Step-by-step explanation:
√((1 + sin x) / (1 − sin x)) + √((1 − sin x) / (1 + sin x))
Square and take the square root.
√[√((1 + sin x) / (1 − sin x)) + √((1 − sin x) / (1 + sin x))]²
√[(1 + sin x) / (1 − sin x) + 2 + (1 − sin x) / (1 + sin x)]
Add the fractions using least common denominator.
√[((1 + sin x)² + (1 − sin x)²) / (1 − sin²x) + 2]
√[(1 + 2 sin x + sin²x + 1 − 2 sin x + sin²x) / (1 − sin²x) + 2]
√[(2 + 2 sin²x) / (1 − sin²x) + 2]
Use Pythagorean identity:
√[(2 + 2 sin²x) / (cos²x) + 2]
√[2 sec²x + 2 tan²x + 2]
√[2 sec²x + 2 (tan²x + 1)]
Use Pythagorean identity:
√[2 sec²x + 2 sec²x]
√[4 sec²x]
±2 sec x
If x is in the second quadrant, then sec x < 0.
-2 sec x
Answer:
The absolute error of the measurement is 0.25 inches
Step-by-step explanation:
we know that
The absolute error of a measurement is equal to one half the unit of measure.
In this problem we have
7.5 inches
The measurement is given by 0.5 inches
So
the absolute error of this measurement is

Therefore
the exact measurement could be between
7.5 (+/-) 0.25 in
That is, between 7.25 in and 7.75 in
Answer:
The answer is C
Step-by-step explanation:
(180-46)/2=67
67+45=112
Answer:
P = $300
r = 0.15
n = 12
$544.61 (to the nearest cent)

$524.70 (to the nearest cent)
Step-by-step explanation:
P = principal amount = $300
r = annual interest rate in decimal form = 15% = 15/100 = 0.15
n = number of times interest is compounded per unit t = 12
<u>How much she'll owe in 4 years</u>
P = 300
r = 0.15
n = 12
t = 4

= $544.61 (to the nearest cent)
<u>Yearly compounding interest rate</u>

<u>How much she'll owe in 4 years at yearly compounding interest</u>

= $524.70 (to the nearest cent)