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: Your answer will be 41.
Step-by-step explanation: All you would need to do to solve is input -2 in for x in the original equation and then solve the subsequent equation. After solving you will get 41.
Answer:
Step-by-step explanation:
If the Australian dollar weakens by 5% over the next year, then the A. L will need 5% more Australian dolar to buy Japanese yen. Calculate exchange rate after oe year as follows:
Thus, the exchange rate over the next year is ¥64.495/AUD
I think it can be written as 7×7×7×7×7
First of all, you organize all of the info that you're given. We know that the points are (x, y). Therefore, 8 is x and 5 is y. 5/7 is your m, since m represents the slope.
x = 8
y = 5
m = 5/7
b = y-intercept, which is the missing info
Then, you put it into a multi-step equation.
The slope equation formula is y = mx + b. Now, we solve for the equation.
y = mx + b
5 = 5/7(8) + b (missing info is the y-intercept, so that's why it stays as "b")
5 = 5/7(8/1) + b (any whole number converted into fractions always have a denominator of 1)
5 = 40/7 + b At this point, since 5 as a fraction is 5/1, you need to
-40/7 -40/7 + b multiply the numerator and denominator by 7 so that
_____________ you're able to subtract 40/7 from it. So, 5 x 7 = 35 and
1 x 7 = 7, giving you the fraction of 35/7. 35/7 - 40/7 =
-5/7.
-5/7 = b
Finally, you've got all the info you need to write the equation. As a result, you just substitute the letters with the numbers:
m = 5/7
b = -5/7
y = 5/7x - 5/7
I hope I helped and that you understood my explanations! :)