Answer:
(-2,-6)
-2
Step-by-step explanation:
To get the vertex take the number that's in the parathenses with the x and flip it's sign (in this case to a negative) which means we have
-2
this is the x coordinate of the vertex.
Next take the number that's being subtracted (or added) on the outside and leave that as is (-6)
This is the y coordinate
which means we have (-2,-6)
the axis of symmetry is just the x coordinate of the graph
which is -2
A) Demand function
price (x) demand (D(x))
4 540
3.50 810
D - 540 810 - 540
----------- = -----------------
x - 4 3.50 - 4
D - 540
----------- = - 540
x - 4
D - 540 = - 540(x - 4)
D = -540x + 2160 + 540
D = 2700 - 540x
D(x) = 2700 - 540x
Revenue function, R(x)
R(x) = price * demand = x * D(x)
R(x) = x* (2700 - 540x) = 2700x - 540x^2
b) Profit, P(x)
profit = revenue - cost
P(x) = R(x) - 30
P(x) = [2700x - 540x^2] - 30
P(x) = 2700x - 540x^2 - 30
Largest possible profit => vertex of the parabola
vertex of 2700x - 540x^2 - 30
When you calculate the vertex you find x = 5 /2
=> P(x) = 3345
Answer: you should charge a log-on fee of $2.5 to have the largest profit, which is $3345.
Answer:
Guo Qi requires 75 days to watch videos on Khan Academy.
Step-by-step explanation:
We are given the following in the question:
Number of videos watched by Guo Qi each day = 15
Average length of each video = 8 minutes
Total minutes of video = 9000 minutes
Total number of videos to be watched =
Guo Qi needs to watch 1125 videos.
Number of days required =
Guo Qi requires 75 days to watch videos on Khan Academy.
Answer:
Step-by-step explanation:
We have been given a function 
. We are asked to find the zeros of our given function.
To find the zeros of our given function, we will equate our given function by 0 as shown below:
Now, we will factor our equation. We can see that all terms of our equation a common factor that is 
.
Upon factoring out , we will get:
Now, we will split the middle term of our equation into parts, whose sum is 
and whose product is 
. We know such two numbers are 
.
Now, we will use zero product property to find the zeros of our given function.
Therefore, the zeros of our given function are .
Area of a semicircle is 1/2* πr^2
Area of a square is s^2
Square’s area: 4mm^2
The radius is 3mm
Plug into the equation
1/2* π(3^2)
1/2* π(9)
We can use 3.14 as an estimate of pi
1/2*28.26
14.13mm^2
Now just add them both
Total area 18.13mm^2
