2^3 x 2^4 = 2^(3 + 4) = 2^7
Answer:
b^(m-n)
Step-by-step explanation:
The new period is <span>
2/3 π</span>
.
The period of the two elementary trig functions, <span>sin<span>(x)</span></span><span> and </span><span>cos<span>(x)</span></span><span> is </span><span>2π</span><span>.
</span>
If we multiply the input variable by a constant has the effect of stretching or contracting the period. If the constant, c>1 then the period is stretched, if c<1 then the period is contracted.
We can see what change has been made to the period, T, by solving the equation:
<span>cT=2π</span>
What we are doing here is checking what new number, T, will effectively input the old period, 2π, to the function in light of the constant. So for our givens:
<span>3T=2π</span>
<span>T=2/3 π</span>
Other method to solve this;
<span><span>sin3</span>x=<span>sin<span>(3x+2π)</span></span>=<span>sin<span>[3<span>(x+<span><span>2π/</span>3</span>)</span>]</span></span>=<span>sin3</span>x</span>
This means "after the arc rotating three time of <span>(x+<span>(2<span>π/3</span>)</span>)</span>, sin 3x comes back to its initial value"
So, the period of sin 3x is <span><span>2π/</span>3 or 2/3 </span>π.
Answer: The walking speed is 4.2 feet per second.
Step-by-step explanation:
If your walking speed is S, then we can use the relation:
Time = distance/speed.
in the moving sidewalk the speed is S + 1.8ft/s.
moving forward:
speed = S + 1.8ft/s
Distance = 100 feet
Time = T
T = 100ft/(S + 1.8ft/s)
moving in the opposite direction (now the velocity of the moving sidewalk must be subtracted)
speed = S - 1.8ft/s
distance = 40 feet
time = T
T = 40ft/(S - 1.8ft/s)
Then we have two equations:
T = 100ft/(S + 1.8ft/s)
T = 40ft/(S - 1.8ft/s)
We can replace T in the second equation by the expression in the first one:
100ft/(S + 1.8ft/s) = 40ft/(S - 1.8ft/s)
now we can solve it for S.
100ft*(S - 1.8ft/s) = 40ft*(S + 1.8ft/s)
100ft*S - (100ft*1.8ft/s) = 40ft*S + (40ft*1.8ft/s)
100ft*S - 40ft*S = (100ft*1.8ft/s)+ (40ft*1.8ft/s)
S*(100ft - 40ft) = S*60ft = (100ft*1.8ft/s)+ (40ft*1.8ft/s)
S = ( (100ft*1.8ft/s)+ (40ft*1.8ft/s) )/60ft = (252ft^2/s)/60ft = 4.2 ft/s
The walking speed is 4.2 feet per second.
Acute, Meaning less than 90 degrees.