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AlekseyPX
2 years ago
13

Please help me with this, no false answers.. Thank you!​

Mathematics
2 answers:
Reptile [31]2 years ago
7 0
  • x=30

The relationship given

\\ \sf\longmapsto y\propto x^2

\\ \sf\longmapsto y=kx^2

Now

  • When y is 2 x is 4(2^2=2)
  • y_1=2
  • x_1=4
  • x_2=30
  • y_2=?

Putting direct variation rule

\\ \sf\longmapsto x_1y_2=x_2y_1

\\ \sf\longmapsto 4y_2=30(2)

\\ \sf\longmapsto 4y_2=60

\\ \sf\longmapsto y_2=15

Lana71 [14]2 years ago
4 0

The variation equation when y varies directly as the square of x is y = kx².

The value of y when x = 30 is 900k.

<h3 /><h3>Definition and types of variation:</h3>

Variation establish relationship between variable. Types of variation includes

  • Direct variation
  • Inverse variation
  • Joint variation
  • Combined variation

y varies directly as the square of x , Therefore,

  • y α x²
  • y = kx²

where

k = constant of proportionality

Solve for y when x = 30.

Therefore,

y = kx²

y = 30²k

y = 900k

learn more on variation here:brainly.com/question/13977805?referrer=searchResults

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Answer:

The half-life of the radioactive substance is of 3.25 days.

Step-by-step explanation:

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The solution is:

Q(t) = Q(0)e^{-kt}

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e^{-13k} = \frac{500}{8000}

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k = -\frac{\ln{\frac{500}{8000}}}{13}

k = 0.2133

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Q(t) = Q(0)e^{-0.2133t}

Determine the half-life of the radioactive substance.

This is t for which Q(t) = 0.5Q(0). So

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0.5Q(0) = Q(0)e^{-0.2133t}

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t = -\frac{\ln{0.5}}{0.2133}

t = 3.25

The half-life of the radioactive substance is of 3.25 days.

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