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2 years ago

Find the measure of angle A

Mathematics

1 answer:

blagie [28]2 years ago

4 0

Answer:

43°

Step-by-step explanation:

(x + 53)° + (x + 74)° + 73° = 180°

(x + 53 + x + 74)° = 180° - 73°

(2x + 127)° = 107°

2x + 127 = 107

2x = 107 - 127

2x = - 20

x = - 20/2

x = - 10

$m\angle A = (x +53)\degree \\\\m\angle A = (-10 +53)\degree \\\\m\angle A = 43\degree \\\\$

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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.

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2 years ago

Read 2 more answers

Nigel travels a total of 312 miles to school each day. He walks 14 mile to the bus stop. He travels 234 miles on the city bus. I

Valentin [98]

The bus drops Nigel off 64 miles away from the school.

Step by step Explanation:

An equation for this would be 312-14-234 (this was the equation I used. Since you would do left to write to solve the equation, you would do, 312-14 which equals 298. Then, the equation is left as 298-234, and when you solve that part to the equation, yoh would be getting 64. And that's how you would get the answer 64miles away from the school.

7 0

2 years ago

Yesterday noah ran 2 1/2 miles in 3/5 hour. Emily ran 3 3/4 miles in 5/6 hour. Anna ran 3 1/2 miles in 3/4 hour how fast in mile

Dmitry_Shevchenko [17]

Answer:

Step-by-step explanation:

To calculate the speed of each one we proceed as follows:

speed=distance/time

a] Noah's speed:

distance=2.5 miles

time=3/5 hours

speed=(2 1/2)/(3/5)

=(5/2)/(3/5)

=5/2×5/3

=25/6

=4 1/6 mi/hr

Emily's speed

distance=3 3/4 miles

time=5/6 hour

thus

speed=(3 3/4)/(5/6)

=15/4)/(5/6)

=15/4×6/5

=4 1/2 mi/hr

Anna's speed:

distance=3 1/3 miles

time=3/5

speed=(3 1/3)/(3/5

=(10/3)/(3/5)

=10/3×5/3

=5 5/9 mi/hr

Anna was the fastest

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2 years ago

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Acellus

USPshnik [31]

Answer:

Step-by-step explanation:

Corresponding angles have the same matching corner when a transversal line crosses tow straight lines.

Thus, in the diagram given, the angle that has the same matching corner with <2 is the angle that corresponds to <2.

<6 has the same matching corner with <2.

Therefore, <6 corresponds with <2

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2 years ago

Can someone pls help me with this problem

VLD [36.1K]

Answer:

Rule= Y × 10

X ÷ 10

Step-by-step explanation:

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2 years ago

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