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2 years ago

(k^8+8k^2+10k+21) / (k+7)

Mathematics

1 answer:

Serga [27]2 years ago

5 0

Answer:

Step-by-step explanation:

$\frac{k^8+8k^2+10k+21}{k+7}$ is already simplified.

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439.5\161 rounded to the nearest hundredths

LuckyWell [14K]

2.73 is 439.5 divided by 161 rounded to the nearest hundredth

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3 years ago

A shopper uses a department-store gift card to pay for 3 sweaters priced at $27 each. What is the change in the value of the gif

LenKa [72]

Well you multiply 27 by 3 to get 71 dollars

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3 years ago

The cost for 75kg of soil is £375. Find the cost for 42kg of soil.

Natasha_Volkova [10]

Answer: The cost for 42kg is $210

Step-by-step explanation:

375/75=$5 for 1kg

$5*42=$210

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2 years ago

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Which of the following statements are true?

Butoxors [25]

Answer:

Step-by-step explanation:

i think it's correct if not I'm sorry

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2 years ago

Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =

irga5000 [103]

Answer: The required solution is $y=50e^{0.1386t}.$

Step-by-step explanation:

We are given to solve the following differential equation :

$\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

$\dfrac{dy}{y}=kdt.$

Integrating both sides, we get

$\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]$

Also, the conditions are

$y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50$

and

$y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.$

Thus, the required solution is $y=50e^{0.1386t}.$

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3 years ago

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