I’m gonna say 24 mm explanation I’m guessing
Answer:
ln|sec θ + tan θ| + C
Step-by-step explanation:
The integrals of basic trig functions are:
∫ sin θ dθ = -cos θ + C
∫ cos θ dθ = sin θ + C
∫ csc θ dθ = -ln|csc θ + cot θ| + C
∫ sec θ dθ = ln|sec θ + tan θ| + C
∫ tan θ dθ = -ln|cos θ| + C
∫ cot θ dθ = ln|sin θ| + C
The integral of sec θ can be proven by multiplying and dividing by sec θ + tan θ, then using ∫ du/u = ln|u| + C.
∫ sec θ dθ
∫ sec θ (sec θ + tan θ) / (sec θ + tan θ) dθ
∫ (sec² θ + sec θ tan θ) / (sec θ + tan θ) dθ
ln|sec θ + tan θ| + C
Answer:
14
Step-by-step explanation:
The interquartile range is the value of quartile 3 minus quartile 1.
The "box" part of this diagram has 3 lines, the left most, the middle, and the rightmost.
The leftmost line is Quartile 1. The right most is Quartile 3.
Hence
interquartile range = quartile 3 - quartile 1
Looking at the box plot, we can see that each small line in the number line is 2 units.
The leftmost line (quartile 1 ) is at 1 unit left of 30, so that is 30 -2 = 28
The rightmost line (quartile 3) is at 1 unit right of 40, so that is 40 + 2 = 42
Hence,
Interquartile range = 42 - 28 = 14
Side a is 13 when using the pythagorean theorem
a^2 + b^2 = c^2
5^2 + 12^2 = c^2
25 + 144 = c^2
c^2 = 169
c = 13
