Which is the graph of g(x) = 2x – 1 + 3?

The statue's height is 152 feet. To answer this question: The total height of the Statue of Liberty alongside its pedestal is 305 feet, which is 153 feet more than the statue’s height. You can derive the height h of the statue using the formula.

Sari's claim is incorrect because dividing 120.78 by 9.9 equals approximately 12.2, and since 12 is less than 12.2, her estimate is not actually greater than the true result.

Answer:

The highest achievable volume for the box is 2000000 cubic meters.

Step-by-step explanation:

Below is an outline of the volume (), measured in cubic centimeters, and surface area (), measured in square centimeters, for a box featuring a square base:

(1)

(2)

Where:

- The length of the base's side, in centimeters.

- The height of the box, in centimeters.

Using (2), we isolate in the formula:

Then, we substitute into (1) and simplify the outcome:

(3)

Next, we calculate the first and second derivatives of this expression:

(4)

(5)

If and , then we find that the critical value for the base's side length is:

Subsequently, we assess this outcome using the second derivative's expression:

According to Second Derivative Test, this critical value signifies an absolute maximum. Consequently, the largest volume obtainable for the box is:

The highest achievable volume for the box is 2000000 cubic meters.

An even function can be reflected over the y-axis and still remain unchanged.
Example: y=x^2
On the other hand, an odd function can be reflected around the origin and also remains unchanged.
Example: y=x^3


A straightforward method to determine this is:

if f(x) is even, then f(-x)=f(x)
if f(x) is odd, then f(-x)=-f(x)


Hence, for an even function
substitute -x in for each and check for equivalence
make sure to fully expand the expressions
g(x)=(x-1)^2+1=x^2-2x+1+1=x^2-2x+2 is the original expression
g(x)=(x-1)^2+1
g(-x)=(-x-1)^2+1
g(-x)=(1)(x+1)^2+1
g(-x)=x^2+2x+1+1
g(-x)=x^2+2x+2
Not the same, as the original contains -2x
Therefore, it is not even
g(x)=2x^2+1
g(-x)=2(-x)^2+1
g(-x)=2x^2+1
It matches, hence it is even
g(x)=4x+2
g(-x)=4(-x)+2
g(-x)=-4x+2
Not equivalent, thus not even
g(x)=2x
g(-x)=2(-x)
g(-x)=-2x
Not equal, therefore not even



g(x)=2x²+1 is the confirmed even function.

Answer:

  (1/10)∛100 ≈ 0.4642

Step-by-step explanation:

For a cubic shape with volume V, the edge length is defined as...

  s = ∛V

and the surface area is given by...

  A = 6s² = 6V^(2/3)

The area-to-volume ratio is therefore...

  r1 = A/V = 6V^(2/3)/V = 6V^(-1/3)

When the volume V is increased by a factor of 10, the new area-to-volume ratio becomes...

  r2 = 6(10V)^(-1/3)

Consequently, the change factor for the ratio is...

  r2/r1 = (6(10V)^(-1/3))/(6V^(-1/3)) = 10^(-1/3) = (1/10)∛100

The change in surface area per unit volume results in a factor of (∛100)/10.

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Example

For a cube with side length 2, the corresponding volume equals 2³ = 8, with a surface area of 6·2² = 24. The resulting area-to-volume ratio is 24/8 = 3.

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The area-to-volume ratio changed by a factor of (0.3∛100)/3 = (∛100)/10, as previously noted.

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