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4 years ago

Which coordinate pair represents the y-intercept of the line with equation 2x + 3y = 12 ?

1 answer:

4 0

So, this equation : 2x + 3y = 12 is in standard form, so lets convert this to the slope intercept form to see the y intercept.

Slope intercept form : y = mx + b

2x + 3y = 12
-2x -2x

3y = -2x + 12
y = -2/3x + 4

Now, we can see the 'b' (aka y intercept) is 4

Answer: (0,4)

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1.2083⁻⁻

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3 years ago

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3 years ago

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2 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

If 3% of a number is 27, what is 44% of that number?

natulia [17]

Answer:

396

Step-by-step explanation:

0.03n=27

n=27/0.03=900

900*0.44=396

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3 years ago

Read 2 more answers