Answer:
x =41.18114952
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
We know the hypotenuse and adjacent sides
cos theta = adjacent / hypotenuse
cos x = 14.3/19
taking the inverse cos of each side
cos^-1 (cos x) = cos ^-1 ( 14.3/19)
x =41.18114952
The answer is 10x^4 - 2x ^3
<h3>
Answer: C) 3</h3>
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Explanation:
f(x) is the outer function, so the final output -8 corresponds to f(x)
We see that f(-4) = -8 in the first column of the table. I'm starting with the output and working my way backward to get the input. So we started with -8 and worked back to -4.
Then we move to the g(x) function to follow the same pattern: start with the output and move to the input. We start at -4 in the g(x) bubble and move to 3 in the x bubble.
In short, g(3) = -4
So,
f(g(x)) = f(g(3)) = f(-4) = -8
We see that x = 3 leads to f(g(x)) = -8
Answer: the expected population of the city in 30 years is 5470781
Step-by-step explanation:
The population growth is exponential. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
A = P(1 + r)^t
Where
A represents the population after t years.
t represents the number of years.
P represents the initial population.
r represents rate of growth.
From the information given,
P = 3.5 × 10^6
r = 1.5% = 1.5/100 = 0.015
t = 30 years
Therefore,
A = 3.5 × 10^6(1 + 0.015)^30
A = 3.5 × 10^6(1.015)^30
A = 5470781
For this case we must find the inverse of the following function:
We follow the steps below:
Replace f(x) with y:
We exchange the variables:
We solve for "y":
Multiply by -2 on both sides of the equation:
We raise both sides of the equation to the square to eliminate the radical:
We subtract 3 from both sides of the equation:
We change y by f ^ {- 1} (x):
Answer:
