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3 years ago

A radioactive isotope has a half life of 4.51 days. If 12.63 grams are now present, how much will be left after 15

Mathematics

1 answer:

Marizza181 [45]3 years ago

7 0

Answer:

Step-by-step explanation:

$f=ir^t\\ \\ \frac{1}{2}=r^{4.51}\\ \\ ln(0.5)=4.51lnr\\ \\ r=e^{\frac{ln0.5}{4.51}}\\ \\ r\approx 0.8575\\ \\ f(15)=12.63(0.8575^{15}\\ \\ f(15)\approx 1.26g$

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10/3 = k/9

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k = 90/3

k = 30

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3 years ago

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Find the Laplace transformation of each of the following functions. In each case, specify the values of s for which the integral

MAVERICK [17]

Answer:

a. $\frac {2} {s-1}$ converges to s> 1.

b. $\frac{3}{e^3 \left(s-5 \right)}$ converges to s> 5.

c. $- \frac {2}{s + 3}$ converges to s> - 3.

d. $\frac {s}{s^2 + 25}$ converges to s> 0.

e. $\frac {10} {s^2 + 1}$ converges even s> 0.

f. $\frac {12}{s^2 + 4}$ converges to s> 0.

g. $-\frac {5\left(\cos\left (1\right) s-2 \sin\left(1\right)\right)}{s^2 + 4}$ converges to s> 0.

h. $\frac {1} {s ^ 2 + 4}$ converges to s> 0.

Step-by-step explanation:

a. $L \left\{2e^t \right\} = 2L \left\{e^t \right\} = 2 \cdot \frac {1} {s-1} = \frac {2} {s-1}$ converges to s> 1.

b. $L \left\{3e^{5t-3} \right\} = 3e^{-3} L \left\{e^{5t} \right\} = 3e^{-3} L \left\{e^{5t} \right\} = \frac{3}{e^3 \left(s-5 \right)}$ converges to s> 5.

c. $L \left\{-2e^{-3t} \right\} = -2L \left\{e^{-3t} \right\} = - \frac {2}{s + 3}$ converges to s> - 3.

d. $L \left\{\cos\left (5t \right)\right\} = \frac {s}{s^2 + 25}$ converges to s> 0.

e. $L \left\{10 \sin\left(t\right)\right\} = 10L\left\{\sin\left(t\right)\right\} = \frac {10} {s^2 + 1}$ converges even s> 0.

f. $L \left\{6\sin \left(2t \right) \right\} = 6L\left\{\sin\left (2t\right)\right\} = \frac {12}{s^2 + 4}$ converges to s> 0.

g. $L \left\{-5\cos\left(2t + 1\right) \right\} = -5L\left\{\cos\left(2t + 1 \right)\right\} = -\frac {5\left(\cos\left (1\right) s-2 \sin\left(1\right)\right)}{s^2 + 4}$ converges to s> 0.

h. $L\left\{\sin \left(t\right)\cos \left(t\right)\right\} = L\left\{\sin\left(2t\right)\frac{1}{2}\right\} =\frac{1}{2}\cdot \frac{2}{s^2+4} = \frac {1} {s ^ 2 + 4}$ converges to s> 0.

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4 years ago

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kakasveta [241]

The answer to this is B.

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kakasveta [241]

Hey there!

Our function is:

f(x) = 4^x

If we want to have f(3), we simply can plug in 3 to our answer, and evalutate from there:

f(x) = 4^3 =
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We just calculated 4 to the fourth power, which is four times four times four times four. Therefore, 4 of four is equal to 64.

Hope this helps!

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3 years ago

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MrRissso [65]

Answer:

Only one circle can be drawn through three non nonlinear points, No circle can be drawn through three nonlinear points

Step-by-step explanation:

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