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Sedbober [7]
3 years ago
6

Please help me and I need the work :<​

Mathematics
1 answer:
nasty-shy [4]3 years ago
7 0

Answer:

C

1/4 inch 1 inch

______ = _____

1 foot 4 feet

3 × 4 = 12

4 × 4 = 16

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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
Which of the following equations names the same line as -2x – 3y = 5?
qaws [65]

Answer:

c

Step-by-step explanation:

_6x -9y =15

_6x÷3=-2x

9y÷3=3y

15÷3=5

so,_2x -3y =5

7 0
2 years ago
Read 2 more answers
A silver ring has a volume of 3 cm- and a mass of 36 grams.<br>Find the density of the silver.​
siniylev [52]
M/V = D. 36g/3cm = 12
8 0
3 years ago
Point , j located at (2,7) is rotated 90° counterclockwise about (-1,-3). What is the y- coordinate of 1'? А 9 B 0 C -11 D-9​
arlik [135]

Answer: the answer is 0

Step-by-step explanation:

4 0
3 years ago
Find the value of X and QR If M is the midpoint of QR. QM=3x+2 and MR=5x-8
Y_Kistochka [10]
The value of X is 5 and QR is 34
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3 years ago
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