During a reading test, Enrique reads a passage with 640 words. It takes him 4 minutes to

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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to achieve a minimum of 200 chocolate bars

c=chocolate bars

2.5c>or=500

Divide both sides by 2.5

c>or=200

Response:

The function is represented by the equation,

x = 3y.

Detailed explanation:

The direct variation function includes the points (-9, -3) and (-12, -4).

Here,

= 3

Thus, the function can be expressed as,

x = 3y.

Response:

0.14 s

Detailed breakdown:

s = -2.7 t² + 40t + 6.5

Set s = 12

12 = -2.7t² + 40t + 6.5     Rearranging yields

-2.7t² + 40t + 6.5 - 12 = 0

      -2.7t² + 40t - 5.5 = 0

Utilize the quadratic formula

a = -2.7; b = 40; c = -5.5

x = 7.41 ± 7.27

x₁ = 0.14; x₂ = 14.68

The graph indicates roots at x₁ = 0.134 and x₂ = 14.68.

The surface of the Moon stands at -12 ft. Thus, the ball will reach a height of 12 ft above the Moon’s surface (crossing the x-axis) at 0.14 s.

The second root indicates when the ball is again 12 ft above the lunar surface as it descends.