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makvit [3.9K]
3 years ago
8

At 11:00 p.m., the temperature in Alaska was −5°. Four hours earlier, the temperature was 40° warmer. What was the temperature a

t 7:00 p.m.?
Mathematics
2 answers:
alukav5142 [94]3 years ago
6 0

Answer:

35

Step-by-step explanation:

If you put 40 - 5 it would equal 35 in the positive

andreev551 [17]3 years ago
6 0
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Write the equation of the line that is PARALLEL to y = -4x + 5 and passes through the point (-2,-1)
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Answer: y    = -4x-9

Step-by-step explanation:

parallel slope means it's the same slope as the given equation

y+1=-4(x+2)

y+1 = -4x-8

y    = -4x-9

6 0
3 years ago
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PSYCHO15rus [73]

Answer:

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Step-by-step explanation:

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3 years ago
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Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 3%. If the rate of deca
Hitman42 [59]

Answer:

The half-life of the radioactive substance is 135.9 hours.

Step-by-step explanation:

The rate of decay is proportional to the amount of the substance present at time t

This means that the amount of the substance can be modeled by the following differential equation:

\frac{dQ}{dt} = -rt

Which has the following solution:

Q(t) = Q(0)e^{-rt}

In which Q(t) is the amount after t hours, Q(0) is the initial amount and r is the decay rate.

After 6 hours the mass had decreased by 3%.

This means that Q(6) = (1-0.03)Q(0) = 0.97Q(0). We use this to find r.

Q(t) = Q(0)e^{-rt}

0.97Q(0) = Q(0)e^{-6r}

e^{-6r} = 0.97

\ln{e^{-6r}} = \ln{0.97}

-6r = \ln{0.97}

r = -\frac{\ln{0.97}}{6}

r = 0.0051

So

Q(t) = Q(0)e^{-0.0051t}

Determine the half-life of the radioactive substance.

This is t for which Q(t) = 0.5Q(0). So

Q(t) = Q(0)e^{-0.0051t}

0.5Q(0) = Q(0)e^{-0.0051t}

e^{-0.0051t} = 0.5

\ln{e^{-0.0051t}} = \ln{0.5}

-0.0051t = \ln{0.5}

t = -\frac{\ln{0.5}}{0.0051}

t = 135.9

The half-life of the radioactive substance is 135.9 hours.

6 0
3 years ago
Derivative of y=cos²x-sin²x
Leona [35]
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\bf y=cos^2(x)-sin^2(x)\implies y=[cos(x)]^2-[sin(x)]^2
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\cfrac{dy}{dx}=-2cos(x)sin(x)-2cos(x)sin(x)
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8 0
3 years ago
Write a rule for the following graph
djyliett [7]

Answer:

y = x + 1

Step-by-step explanation:

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The slope is 1

y = 1x + 1 or

y = x + 1

7 0
3 years ago
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