Answer:
a) 160°
b) 18 sides
Step-by-step explanation:
Interior angle = 180 - exterior
= 180 - 20 = 160°
Each angle of a regular polygon:
[(n-2)×180]/n = 160
180n - 360 = 160n
20n = 360
n = 18
Alternate approach for no. of sides:
360/n = each exterior angle
360/n = 20
n = 360/20 = 18
Answer:
Salena's got to the library first
Step-by-step explanation:
12½ miles = 25/2 miles
2½ miles = 5/2 miles
5¾ miles = 23/4 miles
114 miles = 114 miles
Salena's time of arrival =
if 5/2 miles : 5 minutes
then 25/2 miles : ?
25/2 ÷ 5/2. × 5
25/2 × 2/5 × 5
25 minutes
Justin 's time of arrival=
if 23/4 miles : 12 minutes
25/2 miles : ?
25/2 ÷ 23/4 ×12
25/2 × 4/23 ×12
26 minutes approximately
Brandon 's time of arrival=
if 114 miles : 258 minutes
25/2 miles : ?
25/2 ÷114 ×258
25/2 × 1/114×258
25 × 1/57 × 258
113 minutes approximately
Find <span>tan<span>(<span><span>5π</span>12</span>)</span></span> and sin ((5pi)/12)
Answer: <span>±<span>(2±<span>√3</span>)</span>and±<span><span>√<span>2+<span>√3</span></span></span>2</span></span>
Explanation:
Call tan ((5pi/12) = t.
Use trig identity: <span><span>tan2</span>a=<span><span>2<span>tana</span></span><span>1−<span><span>tan2</span>a</span></span></span></span>
<span><span>tan<span>(<span><span>10π</span>12</span>)</span></span>=<span>tan<span>(<span><span>5π</span>6</span>)</span></span>=−<span>1<span>√3</span></span>=<span><span>2t</span><span>1−<span>t2</span></span></span></span>
<span><span>t2</span>−2<span>√3</span>t−1=0</span>
<span>D=<span>d2</span>=<span>b2</span>−4ac=12+4=16</span>--> <span>d=±4</span>
<span>t=<span>tan<span>(<span><span>5π</span>12</span>)</span></span>=<span><span>2<span>√3</span></span>2</span>±<span>42</span>=2±<span>√3</span></span>
Call <span><span>sin<span>(<span><span>5π</span>12</span>)</span></span>=<span>siny</span></span>
Use trig identity: <span><span>cos2</span>a=1−2<span><span>sin2</span>a</span></span>
<span><span>cos<span>(<span><span>10π</span>12</span>)</span></span>=<span>cos<span>(<span><span>5π</span>6</span>)</span></span>=<span><span>−<span>√3</span></span>2</span>=1−2<span><span>sin2</span>y</span></span>
<span><span><span>sin2</span>y</span>=<span><span>2+<span>√3</span></span>4</span></span>
<span><span>siny</span>=<span>sin<span>(<span><span>5π</span>12</span>)</span></span>=±<span><span><span>√<span>2+<span>√3</span></span></span>2</span></span></span>
