a) The length of p is 21.4 cm
b) The measure of angle P is 45.6°
<h3>Trigonometry </h3>From the question, we are to determine the length of p
From the <em>Pythagorean theorem</em>, we can write that
30² = 21² + p²
p² = 30² - 21²
p² = 900 - 441
p² = 459
p = √459
p = 21.4 cm
∴ The length of p is 21.4 cm
b)
Measure of angle P
Using SOH CAH TOA
cos P = 0.7
P = cos⁻¹(0.7)
P = 45.6°
Hence, the measure of angle P is 45.6°
Learn more on Trigonometry here: brainly.com/question/17831932
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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:
Where:
- Current mass of the isotope, measured in kilograms.
- Time, measured in days.
- Time constant, measured in days.
The solution of the differential equation is:
Where is the initial mass of the isotope, measure in kilograms.
Now, the time constant is cleared:
The half-life of a isotope () as a function of time constant is:
The half-life difference between isotope B and isotope A is:
If ,
and
, the difference in the half-lives of the isotopes is:
The approximate difference in the half-lives of the isotopes is 66 days.