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kirill115 [55]
3 years ago
14

X+2y=3 x-y=3 x=? y=?

Mathematics
1 answer:
alexgriva [62]3 years ago
7 0

Answer:

x = 3

y = 0

Step-by-step explanation:

x + 2y = 3 ---------eqn 1

x - y = 3 --------eqn 2

Using eqn 2 to find the value of y

x - y = 3

Making y the subject of the formula

x - 3 = y

y = x - 3

Substitute the value of y into eqn 1

x + 2y = 3

x + 2(x - 3) = 3

Open the bracket

x + 2x - 6 = 3

3x - 6 = 3

3x = 3 +6

3x = 9

Divide both sides by 3, to get value of x

3x/3 = 9/3

x = 3

To get the value of y, use eqn 2

x - y = 3

3 - y = 3

3 - 3 = y

y = 0

Hint, to know maybe the values are correct, insert the values into the equation

Let's use eqn 2

x - y = 3

x = 3

y = 0

Insert into the equation

x - y = 3

3 - 0 = 3

Our values are correct

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The question is incomplete. Here is the complete question.

Uninhibited growth can be modeled by exponential functions other than A(t)=A_{0}e^{kt}. for example, if an initial population P₀ requires n units of time to triple, then the function P(t)=P_{0}(3)^{\frac{t}{n} } models the size of the population at time t. An insect population grows exponentially. Complete the parts a through d below.

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a) n is time necessary to triple the population of insects, i.e., n = 30 and P₀ = 50. So, Exponential equation for growth is

P(t)=50(3)^{\frac{t}{30} }

b) In t = 47 days:

P(t)=50(3)^{\frac{t}{30} }

P(47)=50(3)^{\frac{47}{30} }

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P(47) = 280

In 47 days, population of insects will be 280

c) P(t) = 750

750=50(3)^{\frac{t}{30} }

\frac{750}{50}=(3)^{\frac{t}{30} }

(3)^{\frac{t}{n} }=15

Using the property <u>Power</u> <u>Rule</u> of logarithm:

log(3)^{\frac{t}{30} }=log15

\frac{t}{30}log(3)=log15

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t = 74

To reach a population of 750 insects, it will take 74 days

d) To express the population growth into the described form, determine the constant k, using the following:

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3=e^{30k}

Use Power Rule again:

ln3=ln(e^{30k})

ln3=30k

k=\frac{ln3}{30}

k = 0.037

Equation for exponential growth will be:

A(t)=50e^{0.037t}

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