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2 years ago

I have 2 questions:

Mathematics

1 answer:

Aneli [31]2 years ago

3 0

The first answer is 48. The next answer is also 48.

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Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its te

Aleonysh [2.5K]

Answer:

t=5.18 minute

Step-by-step explanation:

Using Newton's law of cooling

$\frac{dT}{dt}=-k(T-T_{s})$

T is temperature of a cup of coffee at any time t $T_{s}$ , is the temperature of the surrounding and k is a constant of proportionality in this negative because temperature is decreasing.

$T(0)=190\\T(1)=170\\T_{s}=66$

$\frac{dT}{dt}=-k(T-T_{s})\\\frac{dT}{(T-T_{s})}=-k*dt\\\int\limits {\frac{1}{T-T_{s} } } \, dT=-\int\limits {k} \, dt\\ln(T-T_{s})=k*t+C\\e*ln(T-T_{s})=e^{k*t+C} \\T-T_{s}=e^{k*t}*e^{C}\\e^{C}=C\\T-T_{s}=e^{k*t}*C\\T=T_{s}+e^{k*t}*C$

To find constant knowing the time and the temperature the first step of the change of energy in cup of coffee

$T=T_{s} +e^{-k*t}*C\\ C=190-66=124\\170=66+124*e^{-k*2}\\ 170-66=124*e^{-k*2}\\ln(\frac{104}{124})=ln*e^{-k*2}\\-0.175=-k*2\\k=0.08794$

Now using the constant of decreasing can find the time to be a 145 temperature the cup of coffee

$145=66+124*e^{-k*t} \\145-66=124*^{-0.087*t}$

$ln(0.637)=ln*e(-0.087*t)\\-0.45=-0.087*t\\t=5.18minutes$

4 0

3 years ago

Explain how, in general, riemann sum approximations to the area of a region under a curve change as the number of subintervals

Lyrx [107]

As you increase the subintervals the area will be closer and closer to the real value. In other words your approximation gets better.

As you increase the intervals, there will be more rectanagles and the added area of these rectangles are converging towards the actual area under the curve.

5 0

3 years ago

What is the value of y in the equation 4y – 2(1 – y) = –44?

Sergio039 [100]

Answer:

-7

Step-by-step explanation:

To find y, follow these steps:

4y - 2 (1 - y) = -44

First, distribute the -2 into the parenthesis:

4y - 2 + 2y = -44

The reason the 2y is positive is due to the fact that negative and negative cancel each other out and form a positive.

Now, combine like terms:

6y - 2 = -44

To get y, you need to isolate it from the constants. In order to do so, do the inverse relationship for the constant -2. To do this, add 2 to -44:

6y = -42

Now, divide six on both sides. You divide because six is currently being multiplied with y. Keep in mind that the 42 is still negative!

y = -7

Hope this helps!

4 0

2 years ago

Read 2 more answers

Calculate the area of triangle ABC with altitude AD, given A(-5, 4), B(-6, 1), C(0, 1), and D(-5, 1).

snow_lady [41]

Answer:

the area of triangle ABC = 9

Step-by-step explanation:

Check the photo below for the details.

3 0

3 years ago

Help please please help…….

olga nikolaevna [1]

Answer:

Choice A

Step-by-step explanation:

y-intercept = -3

double-checked on calculator

8 0

2 years ago