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What is the area of a rectangle with length 5 inch and width 2.7 inch
1 answer:
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Answer:
The function h (x) = StartFraction 11 Over x minus 4 EndFraction
has the domain of h (x) = ( - ∞, 4) U (4, ∞ ) which is same as the
domain of (m ∘ n)(x) = ( - ∞, 4) U (4, ∞ ).
Step-by-step explanation:
m (x) = StartFraction x + 5 Over x minus 1 and n(x) = x – 3
As m (x) could be written as:
n(x) = x – 3
(m ∘ n)(x) = m(n(x)) = m(x – 3)
=
=
In order to find the domain of (m ∘ n)(x) = , we need to
make sure that denominator can not be zero,
So,
x - 4 = 0
x = 4
So, our domain can be anything except for 4.
Hence, Domain = D = ( - ∞, 4) U (4, ∞ )
Now, compare the domain of (m ∘ n)(x) i.e D = ( - ∞, 4) U (4, ∞ ) with all the options:
Option A: h (x) = x + 5 / 11
Option A has the Domain of h (x) = Set of all real numbers
So, Option A is false.
Option B: h (x) = 11 / x - 1
x - 1 = 0
x = 1
Option B has the domain of h (x) = ( - ∞, 1) U (1, ∞ )
So, Option B is false.
Option C: h (x) = 11 / x - 4
x - 4 = 0
x = 4
Domain C has the domain of h (x) = ( - ∞, 4) U (4, ∞ )
So, Option C is true.
Option D: h (x) = 11 / x - 3
x - 3 = 0
x = 3
Option D has the domain of h (x) = ( - ∞, 3) U (3, ∞ )
So, option D is also false.
Hence, only option C is true as the option C i.e. h (x) = StartFraction 11 Over x minus 4 EndFraction has the domain of h (x) = ( - ∞, 4) U (4, ∞ ) which is same as the domain of (m ∘ n)(x) = ( - ∞, 4) U (4, ∞ ).
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Answer:
a)
b)
The total amount accrued, principal plus interest, from compound interest on an original principal of $ 4,200.00 at a rate of 3.6% per year compounded 12 times per year over 10 years is $5667.28.
Step-by-step explanation:
a. Write the function that represents the value of the account at any time, t.
The function that represents the value of the account at any time, t
where
P represents the principal amount
r represents Annual Rate
n represents the number of compounding periods per unit t, at the end of each period
t represents the time Involve
b) What will the value be after 10 years?
Given
The principal amount P = $4200
Annual Rate r = 3.6% = 3.6/100 = 0.036
Compounded monthly = n = 12
Time Period = t
To Determine:
The total amount A = ?
Using the formula
substituting the values
$
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 4,200.00 at a rate of 3.6% per year compounded 12 times per year over 10 years is $5667.28.