Answer:
domain: x>3/5
Step-by-step explanation:
First we need to derive our function g(x) to get a new function g'(x)
To do this we will have to apply chain rule because we have an inner and outer functions.
Our G(x) = square root(3-5x)
Chain rule formula states that: d/dx(g(f(x)) = g'(f(x))f'(x)
where d/dx(g(f(x)) = g'(x)
g(x) is the outer function which is x^1/2
f(x) is our inner function which is 3-5x
therefore f'(x)= 1/2x^(-1/2) and f'(x) = -5
g'(f(x)) = -1/2(3-5x)^(-1/2)
Applying chain rule then g'(x) = 1/2 (3-5x)^(-/1/2)*(-5)
But the domain is the values of x where the function g'(x) is not defined
In this case it will be 3-5x > 0, because 3-5x is a denominator and anything divide by zero is infinity/undefined
which gives us x >3/5
<span>Answer: a) Greater than or equal to 38 feet
b)Since there is no restriction on the perimeter there exists many possible values for the length of the deck.
Explanation: Given that the width of the deck is 29 ft.
and the perimeter of the deck is at least 134 ft.
134 = 2(length + width)
134 = (2 x length) + (2 x 29)
134 = (2 x length) + 58
2 x length = 134 - 58
2 x length = 76
length = 76 / 2
length = 38 ft
Thus, the inequality will be:
a)Length ≥ 38 ft
b)since there is no restriction on the perimeter there exists many possible values for length of deck.</span>
How did who figure out what answer?
Answer:
Domain: all real numbers. Range: (-∞, 2000]
Step-by-step explanation:
f(x)=2.5x is a simple "ramp" function, a linear function and a polynomial. As such, its domain contains "all real numbers." That value 800 defines the largest value that this f(x) can have: f(800) = 2.5(800) = 2000.
Thus, the range is "all real numbers from -∞ through and including 2000."
