Using a linear function, we have that:
a) The amount of water in the aquarium at 0 minutes is of 300 liters.
b) As time increases, the amount of water decreases at a rate of 60 liters per minute.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = ax + b
In which:
- a is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
In this problem, we have that the y-intercept is of 300, hence the amount of water in the aquarium at 0 minutes is of 300 liters.
The amount <u>decreases 60 liters in a minute,</u> hence:
As time increases, the amount of water decreases at a rate of 60 liters per minute.
More can be learned about linear functions at brainly.com/question/24808124
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Answer:
6 cm by 17 cm
Step-by-step explanation:
The area is the product of the dimensions; the perimeter is double the sum of the dimensions.
So, we want to find two numbers whose product is 102 and whose sum is 23.
102 = 1·102 = 2·51 = 3·34 = 6·17
The last of these factor pairs has a sum of 23.
The dimensions are 6 cm by 17 cm.
Answer:
A.) gf(x) = 3x^2 + 12x + 9
B.) g'(x) = 2
Step-by-step explanation:
A.) The two given functions are:
f(x) = (x + 2)^2 and g(x) = 3(x - 1)
Open the bracket of the two functions
f(x) = (x + 2)^2
f(x) = x^2 + 2x + 2x + 4
f(x) = x^2 + 4x + 4
and
g(x) = 3(x - 1)
g(x) = 3x - 3
To find gf(x), substitute f(x) for x in g(x)
gf(x) = 3( x^2 + 4x + 4 ) - 3
gf(x) = 3x^2 + 12x + 12 - 3
gf(x) = 3x^2 + 12x + 9
Where
a = 3, b = 12, c = 9
B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)
To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula
Y = 3x + 3
X = 3y + 3
Make y the subject of formula
3y = x - 3
Y = x/3 - 3/3
Y = x/3 - 1
Therefore, g'(x) = x/3 - 1
For g'(12), substitute 12 for x in g' (x)
g'(x) = 12/4 - 1
g'(x) = 3 - 1
g'(x) = 2.
