An equation is formed of two equal expressions. It will take for the radioactive element to decay from 960 grams to 295 grams in 25.54 minutes.

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The radioactive decay of an element is given by the formula,

$N = N_0 \cdot e^{-\lambda t}$

Given the half-life of the element is 15 minutes, therefore, we can write,

$\dfrac12 = e^{-\lambda\times 15}\\\\\ln (0.5) = -\lambda\times 15\\\\\lambda = 0.0462$

Now, the time it will take for 960 grams to decay to 295 grams is,

$295 = 960 \cdot e^{-0.0462 \times t}\\\\\ln (\dfrac{295}{960}) = -0.0462 \times t\\\\t = 25.54\rm\ minutes$

Hence, it will take for the radioactive element to decay from 960 grams to 295 grams in 25.54 minutes.

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8 0

2 years ago

A segment with endpoints at $A(2, -2)$ and $B(14, 4)$ is extended through $B$ to point $C$. If $BC = \frac{1}{3} \cdot AB$, what

Mama L [17]

Answer:

C = (18, 6)

Step-by-step explanation:

You have ...

AB : BC = 1 : 1/3 = 3 : 1

(B -A) / (C -B) = 3/1 . . . . . another way to write the distance relation

B -A = 3(C -B) . . . . . . . . . multiply by (C-B)

4B -A = 3C . . . . . . . . . . . add 3B

C = (4B -A)/3 . . . . . . . . . divide by 3 to get an expression for C

C = (4(14, 4) -(2, -2))/3 = (54, 18)/3

C = (18, 6)

4 0

3 years ago

Evaluate sigma from (n-1 to 14) 3n+2

Harman [31]

The given series 3n + 2 represents an Arithmetic sequence.

Consider the first few terms of the sequence.

For n = 1, the term is 5
For n = 2, the term is 8
For n = 3, the term is 11

Notice that the difference between the terms is constant. Hence it is an arithmetic sequence. We are to find the sum of first 14 terms of the sequence.

The formula for the sum of AP is:

$S_{n}= \frac{n}{2}(2a_{1}+(n-1)*d)$

n = number of terms = 14
a1 = first term = 5
d = common difference = 3

Using the values, we get:

$S_{14}= \frac{14}{2}(2*5+(13)*3) \\ \\ 
S_{14}= 343$

So, the answer to this question is 343

8 0

4 years ago

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