Answer:
The radius of the circle is 
Step-by-step explanation:
we know that
The circumference of a circle is equal to
we have
assume
substitute and solve for r
Answer:
a = 1√6
b = -2
Step-by-step explanation:
Hello,
To solve this trigonometric problem, we need to convert this values into fractions
a).
Sin45° = 1/√2
cos30° = √3/2
Sin60° = √3/2
Sin45° / (cos30° + sin60°) = [(1/√2) ÷ (√3/2 + √3/2)]
(1/√2) ÷ (√3/2 + √3/2)
Add √3/2 + √3/2
1/√2 ÷ 2√3/2
1/√2 × 2/2√3
2/2√(2×3)
2/2√6
1/√6
b
Cos 180° = -1
Sin150° = ½
Tan135° = -1
2cos180° - 2sin150° - tan135°
(2 × -1) - (2×½) - (-1)
-2 - 1 + 1 = -2
-5/4 ÷ 2 3/5
Let's turn 2 3/5 into a complete fraction so multiply bottom by two and add it to the top. Take the answer and put it over the original bottom. SO: 13/5
Now KEEP CHANGE FLIP
keep -5/4
change sign to ×
flip 13/5 to 5/13
Thus: -5/4 × 5/13
Simply, multiply
-25/52
Done, hope that helps :)
Answer:
15.035 years
Step-by-step explanation:
The exponential function to calculate population growth is
P(t) = Poe^kt
P(t) = Population size after t years = 3.6 million
Po = Initial population size = 2.1 million
k = growth rate = 3.65% = 0.0365
t = time in years = ???
Hence:
3600000 = 2100000 × e ^0.0365t
Divide both sides by 2100000
3600000/2100000 = e^0.0365t
1.7142857143 = e^0.0365t
Find the log of both sides
Log 1.7142857143 = log (e^0.0365t)
Log 1.7142857143 /Log 0.0365 = t
t = 15.035 years
Answer:
77
Step-by-step explanation:
At first, you would probably think that the side lengths are 1², 2², 3² = 1, 4 and 9 but these side lengths don't form a triangle. The Triangle Inequality states that the sum of the two shortest side lengths must be greater than the largest side length, and since 1 + 4 > 9 is a false statement, it's not a triangle. Let's try 2², 3², 4² = 4, 9, 16. 4 + 9 > 16 is also false so that doesn't work. 3², 4², 5² = 9, 16, 25 but since 9 + 16 > 25 is false (25 isn't greater than 25), that doesn't work either. 4², 5², 6² = 16, 25, 36 and since 16 + 25 > 36 is true, this is our triangle which means that the perimeter is 16 + 25 + 36 = 77.
