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2 years ago

Andre says that 1/4 is less than -3/4 because, of the two numbers, 1/4 is closer to 0. Do you agree? Explain your reasoning.

Mathematics

1 answer:

yKpoI14uk [10]2 years ago

8 0

Answer:

Andre is wrong

Step-by-step explanation:

Andre is wrong because 1/4 is a positive number and -3/4 is a negative number so that makes Andre wrong for that, but if it is who is closer to 0 then Andre is right because when you look at it on a table you can see that 1/4 is closer.

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adiocarbon dating of blackened grains from the site of ancient Jericho provides a date of 1315 BC ± 13 years for the fall of the

Zigmanuir [339]

Answer:

$\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659$ and $\left(\frac{m(t)}{m_{o}} \right)_{max} \approx 0.661$

Step-by-step explanation:

The equation of the isotope decay is:

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

14-Carbon has a half-life of 5568 years, the time constant of the isotope is:

$\tau = \frac{5568\,years}{\ln 2}$

$\tau \approx 8032.926\,years$

The decay time is:

$t = 1315\,years + 2007\,years \pm 13\,years$ (There is no a year 0 in chronology).

$t = 3335 \pm 13\,years$

Lastly, the relative amount is estimated by direct substitution:

$\frac{m(t)}{m_{o}} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\mp\frac{13\,years}{8032.926\,years} }$

$\left(\frac{m(t)}{m_{o}} \right)_{min} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{-\frac{13\,years}{8032.926\,years} }$

$\left(\frac{m(t)}{m_{o}} \right)_{min} \approx 0.659$

$\left(\frac{m(t)}{m_{o}} \right)_{max} = e^{-\frac{3335\,years}{8032.926\,years} }\cdot e^{\frac{13\,years}{8032.926\,years} }$

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3 years ago

Angelina factored (x - 4^8 ) and wrote that it was equal to (x^2 - 4^2)^2(x^2 + 4^2). Use complete sentences to explain how you

nikitadnepr [17]

Given is (x - 4⁸)

Her factors are (x² - 4²)² (x² + 4²)

Let us prove whether her solution is correct or not.

(x² - 4²)² (x² + 4²)
(x⁴ - 4⁴) (x² + 4²) ; Follow PEMDAS rule as well as exponential multiplication rule which tells that when exponents are multiplied, the exponents will be added.

By using FOIL(First, Outside, Inside, Last) Method, we can prove if Angelina's solution is correct. NOTE: Do not disregard the positive or negative.

(x⁴ - 4⁴) (x² + 4²) ; For the First, multiply the first terms. They are underlined.
This gives you a partial answer: x⁶ (Exponential Law of Multiplication is applied)

(x⁴ - 4⁴) (x² + 4²) ; For the Outside, multiply the outside terms. They are underlined. This gives you an additional to the partial answer: x⁶ + 4²x⁴

(x⁴ - 4⁴) (x² + 4²) ; For the Inside, multiply the inside terms. They are underlined. This gives you an additional to the partial answer: x⁶ + 4²x⁴ - 4⁴x²

(x⁴ - 4⁴) (x² + 4²) ; For the Last, multiply the last terms. They are underlined. This will give you an additional to the final answer: x⁶ + 4²x⁴ - 4⁴x² - 16⁶ = 0

Final Answer in complete sentence:
The result of multiplying the factors is x⁶ + 4²x⁴ - 4⁴x² - 16⁶ = 0 and is too far compared to (x - 4⁸) which is already a factor.

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3 years ago

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