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slamgirl [31]
2 years ago
14

10 gallons of gasoline costs $130. The cost of gasoline per gallon is

Mathematics
1 answer:
antoniya [11.8K]2 years ago
3 0
13 dollars per gallon

130\10 = 13
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the answer to your question is
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3 years ago
A sample of radium has a weight of 100 mg and a half-life of
Anestetic [448]

Answer:

1a ) N_6 = 50 mg

1b) N_3 = 70.7 mg

1c) N_1 = 89.1 mg

2) f(t) = 100e^(-0.1155t)

Step-by-step explanation:

Formula to get amount remaining is;

N_t = N_o × ½^(t/t_½)

We are given;

N_o = 100 mg

t_½ = 6 years

We have; N_t = 100(½^(t/6))

Thus;

1a) amount left after 6 years is;

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N_6 = 50 mg

1b) amount left after 3 years is;

N_3 = 100 × ½^(3/6)

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1c) amount left after 1 year is;

N_1 = 100 × ½^(1/6)

N_1 = 89.1 mg

2) to find the function to model the amount left after t years, let's use the formula;

f(t) = f_o × e^(-rt)

Where r is decay constant

Thus;

f(t) = 100e^(-rt)

We recall that N_t = 100(½^(t/6))

Thus;

100(½^(t/6)) = 100e^(-rt)

Divide both sides by 100 to get;

(½^(t/6)) = e^(-rt)

In (½^(t/6)) = In e^(-rt)

Using power rule, we have;

(t/6) In ½ = -rt In e

-0.6931t/6 = - rt (because In e = 1)

t will cancel out to give;

r = 0.6931/6

r = 0.1155

Thus;

f(t) = 100e^(-0.1155t)

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Answer:

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To convert to vertex form:

y = 3x² – 12x + 11

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y = 3(x² – 4x + 4) + 11 – 12

y = 3(x – 2)² + 11 – 12

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Answer:

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Step-by-step explanation:

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