Here we have a problem of maximization and quadratic equations.
The unit prize that maximizes the revenue is $1,500, and the maximum revenue is $18,000.
We know that the revenue equation is:
R(P) = - 8p^2 + 24,000p
Where the variable p is the price.
Now we want to find the value of p that maximizes the revenue.
To do it, we can see that the revenue equation is a quadratic equation with a negative leading coefficient.
This means that the arms of the graph will go downwards, then the maximum point of the graph will be at the vertex.
Remember that for an equation like:
y = a*x^2 + b*x+ c
The x-value of the vertex is at:
x = -b/(2*a)
Then for the equation:
R(P) = - 8p^2 + 24,000p
The vertex is at:
p = -(24,000)/(2*-8) = 1,500
The value of p that maximizes the revenue is p = $1,500
To get the maximum revenue, we need to evaluate the revenue equation in that p value.
R(1,500) = - 8*(1,500)^2 + 24,000*1,500 = 18,000
And the revenue equation is in dollars, then the maximum revenue is 18,000 dollars.
If you want to learn more, you can read:
https://brainly.com/question/18269297
p = 1500 $ the unit price
R(p) = 18000000 $ maximum revenue
We will use two different procedures to calculate the maximum revenue.
That is equivalent to solve the problem and after that to test the solution
The first one is:
R(p) = - 8*p² + 24000*p
we realize that R(p) is a quadratic function ( a parabola) of the form:
y = a*x² + b*x + c ( c = 0 in this case)
We also know that as the coefficient of p² is negative the parabola opens downwards then the vertex is a maximum value for R(p), and the x coordinate of p is:
x = p = - b/2*a then by substitution
p = - ( 24000)/ 2 ( - 8)
p = 1500 $ and for that value of p
R(p) = - 8 ( 1500)² + 24000* (1500) = - 18000000 + 36000000
R(p) = 18000000 $
The second procedure is solving with the help of derivatives.
R(p) = - 8*p² + 24000*p
Tacking derivatives on both sides of the equation we get:
R´(p) = -16p + 24000
If R´(p) = 0 then -16p + 24000 = 0
p = 24000/ 16 p = 1500
if we check for the second derivative
R´´(p) = -16 -16 < 0 therefore there is a maximum value for R(p) when p = 1500, and that value is:
By substitution in R(p)
R(p) = -8 *(1500)² + 24000* 1500
R(p) = - 18000000 + 36000000
R(p) = 18000000 $
What is the domain of the function in the graph?
Answer:
1≤x≤5
Step-by-step explanation:
The domain is the values for the inputs
The domain goes from 1 to 5
1≤x≤5
Factorise 24e^2-28e-12
Answer:
4(2e - 3)(3e + 1)
Step-by-step explanation:
Given
24e² - 28e - 12 ← factor out 4 from each term
= 4(6e² - 7e - 3) ← factor the quadratic
Consider the factors of the product of the e² term and the constant term which sum to give the coefficient of the e- term.
product = 6 × - 3 = - 18 and sum = - 7
The factors are - 9 and + 2
Use these factors to split the e- term
6e² - 9e + 2e - 3 ( factor the first/second and third/fourth terms )
= 3e(2e - 3) + 1 (2e - 3) ← factor out (2e - 3) from each term
= (2e - 3)(3e + 1)
Then
24e² - 28e - 12 = 4(2e - 3)(3e + 1) ← in factored form
In 1815, Sophie Germain won a mathematical prize given by the Institut de France for her work on the theory of elasticity. The prize was a medal made of 1 kilogram of gold. How much is the medal worth today in U.S. dollars and in euros
Answer:
gold price : $58.72/gram
$58,720 per kilo(1000) grams
Step-by-step explanation:
[tex] \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = what[/tex]
Answer I'll make and mark as brainlist.
Answer Fast.
Post on - 2 Aug 2021
8.113 as a fraction PLEASE HELPP
Answer:
8 113/1000(as a mixed number) 8113/1000(as an improper fraction)
Step-by-step explanation:
1. Convert 0.113 to a fraction...113/1000
2. As there is no further simplification needed, add 8 to 113/1000....8 113/1000
3. To convert 8 113/1000 from a mixed number to an improper fraction, multiply 8 (the whole number) and 1,000(the denominator)...8,000. Then add 113 (the numerator) to 8,000...8113. After that, you put 8113 over the denominator of the previous mixed number, getting 8113/1000 as the improper fraction.
Explain how to graph a scatterplot and its regression line using a regression calculator.
Answer:
Before entering data into the regression calculator, it is important to determine which variable should be associated with the x-axis and which with the y-axis. Enter the data pairs. Press the Linear Regression button to generate the regression line.
Step-by-step explanation:
edg 2022
The expression 2(l + w) is used to calculate the perimeter of a rectangle, where l is length and w is width. If the length is Fraction 2 over 5 unit and the width is Fraction 1 over 5 unit, what is the perimeter of the rectangle in units?
Fraction 3 over 5 unit
1 unit
1Fraction 1 over 5 units
2Fraction 3 over 5 units
Answer:
Step-by-step explanation:
L = ⅖ unit
W = ⅕ unit
L+W = ⅗ unit
Perimeter = 2×⅗ = 6/5 units = 1⅕ units
Answer:
L = ⅖ unit
W = ⅕ unit
L+W = ⅗ unit
Perimeter = 2×⅗ = 6/5 units = 1⅕ units
Step-by-step explanation:
Simplify i12
A.-1
B.-i
C.i
D.1
Answer:
D 1
Step-by-step explanation:
i^12
We know i^4 = 1
Rewriting
i^4^3
1^3
1
Answer:
part 1- D. 1
part 2- Square root of -144 =12i
Step-by-step explanation:
Got them correct
You pay $16 to buy four pizzas, How much did each pizza cost?
Answer:
16 dollars = 4 pizzas
4 dollars = 1 pizza
Each pizza costs 4 dollars.
Let me know if this helps!
Answer: $4
Step-by-step explanation:
16 divided by 4, equals 4.
Which box holds more popcorn?
Answer:
Amanda's popcorn container holds more popcorn
Step-by-step explanation:
First we'll have to find the volume.
The Volume helps us determine which is bigger.
Step 1
We'll find Amanda's popcorn container
10cm*10cm*13.5cm=1350cm
Step 2
We'll find Mary's popcorn container
8cm*8cm*20cm=320cm
Step 3
Since Amanda's popcorn container has 1350cm (volume) and Mary's popcorn container has 320cm (volume) we'll have this. 1350cm>320cm. We can determine the Amanda's popcorn container has holds more,
Final Answer
Amanda's popcorn container holds more popcorn
PLEASE HELP! ASAP Thanks xoxo!
Step-by-step explanation:
For the question in:First Picture -Answer is 115°
Second Picture-Answer is Definition of parallelogram
Third Picture -Answer is 114°
Write each decimal as a fraction or mixed number in simplest form.
1 3/8
3/2
Step One: 1 3/8, transform the number into a improper fraction:
To have a mixed number in to a improper fraction, you need to use addition and multiplication. For 1 3/8, We first multiply the denominator (8, also know to be the bottom number of the fraction) to the whole number (1). 8x1= 8NOTE: The original denominator (8) will be use for are improper, again playing as the denominator, we only multiply the denominator for the numerator (which is the top number of a fraction).After multiplying, we'll add are product with the numerator (3) for the process. 8+3= 12 Now we have both numerator and denominator for 1 3/8, we can create the improper fraction. 12 as the numerator and 8 as the denominator. 12/8We still need to simplify the number. To that, we need the biggest whole number, or rather I call it the lowest number, that can be divide both in 12 and 8. 4 can be divide by both number so: 12/4= 3 and 8/4=2Now 3 is are simplify numerator and 2 is are simplify denominator.Which group of numbers is ordered from LEAST to GREATEST?
Select one:
A.
246,263, 250,100, 250,000
B.
250,100, 246,263, 250,000,
C.
246,263, 250,000, 250,100,
D.
250,100, 250,000, 246,263,
Nicole took a taxi from her house to the airport. The taxi company charged a pick-up fee of $2.90 plus $1.75 per mile. The total fare was $44.90, not including the tip. Write and solve an equation which can be used to determine xx, the number of miles in the taxi ride.
9514 1404 393
Answer:
24 miles
Step-by-step explanation:
The total fare is the sum of the pickup fee and the mileage charge. For xx miles, the mileage charge will be 1.75xx, so the total is ...
1.75xx +2.90 = 44.90 . . . equation for xx
1.75xx = 42.00 . . . . . subtract 2.90
xx = 24 . . . . . . . . . divide by 1.75
The number of miles in Nicole's taxi ride was 24.
If 2m−6=8m
2
m
-
6
=
8
m
then 3m=
3
m
=
A. 3
B. -1
C. -3
D. -6
E. I don't know.
Answer:
3m = -3
Step-by-step explanation:
2m−6=8m
Subtract 2m from each side
2m−6-2m=8m-2m
-6 = 6m
Divide by 6
-6/6 = 6m/6
-1 = m
3m = 3(-1) = -3
2m - 6 = 8m
2m - 8m = 6
-6m = 6
m = -6/6
m = -1
Hence, the answer is -1Solving a word problem on proportions using a unit rate
Lucy made $95 for 5 hours of work.
At the same rate, how much would she make for 13 hours of work?
sl
X Х
5
?
Answer:
$247
Step-by-step explanation:
$95 = 5 h
1 h = 95 ÷ 5 = $19/h
$19 × 13h = $247
she would make $247 after 13 hours of work.
Change the word phrase to an algebraic expression. Use x as the variable to represent the number.
16 subtracted from a number
Let x = the number.
16 subtracted from a number can be written as…
Answer:
I think the answer is
x-16
since 16 is subtracted from x.
I hope this helps
Consider the line L(t)=⟨5+t,1+5t⟩. Then:
Choose perpendicular, parallel or neither. (PS. Answers below may not be true.)
If L(t) = ⟨5 + t, 1 + 5t⟩, then the tangent vector to L(t) is
dL/dt = ⟨1, 5⟩
Any line parallel to L(t) will have the same tangent vector, up to some scalar factor (that is, if the tangent vector is a multiple of ⟨1, 5⟩).
Any line r(t) with tangent vector T(t) = dr/dt that is perpendicular to L(t) will satisfy
T(t) • ⟨1, 5⟩ = 0
• r(t) = ⟨-5, -2t, 1 - 10t⟩ is parallel to L(t) because its tangent vector is
T(t) = ⟨-2, -10⟩ = -2 ⟨1, 5⟩
• r(t) = ⟨1 + 1.5t, 3 + 7.5t⟩ is parallel to L(t) because
T(t) = ⟨1.5, 7.5⟩ = 1.5 ⟨1, 5⟩
• r(t) = ⟨-2 - t, 2 - 2t⟩ is neither parallel nor perpendicular to L(t) because
T(t) = ⟨-1, -2⟩ ≠ k ⟨1, 5⟩
for any real k (in other words, there is no k such that -1 = k and -2 = 5k), and
⟨-1, -2⟩ • ⟨1, 5⟩ = -1 - 10 = -11 ≠ 0
• r(t) = ⟨3 + 15t, -3t⟩ is perpendicular to L(t) because
T(t) = ⟨15, -3⟩
and
⟨15, -3⟩ • ⟨1, 5⟩ = 15 - 15 = 0
Solve the equation.
0.50x +0.45(50) = 48.5
x=?
Answer:
x=52 Here is y
Step-by-step explanation:
please solve it fastand give the correct answer pleaseeeeee
Answer:
a. False b. True c. True d. False e. False
Step-by-step explanation:
Please find the answer !
Answer:
ring volume is 12cm3
Step-by-step explanation:
Lr ccm=volume of water and ring - Volume of water
ring cubic centimeters =x
x=9.2cm*4.5cm*7cm - 8.8cm*4.5cm*7cm
x=289.2cm3 - 277.2cm3
x=12cm3
A macaroni and cheese recipe calls for 2/5 of a 2 1/2 pound a block of cheese. How many pounds are needed?
I
2/5 of 2.5. = 2x2.5 / 5x1 = 5/5 = 1 pound
A(6, -5) and B(-1, 2) in the ratio of 2:5
Answer:
p(x,y)= (4,-3)
Step-by-step explanation:
all explainations are in the picture below.
Derivatives concept:
Exercise "position and instantaneous velocity"
(Full development)
(A) The blue line has a slope of 5/2, red has slope 4/4 = 1, and purple has slope 3/9 = 1/3.
To find the slope, take any two points (a, b) and (c, d) on the line, then
slope = (d - b)/(c - a)
i.e. the ratio between the changes in the y and x coordinates.
(B) Each line has equation
• blue: y = 5/2 x
• red: y = x
• purple: y = 1/3 x
This follows from the general equation for a line with slope m and y-intercept b,
y = mx + b
or from the more general equation for a line with slope m passing through a point (a, b),
y - b = m (x - a)
(C) Consider the blue line. If you take units into account, its slope is
(5 units of distance)/(2 units of time) = 5/2 (units of distance/time)
which means, per unit time, some object travels a 5/2 units of distance, and this is the definition of speed.
(D) The competitor with the blue line, Mary, would win the race because their speed is the highest (5/2 > 1 > 1/3).
(E) Average velocity is defined as
v (ave) = ∆d/∆t = (change in distance)/(change in time)
At time 0, no one has moved yet. At time 4,
• Mary has covered a distance of 5/2 × 4 = 10, giving her an average velocity of (10 - 0)/(4 - 0) = 5/2
• Mike has covered a distance of 4, so his average velocity is (4 - 0)/(4 - 0) = 1
• Sam has covered a distance of 1/3 × 4 = 4/3, so his average velocity is (4/3 - 0)/(4 - 0) = 1/3
It's not a coincidence that the average velocities are the same as the slopes, because each racer travels at a constant speed.
(F) The racers' instantaneous velocities are the same as their respective average velocities, again because they are each moving at a constant speed.
Which of the following ordered pairs is a solution of the function f(x)=3x-1
Geometry please help me!In the figure below, what value of x will satisfy the midsegment theorea? X=
Answer:
x=30.5
Step-by-step explanation:
Using midsegment 's theorea:
[tex]2=\dfrac{RG}{RS} =\dfrac{RH}{RQ} =\dfrac{GH}{SQ} \\\\4x-65=2x-4\\\\2x=61\\\\x=\dfrac{61}{2} \\\\x=30.5\\[/tex]
Find the value of each expression.
30 ÷ 3 × 2
Answer:
Step-by-step explanation:
1) First division has to be done.
2) After that multiplication has to be done.
30 ÷ 3 * 2 = 10 * 2
= 20
Answer:
20
Step-by-step explanation:
30 ÷ 3 × 2
(Since it’s division and multi platoon, we just go left to right)
10 × 2
20
What is the value of x in the geometric sequence x,3,−1/3
Answer:
x=27
Step-by-step explanation:
the answer is proved in the diagram above
The value of x is 27
What is Geometric progression?A geometric progression is a special type of progression where the successive terms bear a constant ratio known as a common ratio. It is also known as GP. The GP is generally represented in form a, ar, ar2.... where a is the first term and r is the common ratio of the progression. The common ratio can have both negative as well as positive values. To find the terms of a geometric series, we only need the first term and the constant ratio.
The geometric progression is of two types. They are
finite geometric progression andinfinite geometric progression.Given:
x,3,−1/3
First term, a
second term
ar= 3
a= 3/r
third term
ar² = -1/3
a= -1/3r²
So,
3/r= - 1/3r²
9r= 1
r= 1/9
So,
ar= 3
a= 27.
Learn more about Geometric progression here:
https://brainly.com/question/4853032
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What is the relationship between the value of the digit 3 in 4,231 and in the value of the digit 3 in the number 3,421?
A.
In 4,231, the value of the digit 3 is
1
10
the value of the digit 3 in 3,421.
B.
In 4,231, the value of the digit 3 is 10 times the value of the digit 3 in 3,421.
C.
In 4,231, the value of the digit 3 is
1
100
the value of the digit 3 in 3,421.
D.
In 4,231, the value of the digit 3 is 100 times the value of the digit 3 in 3,421.
Answer D
Step-by-step explanation:
looks right
PLEASE HELP i’ll give brainliest to best and correct answer
Step-by-step explanation:
|- 9| + |- 3|
9 + 3
12
I hope this answers your question
