Given:

To find:
The exact value of cos 15°.
Solution:

Using half-angle identity:


Using the trigonometric identity: 

Let us first solve the fraction in the numerator.

Using fraction rule: 

Apply radical rule: ![\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7B%5Cfrac%7Ba%7D%7Bb%7D%7D%3D%5Cfrac%7B%5Csqrt%5Bn%5D%7Ba%7D%7D%7B%5Csqrt%5Bn%5D%7Bb%7D%7D)

Using
:


Step-by-step explanation:
1 t=16/21
2.m=2
3.n=13/7
4.a=2
5.x=6/17
6.x=15
7.s=21/4
8. t=7/3
9. s=1
10. s=6/61
11. x=1/3
12. r=27/16
13. c=−1
14.m=9/5n
15. j=−117/58
Answer: 2 minutes
Step-by-step explanation:
Given the following :
Plane A's descent :
y = -2,500x + 14,000
Plane B's Ascent :
y = 4,000x + 1,000
where y = altitude x = minute
Time to be at the same altitude :
Being at the same altitude means ;
Plane A's descent = Plane B's Ascent
-2,500x + 14,000 = 4,000x + 1,000
-2500x - 4000x = 1000 - 14000
-6500x = - 13000
x = 13000 / 6500
x = 2
x = 2minutes.
You're looking for the largest number <em>x</em> such that
<em>x</em> ≡ 1 (mod 451)
<em>x</em> ≡ 4 (mod 328)
<em>x</em> ≡ 1 (mod 673)
Recall that
<em>x</em> ≡ <em>a</em> (mod <em>m</em>)
<em>x</em> ≡ <em>b</em> (mod <em>n</em>)
is solvable only when <em>a</em> ≡ <em>b</em> (mod gcd(<em>m</em>, <em>n</em>)). But this is not the case here; with <em>m</em> = 451 and <em>n</em> = 328, we have gcd(<em>m</em>, <em>n</em>) = 41, and clearly
1 ≡ 4 (mod 41)
is not true.
So there is no such number.
What does the central limit theorem tell us about the
distribution of those mean ages?
<span>A. </span>Because n>30, the sampling
dist of the mean ages can be approximated by a normal dist with a mean u and a
SD o/sqrt 54,
Whenever n<span>>30 the central limit theory applies.</span>