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2 years ago

2x - y2 Z-5 Evaluate when x = 2, y = 4 z=3

Mathematics

1 answer:

kolezko [41]2 years ago

5 0

Answer:

Putting the value in x = 2 , y =4 in 2x - 2y we get,

2 × 2 - 4× 2= 4-8 = -4

Putting the value in z = 3 in z - 5 we get,

z - 5 = 3 - 5 = -2

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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:

$\Delta t_{1/2} = \left|-\left(\frac{33\,days}{\ln 0.90} \right)\cdot \ln 2 + \left(\frac{43\,days}{\ln 0.90} \right)\cdot \ln 2\right|$

$\Delta t_{1/2} \approx 65.788\,days$

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

4 0

3 years ago

Read 2 more answers

Kerry has a net spendable income of $1,800 per month. She also has a significant amount of debt and payments of $150 per month.

Firdavs [7]

A the rent all together is
$450 + 60 + 40 + 80 = 630$
b the rent alltogether would be
$500 + 50 + 40 + 70 = 660$
the rent for c would cost

640 including everything
and the rent for d would be
$475 + 50 + 40 + 35 = 60$
so the answer would be D
hope this helped sorry for late answer

7 0

3 years ago

Which of the following are geometric sequences?<br> Check all that apply.

kolezko [41]

Answers:

Step-by-step explanation:

There are two general types of sequences that follow a pattern, geometric and arithmetic. Let's see the difference between the two:

An arithmetic sequence is produced by adding the same number to all the terms in the sequence.

EXAMPLE:

5, 7, 9, 11, 13, 15, 17 (The number 2 is added to all terms)

To figure out if a sequence is arithmetic, subtract the first term from the second, then the second from the third and so on until you have checked all the terms.

7 - 5 = 2

9 - 7 = 2

11 - 9 = 2

13 - 11 = 2

15 - 13 = 2

17 - 15 = 2

All results equal 2, so the sequence is arithmetic

From your list: The following sequences are arithmetic

A. 5, 10, 15, 20, 25 (common difference of 5)

The next type of sequence is the geometric sequence.

A geometric sequence is produced when the all the terms in the sequence are multiplied or divided by the same number.

EXAMPLE:

100, 50, 25 (Each term is divided by 2)

To figure this out, we divide each term in the sequence by the next term.

100 / 50 = 2

50 / 25 = 2

All results are two, so this sequence can be confirmed to be geometric

From your list: The following sequences are geometric

C. 10, 5, 2.5, 1.25, 0.625, 0.3125 (common quotient of 2)

D. -9, -3, -1, -1/3, -1/9, -1/27 (common quotient of -3)

There is one final type of sequence, which has no common difference, sum, quotient, or product.

EXAMPLE:

5, 6, 8, 9, 11, 12, 14, 15

This sequence has a pattern, the differences between the numbers are not common.

6 - 5 = 1

8 - 6 = 2

9 - 8 = 1

11 - 9 = 2

12 - 11 = 1

14 - 12 = 2

15 - 14 = 1

From your list: The following sequences are neither geometric nor arithmetic

B. 1, 1, 2, 3, 5, 8, 13 (No pattern)

I'n always happy to help :)

6 0

3 years ago

Find an angle between 0° and 360° that is coterminal with 456°.

Ipatiy [6.2K]

Co-terminal angle = 456 - 360 = 96 degrees

4 0

3 years ago

Read 2 more answers

Write the slope-intercept form of a linear equation given the slope and y-intercept. Slope : y – intercept: -3

Alexxx [7]

Answer:

this question doesn't make sense you forgot a number

Step-by-step explanation:

yeet

7 0

2 years ago