Stan wants to add trim all around the edge of a rectangular tablecloth that measures 5 feet long by 7 feet wide. The perimeter o
1 answer:
You might be interested in
Always remember two steps while finding the domain of composite function.
1) <em>First find the domain of inside/ input function( A common mistake is to skip this point).</em>
2) <em>Find the domain of new function after performing the composition.</em>
In our case, the given functions are
,
Now,
1) (f ° g)(x)
= f[g(x)]
=f[x²-81]
(this is (f ° g)(x) function)
Now, its domain
First find the domain of input function which is x²-81, its domain is the set of all real numbers.
domain of new function after performing composition which is .
x²-81=0 ⇒ (x-9)(x+9)=0
(x-9)=0 , (x+9)=0
x=9 , x=-9 (exclude these points from the domain because anything/0 does not exist in math)
So, the Domain of Composite function (f °g)(x) is the set of all real numbers except x=9, x=-9.
Domain= (-infinity, -9)U(-9, 9)U(9, infinity)
2) (g °f)(x)
= g[f(x)]
= g[3/x]
= (3/x)² -81
= 9/x² -81
First find the domain of input function 3/x which is set of all real numbers except x=0
Domain of above function after performing composition is set of all real numbers except x=0
So, the domain of (g° f)(x) is the set of all real numbers except x=0.
Domain= (-infinity, 0)U(0, infinity)
Answer:
a. $ 381.969,
b. $ 369.171,
c. Kings Savings
d. Reliability.
Step-by-step explanation:
∵ Amount formula in compound interest,
And, amount formula in continuously,
,
Where,
P = principal amount,
r = rate per periods,
t = number of periods,
a. In State bank,
P = $ 9000, r = 2.1% = 0.021, t = 2 years,
Also, interest earned compound annually,
Thus, amount,
So, interest earned = A - P = 9381.969 - 9000 = $ 381.969,
b. In Kings Savings,
P = $ 9000, r = 2.01% = 0.0201, t = 2 years,
Also, interest earned compound continuously,
Thus, amount,
So, interest earned = A - P = 9369.171 - 9000 = $ 369.171,
c. ∵ 369.171 > 381.969
Thus, King saving pays higher interest.
d. Since, the other factors might affect Whitney's choice besides interest would be reliability.
Answer:
the time taken for the radioactive element to decay to 1 g is 304.8 s.
Step-by-step explanation:
Given;
half-life of the given Dubnium = 34 s
initial mass of the given Dubnium, m₀ = 500 grams
final mass of the element, mf = 1 g
The time taken for the radioactive element to decay to its final mass is calculated as follows;
Therefore, the time taken for the radioactive element to decay to 1 g is 304.8 s.