Answer:
<h2>It must be shown that both j(k(x)) and k(j(x)) equal x</h2>
Step-by-step explanation:
Given the function j(x) = 11.6
and k(x) = 
, to show that both equality functions are true, all we need to show is that both j(k(x)) and k(j(x)) equal x,
For j(k(x));
j(k(x)) = j[(ln x/11.6)]
j[(ln (x/11.6)] = 11.6e^{ln (x/11.6)}
j[(ln x/11.6)] = 11.6(x/11.6) (exponential function will cancel out the natural logarithm)
j[(ln x/11.6)] = 11.6 * x/11.6
j[(ln x/11.6)] = x
Hence j[k(x)] = x
Similarly for k[j(x)];
k[j(x)] = k[11.6e^x]
k[11.6e^x] = ln (11.6e^x/11.6)
k[11.6e^x] = ln(e^x)
exponential function will cancel out the natural logarithm leaving x
k[11.6e^x] = x
Hence k[j(x)] = x
From the calculations above, it can be seen that j[k(x)] = k[j(x)] = x, this shows that the functions j(x) = 11.6 and k(x) = are inverse functions.
Answer:
Step-by-step explanation:
The cost of an adult ticket to the show is $5.5
The cost of a student ticket to the show is $4.25
A family is purchasing 2 adult tickets and 3 student tickets. This means that the total cost of 2 adult tickets would be
2 × 5.5 = $11
It also means that the total cost of 3 student tickets would be
3 × 4.25 = $12.75
The total cost of 2 adult tickets and 3 student tickets would be
11 + 12.75 = $23.75
If the family pays $25, the exact amount of change they should receive is
25 - 23.75 = $1.25
Answer:
The nth term of the sequence is
<h2>5 + 2n</h2>
Step-by-step explanation:
The sequence above is an arithmetic sequence
For an nth term in an arithmetic sequence
A(n) = a + ( n - 1)d
where a is the first term
n is the number of terms
d is the common difference
From the question
a = 7
d = 9 - 7 = 2 or 11 - 9 = 2
So the nth term for the sequence is
A(n) = 7 + ( n - 1)2
= 7 + 2n - 2
<h3>A(n) = 5 + 2n</h3>
Hope this helps you
Answer:
Weight of the truck=9408 N
Step-by-step explanation:
Boat is experiencing the buoyant force as it is in the water and is sinking
According to the force balance in y direction. As both is floating, two forces balance each other:
where:
is the buoyant force
is the weight=mg
Eq (1)
Buoyant force is equal to the mass of water displaced * gravitational acceleration.
Taking density of water to be 1000 Kg/m^3
From Eq(1):
Weight of the truck=9408 N
The answer is C. The numerator 7x+14 can be factored as 7(x+2). The denominator 2x^2+2x-6 can be factored as (x+2)(2x-3). The greatest common divisor of 7(x+2) and (x+2)(2x-3) is obviously x+2, which is contained in both of the two expressions.
