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4 years ago

Evaluate the function at the specified value of the independent variable and simplify.

1 answer:

3 0

$q(t)=\dfrac{5t^2+6}{t^2}\\\\1.\\q(2)=\dfrac{5\cdot2^2+6}{2^2}=\dfrac{5\cdot4+6}{4}=\dfrac{20+6}{4}=\dfrac{26}{4}=7.5\\\\2.\\q(0)=\dfrac{5\cdot0^2+6}{0^2}=\dfrac{6}{0}-unde fined\\\\3.\\q(-x)=\dfrac{5\cdot(-x)^2+6}{(-x)^2}=\dfrac{5x^2+6}{x^2}$

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Answer:

The answer your looking for is <em><u>A</u></em>

Step-by-step explanation:

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4 years ago

A contaminant is leaking into a lake at a rate of R(t) = 1700e^0.06t gal/h. Enzymes that neutralize the contaminant have been ad

olasank [31]

Answer:

16,460 gallons

Step-by-step explanation:

This is a differential equation problem, we have a constant flow of contaminant into the lake, but also we know that only a fraction of that quantity of contaminant remains because of the enzymes. For that reason, the differential equation of contaminant's flow into the lake would be:

$\frac{dQ}{dt} =1700exp(0.06t)*exp(-0.32t)\\\frac{dQ}{dt} =1700exp(-0.26t)\\$

Then, we have to integrate in order to find the equation for Q(t), as the quantity of contaminant in the lake, in function of time.

$\int\limits^0_t {dQ}=\int\limits^0_t {1700exp(-0.26t)dt}\\Q(t)=\frac{1700}{-0.26} exp(-0.26t)+C \\$

Now, we use the given conditions to replace them in the equation, in order to solve for $C$

$t_{0} =0\\Q_{0}=10,000\\Q_{0}=-6538exp(-0.26*0)+C\\C=10,000+6538=16538$

Then, we reorganize the equation and we replace t for 17 hours, in order to determine the quantity of contaminant at that time:

$Q_{t} =-6538exp(-0.26t)+16538\\Q_{17} =-6538exp(-0.26*17)+16538\\Q_{17} =16460 gallons$

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3 years ago

Paula has buttons. she gives away 28 buttons. choose the expression that shows the number of buttons paula has left.

mamaluj [8]

Answer:

y = 28 - x

Step-by-step explanation:

The variable x represents how many buttons Paula had before giving 28 away and the variable y represents how many buttons she has now.

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2 years ago

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vekshin1

Answer:

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Step-by-step explanation:

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3 years ago

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lana66690 [7]

Everything is correct until they got to switching 55 instead of x<5 of that makes sense

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3 years ago