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2 years ago

Help!!!

Mathematics

1 answer:

sesenic [268]2 years ago

6 0

Answer:

Time it will take t = 23.1 (round to the nearest tenth)

Step-by-step explanation:

Given: A population of bacteria is growing exponentially;

According to the model;

$P = 100e^{0.60t}$ ......[1]; where P is the number of colonies and t be the time measured in hours.

After how many hours will 400 colonies be present.

Substitute value of P = 400 in [1];

$400 = 100 e^{0.06t}$

Divide both sides by 100 we get;

$4 = e^{0.06t}$

Taking ln both sides we get;

$ln 4 = ln e^{0.06t}$

Since; $ln e^x = x$

then;

$ln 4 = 0.06 t$

Divide both sides by 0.06 we get;

$t = \frac{ln 4}{0.06}$

$t =\frac{1.38629436112}{0.06} =23.104906$ hours

Therefore, the time it will take is, t = 23.1 (round to the nearest tenth)

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<em>Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!</em>

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2 years ago

Gabrielle is 13 years older than Mikhail. the sum of their ages is 113. what is mikhails age?

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2 years ago

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Arrange the following numbers in increasing order: \begin{align*} A &= \frac{2^{1/2}}{4^{1/6}}\\ B &= \sqrt[12]{128}\vph

prisoha [69]

Answer:

The order is "D, B, A, E, C".

Step-by-step explanation:

The numbers are as follows:

$A=\frac{2^{1/2}}{4^{1/6}}\\\\B = \sqrt[12]{128}\\\\C=(\frac{1}{8^{1/5}})^{2}\\\\D = \sqrt{\frac{4^{-1}}{2^{-1}\cdot 8^{-1}}}\\\\E = \sqrt[3]{2^{1/2}}\cdot 4^{-1/4}$

Simplify the value of A, B, C, D and E as follows:

$A=\frac{2^{1/2}}{4^{1/6}}=\frac{2^{1/2}}{2^{2/6}}=\frac{2^{1/2}}{2^{1/3}}=2^{1/2-1/3}=2^{1/6}=1.1225\\\\B = \sqrt[12]{128}=(128)^{1/12}=(2^{7})^{1/12}=2^{7/12}=1.4983\\\\C=(\frac{1}{8^{1/5}})^{2}=(\frac{1}{(2^{3})^{1/5}})^{2}=(\frac{1}{2^{3/5}})^{2}=\frac{1}{2^{3/5\times2}}=\frac{1}{2^{6/5}}=2^{-6/5}=0.4353\\\\D = \sqrt{\frac{4^{-1}}{2^{-1}\cdot 8^{-1}}}=\sqrt{\frac{2^{-2}}{2^{-1}\cdot 2^{-3}}}=\sqrt{2^{-2+1+3}}=2\\\\E = \sqrt[3]{2^{1/2}}\cdot 4^{-1/4}= (2^{1/2})^{1/3}\cdot 2^{-2/4}=2^{-1/3}=0.7937$

Arrange the following numbers in increasing order as follows:

D > B > A > E > C

Thus, the order is "D, B, A, E, C".

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2 years ago

Use the discriminant to describe the roots of each equation. Then select the best description. x^2 + 9x + 14 = 0

NISA [10]

given a quadratic equation in standard form

ax² + bx + c = 0

Then we can describe the nature of the roots using the discriminant

Δ = b² - 4ac

• if b² - 4ac > 0, then 2 real, distinct and irrational roots

• if b² - 4ac > 0 and a perfect square, then real and rational roots

• if b² - 4ac = 0, then real and equal roots

• if b² - 4ac < 0, then roots are not real

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with a = 1, b= 9 and c = 14, then

b² - 4ac = 9² - (4 × 1 × 14 ) = 81 - 56 = 25

Since b² - 4ac > 0 and a perfect square, then roots are real and rational

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2 years ago