An electronics store sells about 40 MP3 players per month for $90 each. For each $5 decrease in price, the store expects to sell 4 more MP3 players.
What value of x gives the maximum monthly revenue?
x =
How much should the store charge per MP3 player to maximize monthly revenue? Round your answer to the nearest dollar.
Answers
Step-by-step explanation:
Let's establish our equation first:
for every $5 decrease, there's an additional of 4 MP3 players sold.to get the monthly revenue, we need to multiple the cost of each player to the number of units sold\( \frac{40mp3}{month} \times \frac{90dollars}{mp3} = 3600 \frac{dollars}{month} \)
The equation above is for the basis month.
But the next month, we decreased the cost of mp3 player to sold 4 more units.
\( \frac{(40 + 4)mp3}{month} \times \frac{(90 - 5)dollars}{mp3} = 3740 \frac{dollars}{month} \)
And the next month, we decreased the cost again to gain 4 more additional units sold.
\( \frac{(40 + 4x)mp3}{month} \times \frac{(90 - 5x)dollars}{mp3} = revenue per \: month\)
If we substitute x with 2, we get 3840.
If we substitute x with 3, we get 3900.
If we substitute x with 4, we get 3920.
If we substitute x with 5, we get 3900.
At fifth time we decreased our price, we also got lesser revenue.
Therefore, our highest revenue would be $3,900.00 per month at our 4th price decrease with a price of $70.00.
Related Questions
find the point(s) on the ellipsoid x 2 4y 2 z 2 = 9 where the tangent plane (a) is horizontal; (b) is perpendicular to the line with parametric equation l(t) = th−4, 8, −2i h2, 1, 3i.
Answers
The point(s) on the ellipsoid x 2 4y 2 z 2 = 9 where the tangent plane is horizontal is (3h/4 - 3, 6, 7/4) and (3h/2 - 6, 12, 11/2) and tangent is perpendicular to the line (0, 0, -3/2).
The gradient vector of the ellipsoid is given by: grad(f) = (2x, 8y, 2z)
Since the ellipsoid equation is x^2/9 + y^2/4 + z^2/9 = 1, we can substitute the parametric equation of the line into the ellipsoid equation and solve for t to get:
(2(th - 4))^2/9 + (8(2t))^2/4 + (2(-2t))^2/9 = 1
Simplifying the equation, we get:
36t^2 - 64t + 27 = 0
Solving this quadratic equation, we get two possible values of t:
t = 3/4 or t = 3/2
Substituting the value of t = 3/4 into the parametric equation of the line, we get:
l(3/4) = (3h/4 - 3, 6, 7/4)
Similarly, substituting the value of t = 3/2 into the parametric equation of the line, we get:
l(3/2) = (3h/2 - 6, 12, 11/2)
Therefore, the two points of intersection of the line and the ellipsoid, where the tangent plane is horizontal, are:
(3h/4 - 3, 6, 7/4) and (3h/2 - 6, 12, 11/2)
The gradient of the ellipsoid equation x^2 + 4y^2 + z^2 = 9 is given by:
grad(f) = (2x, 8y, 2z)
Use the gradient to find the equation of the tangent plane.
At a point (x0, y0, z0) on the ellipsoid, the equation of the tangent plane is given by:
2x0(x - x0) + 8y0(y - y0) + 2z0(z - z0) = 0
Use the given line to find the direction vector of the plane perpendicular to the line.
The direction vector of the line is h2, 1, 3i. To find a vector perpendicular to this, we take the cross product of the line direction vector with any other vector not parallel to it. Let's take (1, 0, 0). Then:
h2, 1, 3i x (1, 0, 0) = (0, 3, -1)
Equate the direction vector to the normal vector of the tangent plane to find the point(s) of intersection.
Let (x0, y0, z0) be a point on the ellipsoid where the tangent plane is perpendicular to the given line. Then the normal vector of the tangent plane is given by:
(2x0, 8y0, 2z0)
We need to find a point (x0, y0, z0) such that this normal vector is parallel to (0, 3, -1). Equating corresponding components, we get:
2x0/0 = 8y0/3 = 2z0/-1
Solving these equations, we get:
x0 = 0, y0 = 0, z0 = -3/2
Thus, the point on the ellipsoid where the tangent plane is perpendicular to the given line is (0, 0, -3/2).
To know more about Ellipsoid:
https://brainly.com/question/29853961
#SPJ4
in a classroom at time t = 0, a sphere is thrown upward at a 45 angle to the horizontal at time while the sphere is still rising it bounces off the ceiling elastically
Answers
A sphere thrown upward at a 45-degree angle to the horizontal in a classroom elastically bounces off the ceiling while still rising
At time t = 0, a sphere is launched with an initial velocity at a 45-degree angle to the horizontal in a classroom. The sphere follows a parabolic trajectory as it rises due to the upward component of its initial velocity and experiences the downward pull of gravity. While the sphere is still ascending, it reaches the ceiling and collides with it.
During the elastic collision, the sphere's motion is reversed. It rebounds off the ceiling, changing its direction but maintaining its kinetic energy. As a result, the sphere starts descending with the same speed it had before the collision but in the opposite direction. The angle of descent will also be 45 degrees to the horizontal, mirroring the angle of the initial launch.
Throughout the entire process, neglecting air resistance, the total mechanical energy of the sphere is conserved since the collision with the ceiling is elastic.
learn more about initial velocity here:
https://brainly.com/question/31023940
#SPJ11
Daniel has dinner at a restaurant and the cost of his meal is $28.00. Because of the service, he wants to leave a 20% tip. What is his total bill including tip?
Answers
Answer: answer is $33.60
Step-by-step explanation:
I need the answer to all of them Rolly quick Bc my phone is dying
Answers
Answer:
1: $5
2: 7
3: 18
4: 17
5: 2
6: 1,029
Step-by-step explanation:
If 18 meters of high-resistance wire with a diameter of 1.2 mm has a resistance of 10 ohms, what is the resistance of 27 m of the same type of wire with a diameter of 1.5 mm?
Answers
2
=
9.61
O
h
m
s
Explanation:
l
1
=
18
m
r
1
=
1.2
2
=
0.6
m
m
=
6
⋅
10
−
4
m
R
1
=
10
O
h
m
s
R
1
=
τ
⋅
l
π
⋅
r
2
1
R
1
=
τ
⋅
18
π
⋅
36
⋅
10
−
8
10
=
τ
⋅
18
36
⋅
π
⋅
10
−
8
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
l
2
=
27
m
r
2
=
1
⋅
5
2
=
0.75
⋅
10
−
3
=
7.5
⋅
10
−
4
m
R
2
=
τ
⋅
l
2
π
⋅
r
2
2
R
2
=
τ
⋅
27
π
⋅
56.2
⋅
10
−
8
R
2
=
τ
⋅
27
56.2
π
⋅
10
−
8
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
.
.
10
R
2
=
τ
⋅
18
36
⋅
π
⋅
10
−
8
⋅
56.2
⋅
π
⋅
10
−
8
τ
⋅
27
10
R
2
=
18
⋅
56.2
36
⋅
27
10
R
2
=
56.2
54
R
2
=
540
56.2
R
2
=
9.61
O
h
m
s
Which expression represents the same solution as (4) (negative 3 and StartFraction 1 over 8 EndFraction? (4) (negative 3) + (4) (StartFraction 1 over 8 EndFraction) (4) (negative 3) + (4) (StartFraction negative 1 over 8 EndFraction) (4 + negative 3) times (4 + StartFraction 1 over 8 EndFraction) (4 + negative 3) times (4 + StartFraction negative 1 over 8 EndFraction)
Answers
Answer:
Option B.
Step-by-step explanation:
The given expression is
\((4)(-3\dfrac{1}{8})\)
We need an expression Which represents the same solution as the given expression.
It can be written as
\((4)[-(3+\dfrac{1}{8})]\)
\((4)[-3-\dfrac{1}{8}]\)
\((4)(-3)+(4)(-\dfrac{1}{8})\)
Since \((4)(-3)+(4)(-\dfrac{1}{8})\) is equivalent to given equation, therefore this equation represents the same solution as the given expression.
Hence, option B is correct.
Answer:
B
Step-by-step explanation:
How do you find theGreatest common factor for 15 and 40
Answers
Answer:
See Explanation
Step-by-step explanation:
\(15 = 3 \times \bold{ \red{ \boxed5}} \\ \\ 40 = 2 \times 2 \times 2 \times \bold{ \purple{ \boxed5}} \\ \\ common \: factor \: of \: 15 \: and \: 40= 5 \\ \\ \therefore \: gcf \: of \: 15 \: and \: 40 = 5\)
: Use the following information to find the curvature of each polar curve. For a curve C that is given by the polar equation r ro), the curvature K at the point (, 0) is given by the equation 2(r) (a) r = 1 + sin θ (b) r=θ (c) r=asin θ (d) r=e' Need Help? ReadTalk to a Tutor
Answers
On solving the provided question, we can say that - => K not equal to 0 at x= 0 and so, center of curvature exists.
What is center of curvature?In geometry, a curve's center of curvature is located at a point that is offset from the curve by an amount equal to the radius of curvature that lies on the normal vector. zero-curvature point at infinity. The center of the curve serves as the osculating circle. The sphere holding the spherical mirror's center serves as its center of curvature. A "C" is used to symbolize this. the center of a circle with a radius equal to the radius of curvature of a particular point on the curve, whose center is on the concave side of the curve and which is normal to that point.
The curvature K at the point (x,y) is given by if C is a graph of the twice differentiable function y = f(x)y=f(x).
\(K = \frac{|y^{''}|}{[1 + (y')^2 ]^{3/2}}\)
Curvature of the given curve at x=0x=0 is
=> K not equal to 0 at x= 0
so,
center of curvature exists.
To know more about center of curvature visit:
https://brainly.com/question/1462533
#SPJ4
A scientist determines that an antibiotic reduces a population of 20,000 bacteria to 5,000 in 24 hours. Find
the rate of decline caused by the antibiotic.
Answers
Answer:
5.8%
Step-by-step explanation:
H= 1/r (in P - in A)
H=24
P=2000
A=5000
24= 1/r (in2000 - in5000)
24r = in 2000 - in 5000
r = in 2000 - in 5000
_________________
24 r
= 05 .7762265
= 5.8 %
a restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts. how many possible 3-course meals are there?
Answers
Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.
Given,
In the question:
A restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts.
To find the how many possible 3-course meals are there?
Now, According to the question:
Let's know:
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:
\(N=n_1\) × \(n_2\) × \(n_3\)... ×\(n_n\)
In this problem, considering the number of salads, main courses and desserts, we have that:
\(n_1=4 , n_2=5,n_3=3\)
The total number of options is given by:
N = 4 × 5 × 3
N = 60
Hence, Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.
Learn more about Fundamental Counting Theorem at:
https://brainly.com/question/28384306
#SPJ4
i have 12 minutesuntil thisisdue
Answers
Answer:
AZ=8
AB=16
Step-by-step explanation:
3x-4=2x
-4=-x
x=4
3x-4
3(4) - 4
12-4
8
Based on the markings of the two triangles, what statement could be made about ΔABC and ΔA′B′C′? Question 1 options: A) The corresponding pairs of sides and angles of ΔABC and ΔA′B′C′ aren't congruent. B) ΔABC and ΔA′B′C′ are congruent. C) ΔABC and ΔA′B′C′ are irregular polygons. D) ΔABC and ΔA′B′C′ aBased on the markings of the two triangles, what statement could be made about ΔABC and ΔA′B′C′? Question 1 options: A) The corresponding pairs of sides and angles of ΔABC and ΔA′B′C′ aren't congruent. B) ΔABC and ΔA′B′C′ are congruent. C) ΔABC and ΔA′B′C′ are irregular polygons. D) ΔABC and ΔA′B′C′ are similar but not congruent.re similar but not congruent.
Answers
Answer:
B) ΔABC and ΔA′B′C′ are congruent.
Step-by-step explanation:
Given
See attachment for \(\triangle ABC\) and \(\triangle A'B'C'\)
Required
Determine the relationship between both triangles
The single line on all sides of both triangles implies that the sides of the triangles are equal
i.e.
\(\triangle ABC \cong \triangle A'B'C'\) --- sides
Similarly, the same mark on the three angles of both triangles means that the angles of the both triangles are equal
i.e.
\(\triangle ABC \cong \triangle A'B'C'\) --- angles
Hence, both triangles are congruent
Answer:
B) ΔABC and ΔA′B′C′ are congruent.
Step-by-step explanation:
Plxzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz helpe me if you can
Write an expression for the sequence of operations described below.
multiply 9 by the difference of 6 and 4
Answers
Answer:
not sure
Step-by-step explanation:
6-4 =2
2*9=18??
I'm not sure, since that was simple math, can you clarify by what you meant the difference of 6 and 4.
There is a picnic table located along Path A. The table is located 1.5 miles along the path from the campsite. Which map shows the picnic table in the correct location?
Answers
The map that shows the picnic table in the correct location is illustrated below.
Firstly, we need to understand the concept of scale on a map. Maps are often drawn to scale, which means that the distances between different points on the map represent a proportional distance in real life. For instance, if one inch on the map equals one mile in real life, then two inches on the map would represent two miles in real life.
To do this, we need to locate the campsite on the map and measure out 1.5 miles along Path A. Once we have done this, we can mark this location on the map as the location of the picnic table.
However, we need to make sure that we are using a map that is drawn to scale. Otherwise, we might not be able to accurately measure the distance and locate the picnic table correctly.
Therefore, we need to examine the different maps that we have and find one that is drawn to scale. Once we have found a suitable map, we can measure out the distance from the campsite to the location of the table along Path A, and mark it on the map.
Finally, we can compare the location we have marked on the map with the location of the table as described in the problem. If they match up, we have found the correct location of the table on the map.
To know more about table here
https://brainly.com/question/17084863
#SPJ1
A carnival ride is in the shape of a wheel with a radius of 25 feet. The wheel has 20 cars attached to the center of the wheel. What is the central angle, arc length, and area of a sector between any two cars? Round answers to the nearest hundredth if applicable. You must show all work and calculations to receive credit.
Answers
Mark me
What is the solution to this equation?
5x+3=2x-6
Answers
Answer:
x=-3
Step-by-step explanation:
5x+3=2x-6
-2x (both sides)
3x+3=-6
-3 (both sides)
3x=-9
divided by 3 (both sides)
answer is x=-3
Answer:
x= -3
Step-by-step explanation:
Combine the like terms to create an equivalent expression.
2q+2+92
Answers
Answer:
2q + 94
Step-by-step explanation:
2q + 2 + 92 ← collect like terms
= 2q + (2 + 92)
= 2q + 94
Answer:
2q + 94Step-by-step explanation:
2q + 2 + 92
Reorder and group
2q + (2 + 92)
Caculate
2q + 94
#CarryOnLearning
Find five rational numbers between −2 and 0
Answers
Answer:
-9/5 , -8/5 , -7/5, -6/5 , -5/5.
Step-by-step explanation:
brainliest plsssss
What is the slope of the line tangent to the polar curve r=4θ^2 at the point where θ=π/4?
Answers
The slope of the line tangent to the polar curve
r=4θ^2 at the point where
θ=π/4 is -8 Given that the polar curve is
r = 4θ². We have to find the slope of the tangent line at
θ = π/4. Now, we know that
r = f(θ) which is defined as below
f(θ) = 4θ²Let's find the first derivative of r with respect to θ. We get
dr/dθ = d/dθ (4θ²)
=> 8θAt θ
= π/4,
dr/dθ
= 8(π/4)
= 2π We can find the slope of the tangent line as below
y/x = tan(θ)
=> y' / x' = slope of the tangent line
=> slope of the tangent line
= y' / x'At θ
= π/4, the point on the curve is (4(π/4)²,
π/4) = (π, π/4) Now, we know that
x = r cosθ and
y = r sinθ Differentiating both the above equations with respect to θ, we get
dx/dθ = cosθ(-4θsinθ) + r cosθ
= -4θsinθcosθ + 4θ²cosθ
dy/dθ = sinθ(4θcosθ) + r sinθ
= 4θsin²θ + 4θ²sinθAt
θ = π/4, we have
dx/dθ = -2√2 and
dy/dθ = 2√2 Hence, slope of the
tangent line = dy/dθ / dx/dθ
= (2√2) / (-2√2)
= -1. So, slope of the tangent line at
θ = π/4 is -8. Therefore, the correct answer is -8.
To know more about tangent visit:
https://brainly.com/question/10053881
#SPJ11
PLEASEEE HELP LOOK AT PICTURE!!!
Answers
Answer:
a 64/3
Step-by-step explanation:
4^3 * 1/3 = 64/3
dy/dx=sec^2(x)(2+y)^2 initial condition y(pi)=-5
Answers
The solution for differential equation is the negative square root, since y(π) = -5. Thus, the final solution is; y = 3 - √(9 - 6 tan(x))
Define the term differential equation?A differential equation is a mathematical equation that relates a function or a set of functions with their derivatives.
Given differential equation; dy/dx = sec²(x) (2+y)²
separate the variables and integrate both sides:
∫ 1/(2+y)² dy = ∫ sec²(x) dx
Using the substitution u = 2+y, du/dy = 1, we can rewrite the left-hand side as:
∫ 1/u² du = -1/u + C₁
Similarly, we can integrate the right-hand side using the identity ∫ sec²(x) dx = tan(x) + C₂, Substituting these expressions back into the original equation, we get:
-1/(2+y) + C₁ = tan(x) + C₂
To determine the values of C₁ and C₂, we use the initial condition y(π) = -5, which implies x = π. Substituting these values, we get:
-1/(2-5) + C₁ = tan(π) + C₂
-1/(-3) + C₁ = 0 + C₂
C₁ = C₂ + 1/3
putting the value of C₁ and C₂ into the previous expression, So,
-1/(2+y) + C₁ = tan(x) + C₁ - 1/3
-1/(2+y) = tan(x) - 1/3
Multiplying both sides by (2+y)², we get:
-(2+y) = (2+y)² tan(x) - (2+y)²/3
Simplifying and solving for y, we get:
y² - 6 - 6 tan(x) = 0
Solve it for y by using the quadratic formula,
y = 3 ± √(9 - 6 tan(x))
Therefore, the solution to the differential equation dy/dx = sec²(x) (2+y)² with the initial condition y(π) = -5 is: y = 3 ± √(9 - 6 tan(x))
We choose the negative square root, since y(π) = -5. Thus, the final solution is: y = 3 - √(9 - 6 tan(x))
To know more about equation, visit:
https://brainly.com/question/2228446
#SPJ1
help please! click on pic.
Answers
Answer:
x=63
y=27
Step-by-step explanation:
to find x
180-117=63
to find y
90-63=27
please mark brainliest if correct
Answer:
x=63, y=27
Step-by-step explanation:
x is part of a line with 117, so you would do 180-117 to find x. Then you do 90-63 to find y, which is 27.
A city has a population of 350,000 people. Suppose that each year the population grows by 3%. What will the population be after years?
Answers
The population of the city will be approximately 408,022 after 5 years with a 3% annual growth rate.
Formula for annual growth rateTo find the population of the city after a certain number of years with a 3% annual growth rate, we can use the formula:
P = P₀(1 + r)ⁿ
where:
P₀ = initial population
r = annual growth rate (as a decimal)
n = number of years
P = population after n years
In this case, we have:
P₀ = 350,000
r = 0.03 (since the annual growth rate is 3 percent, or 0.03 as a decimal)
n = the number of years we want to find the population for
Substituting these values into the formula, we get:
P = 350,000(1 + 0.03)ⁿ
Simplifying:
P = 350,000(1.03)ⁿ
If we want to find the population after, say, 5 years, we can substitute n = 5 into the formula:
P = 350,000(1.03)⁵
P ≈ 408,022
Therefore, the population of the city will be approximately 408,022 after 5 years with a 3% annual growth rate.
To know more about rate, visit:
https://brainly.com/question/14731228
#SPJ1
escribe en cada fila dos divisiones que den el cociente o resultado que se te indica en la primera columna matemáticas con foto
Answers
Answer:
I don't know what you said
Step-by-step explanation:
But thanks for the points.
please helpp I'll give brainiest
Answers
Answer:
q + q + 4
Step-by-step explanation:
q + q +4
Question 16
Find the volume of the composite solid. Round to the nearest tenth, if necessary.
3 in.
5 in.
6 in.
Answers
The volume of the composite figure with a pentagon as its base is equal to 385.5 cubic inches.
How to calculate for the volume of the composite figureVolume of prism = area of base × height
area of pentagon base = 1/2 × apothem × perimeter
apothem = 5in/[2×tan(180/5)] = 3.4 in
perimeter = 5 × 5in = 25 in
area of pentagon base = 1/2 × 3.4 in × 25 in = 42.5 in²
Volume of the top triangular prism = 42.5in² × 3in = 127.5 in³
Volume of pentagon base prism = 42.5in² × 6in = 255 in³
Volume of the composite figure = 127.5 in³ + 255 in³
Volume of the composite figure = 382.5 in³
Therefore, the volume of the composite figure with a pentagon as its base is equal to 385.5 cubic inches.
Read more about volume here:https://brainly.com/question/23621053
#SPJ1
What is the intersection of AB and ED
Answers
Answer:
point c is the intersection of line AB and ED
Please answer it in two minutes
Answers
Answer:
IJ = 6
Step-by-step explanation:
This is a 30-60-90 triangle.
The ratio of the lengths of the sides is:
1 : sqrt(3) : 2
The short leg is the length of the long leg divided by sqrt(3).
The hypotenuse is twice the length of the short leg.
IK = JK/sqrt(3) = 3sqrt(3)/sqrt(3) = 3
IJ = 2IK = 2(3) = 6
Find an equation of the plane tangent to the following surface at the given points. z = In (1+xy); (5,6, In 31) and (-5, -6, In 31).
Answers
An equation of the plane tangent to the following surface at the given points (5,6, ln(31)) and (-5, -6, ln(31)) is (6/31)(x-5) + (5/31)(y-6) + (z-ln(31)) = 0 and (-6/31)(x+5) + (-5/31)(y+6) + (z-ln(31)) = 0 respectively.
The equation of the plane tangent to the surface z = ln(1+xy) at the given points (5,6, ln(31)) and (-5, -6, ln(31)) can be found using the gradient vector and the point-normal form of a plane equation.
To find the equation of the plane tangent to the surface at the given points, we need to find the normal vector to the surface at those points. The normal vector can be obtained by taking the gradient of the surface function.
The gradient of the surface function z = ln(1+xy) is given by:
∇z = (∂z/∂x, ∂z/∂y) = (y/(1+xy), x/(1+xy))
At the points (5,6, ln(31)) and (-5, -6, ln(31)), we can substitute the respective x and y values into the gradient expression to obtain the normal vectors.
For the point (5,6, ln(31)):
∇z = (6/(1+56), 5/(1+56)) = (6/31, 5/31)
Similarly, for the point (-5, -6, ln(31)):
∇z = (-6/(1-56), -5/(1-56)) = (-6/31, -5/31)
Now, we have the normal vectors to the surface at the given points. We can use the point-normal form of the plane equation to find the equation of the tangent plane.
Using the point-normal form: A(x-x0) + B(y-y0) + C(z-z0) = 0, where (x0, y0, z0) is a point on the plane and (A, B, C) is the normal vector, we can substitute the values from the points and normal vectors:
For the point (5,6, ln(31)):
(6/31)(x-5) + (5/31)(y-6) + (z-ln(31)) = 0
For the point (-5, -6, ln(31)):
(-6/31)(x+5) + (-5/31)(y+6) + (z-ln(31)) = 0
These equations represent the planes tangent to the surface z = ln(1+xy) at the given points.
To learn more about point-normal form
brainly.com/question/31502630
#SPJ11
2x + 4y = 12
y = A system of equations. 2 x plus 4 y equals 12. y equals StartFraction one-fourth EndFraction x minus 3.x – 3
What is the solution to the system of equations?
Answers
Answer:
x = 4, y = 1
Step-by-step explanation:
y = (1/4)x
2x + 4y = 12
replace y with something x
2x + 4(1/4)x = 12
3x = 12
x = 4
so y = 1