Find the value of x, and please use explanation for each answer
2 answers:
Answer:
24; 118; 102
Step-by-step explanation:
Starting from A: there are two ways. One, is a theorem that says "the amplitude of the external angle of a triangle is equal to the sum of the amplitudes of the two angles not sharing the vertex". Which translates to the equation which has solution
.
Problem B is a red herring: x and 118° are corresponding angles related to the two parallel lines with a transversal, and they have the same amplitude, thus
Finally, letter C : you know the sum of the internal angles of a triangle is 180°. It means that or, with simple calculations (subtract 41 and 37 from both sides)
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Answer:
5.8%
Step-by-step explanation:
Current yield = 6.1%
Face value of bond = $500
Market price of bond = $475
Let the original coupon rate be CR
Multiply both sides by 475
Cancel out the 475's from the top and bottom of the right side
Flip the sides
Divide both sides by 5000
Cancel out 50000 from the top and bottom of the left side
%
CR = 0.0579 * 100 [convert decimal into a percentage]
CR = 5.79 %
CR = 5.8% [rounded off to the tenth place]
If the radio active isotope has the half life of 24100 years, then the initial quantity is 2.16 grams
The half life in years = 24100
Consider the quantity of the radio active isotope remaining
y =
When t = 1000 the y = 1.2
y = C/2 when t = 1599
Substitute the values in the equation
C/2 =
Cancel the C in both side
1/2 =
Here we have to apply ln to eliminate the e terms
ln (1/2) = 24100k
k = ln(1/2) / 24100
k = -2.87× 10^-5
To find the initial value we have to substitute the value of k and y in the equation
1.2 = Ce^{1000 × -2.87× 10^-5}
C = 1.2 / e^(-0.0287)
C = 2.16 gram
Hence, the initial quantity of the radioactive isotope is 2.16 gram
Learn more about half life here
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