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3 years ago

Express 3^2 = x as a logarithmic equation.

1 answer:

8 0

Taking the log of both sides of the equation, you have
$2\log(3)=\log(x)$
Dividing by log(3), this looks like the change of base formula.
$\log_a(b)=\dfrac{\log(b)}{\log(a)}$

That is, division by log(3) gives
$2=\dfrac{\log(x)}{\log(3)}\\\\2=log_3(x)$

This apparently matches your first choice:
log3(x) = 2

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What is 1.5533 rounded to the nearest cent

marta [7]

Centi = Hundreds.
1.5533.
Round up by seeing if the number to the right of the hundreds place is 5 or higher. If it's not, don't change anything.
1.55 is your answer.

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3 years ago

Ocean currents influence all of the following except

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Radiation from the sun. That depends on the sun.

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2 years ago

g 1) The rate of growth of a certain type of plant is described by a logistic differential equation. Botanists have estimated th

alexira [117]

Answer:

a) The expression for the height, 'H', of the plant after 't' day is;

$H = \dfrac{30}{1 + 5\cdot e^{-(2.02732554 \times 10^{-3}) \cdot t}}$

b) The height of the plant after 30 days is approximately 19.426 inches

Step-by-step explanation:

The given maximum theoretical height of the plant = 30 in.

The height of the plant at the beginning of the experiment = 5 in.

a) The logistic differential equation can be written as follows;

$\dfrac{dH}{dt} = K \cdot H \cdot \left( M - {P} \right)$

Using the solution for the logistic differential equation, we get;

$H = \dfrac{M}{1 + A\cdot e^{-(M\cdot k) \cdot t}}$

Where;

A = The condition of height at the beginning of the experiment

M = The maximum height = 30 in.

Therefore, we get;

$5 = \dfrac{30}{1 + A\cdot e^{-(30\cdot k) \cdot 0}}$

$1 + A = \dfrac{30}{5} = 6$

A = 5

When t = 20, H = 12

We get;

$12 = \dfrac{30}{1 + 5\cdot e^{-(30\cdot k) \cdot 20}}$

$1 + 5\cdot e^{-(30\cdot k) \cdot 20} = \dfrac{30}{12} = 2.5$

$5\cdot e^{-(30\cdot k) \cdot 20} = 2.5 - 1 = 1.5$

∴ -(30·k)·20 = ㏑(1.5)

k = ㏑(1.5)/(30 × 20) ≈ 6·7577518 × 10⁻⁴

k ≈ 6·7577518 × 10⁻⁴

Therefore, the expression for the height, 'H', of the plant after 't' day is given as follows

$H = \dfrac{30}{1 + 5\cdot e^{-(30\times 6.7577518 \times 10^{-4}) \cdot t}} = \dfrac{30}{1 + 5\cdot e^{-(2.02732554 \times 10^{-3}) \cdot t}}$

b) The height of the plant after 30 days is given as follows

$H = \dfrac{30}{1 + 5\cdot e^{-(2.02732554 \times 10^{-3}) \cdot t}}$

At t = 30, we have;

$H = \dfrac{30}{1 + 5\cdot e^{-(2.02732554 \times 10^{-3}) \times 30}} \approx 19.4258866473$

The height of the plant after 30 days, H ≈ 19.426 in.

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3 years ago

Blake has to put up a fence around a pet pen which s rectangular. If the width is 23 feet and the perimeter is 114 feet. What is

ziro4ka [17]

P = 2(L + W)
P = 114
W = 23

114 = 2(L + 23)
114 = 2L + 46
114 - 46 = 2L
68 = 2L
68/2 = L
34 = L <=== so the length is 34 ft

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3 years ago

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