Answer:
(d) f(x) = (x − 3)^2(x − 2)(x − 1)
Step-by-step explanation:
In this context, a crossing of the axis at x=p means there is a factor of (x-p). A "touch" of the axis at x=q means there is a factor of (x -q)^2.
A crossing at x=1 and x=2, and a touch at x=3 means the factors are ...
f(x) = (x -1)(x -2)(x -3)^2 . . . . . matches the last choice
Answer:
if im correct it should be 40
Step-by-step explanation:
A Google or Bing search box can be your friend, if you don't have a calculator with inverse trig functions. Most calculators that have trig functions also have the inverse functions, usually after a 2nd or "shift" key. Often, there is a mode setting for degrees or radians.
arcsin(0.33) ≈ 19°
arccos(0.47) ≈ 62°
arctan(1.21) ≈ 50°
arcsin(0.82) ≈ 55°
Answer:
a) ![A=5000{(1.03)}^{t}](https://tex.z-dn.net/?f=A%3D5000%7B%281.03%29%7D%5E%7Bt%7D)
b) 5464 inhabitants.
Step-by-step explanation:
The formula used for compound interest becomes very helpful in this case.
![A=P{(1+r)}^{t}\\\\When:\\A = Final Value\\P = Initial Value\\r = Rate of Change (Decimal)\\t = Time (Years)](https://tex.z-dn.net/?f=A%3DP%7B%281%2Br%29%7D%5E%7Bt%7D%5C%5C%5C%5CWhen%3A%5C%5CA%20%3D%20Final%20Value%5C%5CP%20%3D%20Initial%20Value%5C%5Cr%20%3D%20Rate%20of%20Change%20%28Decimal%29%5C%5Ct%20%3D%20Time%20%28Years%29)
Knowing this, we can easily calculate the value for any year, counting from the original 5000.
From this formula, we can derive a specific one that will serve for any value of <em>t</em>.
a)
![A=5000{(1+0.03)}^{t}\\A=5000{(1.03)}^{t}](https://tex.z-dn.net/?f=A%3D5000%7B%281%2B0.03%29%7D%5E%7Bt%7D%5C%5CA%3D5000%7B%281.03%29%7D%5E%7Bt%7D)
b) Apply the formula:
![A=5000{(1.03)}^{3}\\A=5000(1.092727)\\A=5463.635=5464](https://tex.z-dn.net/?f=A%3D5000%7B%281.03%29%7D%5E%7B3%7D%5C%5CA%3D5000%281.092727%29%5C%5CA%3D5463.635%3D5464)
The town will have 5464 inhabitants.