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3 years ago

Find the nth term of the sequence 1,-4,9,-16...

Mathematics

1 answer:

Sonja [21]3 years ago

7 0

A₁=1====> 1²

a₂=-4===>-2²

a₃=9====>3²

a₄ =-16==>-4²

a(n) = -(-1)ⁿ (n²)

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I’m confused on this one

ad-work [718]

The question is "What is the scale of the model to the actual statue"

That means you must put 2/15.

2 being the model

15 being the actual statue

Take that fraction and equal is to 1/x.

Multiply 15 to 1 and 2 to x.

In the end, to solve, you divide 15 by 2x.

The answer is X=7.5

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3 years ago

Andrew needs to print a document that is 180 pages long. How much longer will it take to print the document on a Sure-Fire print

drek231 [11]

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3 years ago

Read 2 more answers

Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isot

Andrews [41]

Answer:

The approximate difference in the half-lives of the isotopes is 66 days.

Step-by-step explanation:

The decay of an isotope is represented by the following differential equation:

$\frac{dm}{dt} = -\frac{t}{\tau}$

Where:

$m$ - Current mass of the isotope, measured in kilograms.

$t$ - Time, measured in days.

$\tau$ - Time constant, measured in days.

The solution of the differential equation is:

$m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$

Where $m_{o}$ is the initial mass of the isotope, measure in kilograms.

Now, the time constant is cleared:

$\ln \frac{m(t)}{m_{o}} = -\frac{t}{\tau}$

$\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }$

The half-life of a isotope ( $t_{1/2}$ ) as a function of time constant is:

$t_{1/2} = \tau \cdot \ln2$

$t_{1/2} = -\left(\frac{t}{\ln\frac{m(t)}{m_{o}} }\right) \cdot \ln 2$

The half-life difference between isotope B and isotope A is:

$\Delta t_{1/2} = \left| -\left(\frac{t_{A}}{\ln \frac{m_{A}(t)}{m_{o,A}} } \right)\cdot \ln 2+\left(\frac{t_{B}}{\ln \frac{m_{B}(t)}{m_{o,B}} } \right)\cdot \ln 2\right|$

If $\frac{m_{A}(t)}{m_{o,A}} = \frac{m_{B}(t)}{m_{o,B}} = 0.9$ , $t_{A} = 33\,days$ and $t_{B} = 43\,days$ , the difference in the half-lives of the isotopes is: