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3 years ago

Can you please help me?!

Mathematics

1 answer:

iren2701 [21]3 years ago

7 0

Answer:

43.5 miles per hour

Step-by-step explanation:

Divide 174 miles by 4 hours. Hope this helped :)

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Suppose after 2500 years an initial amount of 1000 grams of a radioactive substance has decayed to 75 grams. What is the half-li

krok68 [10]

Answer:

The correct answer is:

Between 600 and 700 years (B)

Step-by-step explanation:

At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:

$A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years$

First, let us calculate the decay constant (k)

$75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036$

Next, let us calculate the half-life as follows:

$\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2} \approx 669\ years$

Therefore the half-life is between 600 and 700 years

5 0

3 years ago

Given y = 2(x-3) and a domain of (-3,-2 and 5). Find the range.

alexandr402 [8]

The answers are (-3,-12), (-2,-10), (5,4)

4 0

2 years ago

Houa has an action figure collection. She keeps some in a display case and the rest on the wall. 82 of her action figures are on

Law Incorporation [45]

Answer:

u just 82 + 59% = 130.38

Step-by-step explanation:

8 0

2 years ago

Give the answer to the question below.

alexira [117]

Answer:

1/4 assuming x is not 0

Step-by-step explanation:

x^0 is 1 and 1/4 * 1 = 1/4

4 0

3 years ago

4 of 4

Vlada [557]

Answer:

£30

Step-by-step explanation:

Let Brian initially had money in his wallet = £x

and Colin had the money = £y

Since ratio of money in Brian's wallet to Colin's wallet was 5 : 1

Therefore,

⇒ x = 5y -------(1)

Brian spent £27 that day, so money left with him = £(x - 27)

After spending the money Brian had £3 less than Colin.

(x - 27) = (y - 3)

x = y + 27 - 3

x = y + 24 -------(2)

Now we equate the equations (1) and (2) for the value of x,

5y = y + 24

5y - y = 24

4y = 24

y = £6

From equation (2),

x = 6 + 24

x = £30

Therefore, Brian initially had £30.

i hope this helps

3 0

3 years ago