I just realized I forgot a whole unit we did this year, but a(n)=5n-12
is the explicit form if that helps at all
You always start by simplifying.
6b-49=2<span>(</span>b-3) becomes 6b-49=2b-6
From there you can group the b's together by subtracting 2b from both sides, leaving you with 4b-49=-6
Now you can get the b's alone by adding 49 (to cancel out -49) to both sides, giving you 4b=43, You're still trying to get b by itself, so what you'll do is divide both sides by 4, giving you b=10.75
F(x)=12,000(1.08)^x
The answer is the first equation.
The equation increases so 1 is added to 0.08 (8%).
Answer:
3676.44 rad/min
Step-by-step explanation:
It is a problem about the angular speed of the car's wheel.
You can calculate the angular speed by using the following formula, which relates the tangential speed of the wheels (the same as the speed of the car) with the angular speed:
( 1 )
v: speed of the car = tangential speed of the wheels = 47mph
r: radius of the wheels = 27/2 in = 13.5 in
you change the units of the speed:
next, you replace the values of v and r in the equation (1):
Then, the car's tires are turning with an angular speed of 3676.44 rad/min
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>
