Answer:
7 days
Step-by-step explanation:
Let us represent the number of days = a
Kilani currently consumes 1200 calories a day and will increase that number by 100 calories each day.
1200 calories + 100 calories × a
1200 + 100a
Adrian currently consumes 3230 calories a day and will decrease that number by 190 each day.
3230 calories - 190 calories × a
3230 - 190a
The number of days that they would be consuming the same number of calories =
Kilani = Adrian
1200 + 100a = 3230 - 190a
Collect like terms
190a + 100a = 3230 - 1200
290a = 2030
a = 2030/290
a = 7 days
Therefore, the would be consuming the same number of calories in 7 days
To find the x value of the max of
f(x)=ax^2+bx+c
when a is negative (if a is positive, we find the minimum)
we do
-b/2a is the x value
to find the y value, we just sub that x value back into the function
so
R(x)=-0.2x^2+60x+0
-b/2a=-60/(2*0.2)=-60/-0.4=150
x value is 150
make 150 units
sub back to find revenue
R(150)=-0.2(150)^2+60(150)
R(150)=-0.2(22500)+9000
R(150)=-4500+9000
R(150)=4500
max revenue is achieved when 150 units are produced yeilding $4500 in revenue
the Answer is .......... ok
Answer:
Domain -∞ < x < +∞
Range f(x) ≤ - 4
Step-by-step explanation:
The given quadratic function is f(x) = - 4 (x + 1)² - 4
Now, we have to find the domain and range of the quadratic function.
Now, it is clear from the given function that f(x) will have real value for all real value of x.
Therefore, the domain of the function is -∞ < x < +∞ (Answer)
Now, (x + 1)² is always ≥ 0
i.e. (x + 1)² ≥ 0
⇒ - 4 (x + 1)² ≤ 0 {Since the inequality sign changes for multiplying both sides of the equation by a negative term}
⇒ - 4 (x + 1)² - 4 ≤ - 4
⇒ f(x) ≤ - 4
Therefore, this is the required range of the function f(x). (Answer)
