathematical expression?</h3>

A mathematical expression is an expression which uses mathematical symbols and mathematical operations to represent an idea.

Two mathematical expressions are equivalent if they have the same value

The expression that is equivalent to negative two raised to the fourth power divided by negative two raised to the second power can be written as (-2)⁴/(-2)² = 2²

An equivalent expression is negative two raised to the sixth power divided by negative two raised to the fourth power written as : (-2)⁶/(-2)⁴ = 2²

In conclusion, two mathematical expressions are equivalent if they have the same value when fully expressed.

Learn more about mathematical expression at: brainly.com/question/4344214

#SPJ1

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An open metal tank of square base has a volume of 123 m^3
snow_lady [41]

Answer:

  a) h = 123/x^2

  b) S = x^2 +492/x

  c) x ≈ 6.27

  d) S'' = 6; area is a minimum (Y)

  e) Amin ≈ 117.78 m²

Step-by-step explanation:

a) The volume is given by ...

  V = Bh

where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:

  123 = x^2·h

  h = 123/x^2

__

b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.

S=x^2+Ph=x^2+(4x)\dfrac{123}{x^2}\\\\S=x^2+\dfrac{492}{x}

__

c) The derivative of the area with respect to x is ...

S'=2x-\dfrac{492}{x^2}

When this is zero, area is at an extreme.

0=2x -\dfrac{492}{x^2}\\\\0=x^3-246\\\\x=\sqrt[3]{246}\approx 6.26583

__

d) The second derivative is ...

S''=2+\dfrac{2\cdot 492}{x^3}=2+\dfrac{2\cdot 492}{246}=6

This is positive, so the value of x found represents a minimum of the area function.

__

e) The minimum area is ...

S=x^2+\dfrac{2\cdot 246}{x}=(246^{\frac{1}{3}})^2+2\dfrac{246}{246^{\frac{1}{3}}}=3\cdot 246^{\frac{2}{3}}\approx 117.78

The minimum area of metal used is about 117.78 m².

3 0
3 years ago
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