The dimensions √30 inches square and 4 inches high will provide a box with maximum volume.
What are maxima and minima?The Maxima and minima of a function are the extremes within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.
It is given that:
A manufacturer wants to design an open-top box having a square base and a surface area of 120 square inches.
Let's suppose x is the base edge length and h is the box height.
x² + 4xh = 120
h = (120 - x²)/(4x)
h = 30/x - x/4
Volume = x²(30/x - x/4) = 30x - x³/4
dV/dx = 0
30 - x² = 0
x = √30
h = 120/x² = 120/30 = 4 inches
The box is √30 inches square and 4 inches high.
Thus, the dimensions √30 inches square and 4 inches high will provide a box with maximum volume.
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the LCD of 6y/5x and 8/12x is 60x. true or false?
Answer:
true....
Step-by-step explanation:
34.) If a quadrilateral is a parallelogram and the diagonals are perpendicular, then it must be a rectangle.
A. True
B. False
Answer:
The correct answer is: False
HELP! SIMPLIFY!
simplify:
1) (m³ n⁵) (mn⁴)
------------------
m⁻³ n²
2) 6a² b³
-----------
4a
3) 5⁶ a⁶ b³
-----------
5² ab³
Which of the following is true for the relation f(x) = 5x + 1?
Only the inverse is a function.
Only the equation is a function.
Neither the equation nor its inverse is a function.
Both the equation and its inverse are functions.
Answer:
Both the equation and its inverse are functions.
Step-by-step explanation:
A function is relation in which one input gives one and only one output.
Here, the given function,
[tex]f(x)=5x+1[/tex]
Which is a polynomial,
A polynomial is a function because for each input value it gives only one output value.
⇒ f(x) is a function.
Now, For finding the inverse of f(x),
Replace f(x) by y,
y = 5x + 1
Switch x and y,
x = 5y + 1
Isolate y on the left side,
-5y = 1 - x
[tex]y = \frac{1-x}{-5}=\frac{x-1}{5}[/tex]
Replace y by [tex]f^{-1}(x)[/tex],
[tex]f^{-1}(x)=\frac{x-1}{5}[/tex]
Which is also a polynomial,
Hence, the inverse of f(x) is also a function,
Last option is correct.
Irst. write an expression for the probability that both socks are bl
What is the limit ? And how do I get the answer?
How to find the sum of the squares of the roots of an equation?
Final answer:
To calculate the sum of the squares of the roots of a quadratic equation, apply Vieta's formulas to find the sum and product of the roots and use them in the identity (α + β)² - 2αβ to avoid directly solving for the roots.
Explanation:
To find the sum of the squares of the roots of an equation, especially for a quadratic equation of the form ax²+bx+c=0, we use the relationship between the coefficients and the roots provided by Vieta's formulas.
The sum of the roots, denoted as α and β, is given by -b/a, and the product of the roots is c/a. To find the sum of the squares of the roots (α² + β²), you can use the identity (α + β)² = α² + 2αβ + β², or α² + β² = (α + β)² - 2αβ.
By substituting the sum and product of the roots from Vieta's formulas, you can calculate the sum of the squares without actually solving for the roots. This approach is especially useful in equilibrium problems or other situations where you might encounter square roots or higher powers and wish to simplify calculations.
involves triangle centroid
Solve for c:
= 7 + 8 + 9 −10
In order to make an A on her project, Sarah needs at least 160 points. She has already turned in part of her work and has been given 125 point so far. Write and solve an inequality that models this situation and find out how many points Sarah needs on the last part of her project to get an A.
to get an A, she needs >=160 points and she already has 125 points
let 'x' be the number of points on the last part of her project then
125 + x >= 160
x >= 160 - 125
x >= 35
Sarah needs at least 35 points on the last part of her project.
Answer:
P ≥ 35
Step-by-step explanation:
Naming P to the Points needed for the last part of Sarah's project,
we can define an inequation modelling in which cases Sarah will have enough points for an A or better:
It is stated that:
An A is achieved with 160 points.Sarah already has been given 125 points.Then the inequation can be written:
[Points-so-far] + [Points-needed] greater or equal than 160
In math symbols:
[tex]125+P\geq 160\\P\geq 160-125\\P\geq 35[/tex]
A sixth-grade class has 12 boys and 24 girls.
Write two more statements comparing the number of boys in the class to the number of girls
Five divided by the difference of a number and 4 equals the quotient of 10 and the sum of the number and 2. find the number.
Sammy has a 10-foot ladder, which he needs to climb to reach the roof of his house. the roof is 12 feet above the ground. the base of the ladder must be at least 1.5 feet from the base of the house. how far is it from the top of the ladder to the edge of the roof? draw a sketch.
Explain how you can tell without calculating whether the sum of a postitive number and a negative number will be positive, negative or zero.
Sara has 16 red flowers and 24 yellow flowers. She wants to make a bouquet with the same number of each color flowers in each bouquet. How many red flowers will be in each bouquet.
HELP ASAP!
1. Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s. Which statement best describes the meaning of f(250)?
The house sold for $250,000.
The house stayed on the market for an average of 250 days before being sold.
This is the average number of days the house stayed on the market before being sold for $250,000.
The house sold on the market for $250,000 and stayed on the market for an average of 250 days before being sold.
2. Laura rents a movie for a flat fee of $2.00 plus an additional $0.50 for each night she keeps the movie. Choose the cost function that represents this scenario if x equals the number of nights Laura has the movie.
c(x) = 2.00x + 0.50
c(x) = 2.00 + 0.50x
c(x) = 2.50x
c(x) = (2.00 + 0.50)x
Answer:c(x)=2.00 +0.05x
Step-by-step explanation:
Given: B = {(4, 2), (4, -2), (16, 4), . . .} Is B a function and why?
Set B = {(4, 2), (4, -2), (16, 4), . . .} is not a function because it has an 'x' value (4) that corresponds to more than one 'y' value (2,-2), which contradicts the definition of a function.
Explanation:The given set B = {(4, 2), (4, -2), (16, 4), . . .} is not a function. In mathematical terms, for a set of ordered pairs to be considered a function, each input (or 'x' value) must have exactly one output (or 'y' value). However, in B, the input 4 corresponds to two different outputs: 2 and -2. This violates the definition of a function, proving that B is not a function.
It's useful to remember this as a rule: in functions, a particular x-value can only be paired with a single y-value. In contrast, in non-functions, a single x-value can be linked to multiple y-values, as demonstrated by set B.
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You are going to bake an over-sized sheet cake. The recipe calls for 2 cups of sugar for every 3 cups of flour. How many cups of flour are needed if you use 18 cups of sugar?
Answer:27
Step-by-step explanation:
Bill owns a grocery store chain with 2,000 total employees. Nine hundred of his employees are managers. What can we assume about the total productivity of Bill’s chain?
We can assume that Bill's store is in danger of experiencing a diseconomy of scale.
Given Bill's grocery store chain's 2,000 total employees, 900 of whom are managers, it may be more logical to believe that Bill's store is in danger of suffering a diseconomy of scale.
Diseconomies of scale relate to a situation in which a company expands so much that its costs per unit rise.
When a corporation suffers diseconomies of scale, needless expenditures frequently develop as a result of greater management issues and inefficiencies in the flow of work and commodities.
Almost half of Bill's employees are managers of some kind. This will reduce his company's productivity and cause costs to increase as output expands.
Complete question:
Bill owns a grocery store chain with 2,000 total employees. nine hundred of his employees are managers. what can we assume about the total productivity of bill’s chain?
a. bill’s store is in danger of experiencing a diseconomy of scale
b. the grocery store is experiencing a constant return to scale
c. the grocery store is experiencing an economy of scale
d. bill’s store is run very efficiently.
How to find the circular permutation for 5 things taken 5 at a time
Which statement about the triangle is true
Answer:
the other answer is wrong number 2 is correct
Step-by-step explanation:
Consider the two conditional statements. Draw a conclusion from the given conditional statements, and write the contrapositive of each conditional statement. Then, draw a conclusion from the two contrapositives. How does the first conclusion relate to the second conclusion?
If you are eating a banana, then you are eating fruit.
If you are eating fruit, then you are eating food.
a.If you are eating a banana, then you are eating food.
If you are not eating a banana, then you are not eating fruit. If you are not eating fruit, then you are not eating food.
If you are not eating a banana, then you are not eating food.
The second conclusion is the contrapositive of the first conclusion.
b.
If you are eating a banana, then you are eating food.
If you are eating fruit, then you are eating a banana. If you are eating food, then you are eating fruit.
If you are eating food, then you are eating a banana.
The second conclusion is the contrapositive of the first conclusion.
c.If you are eating a banana, then you are eating food.
If you are not eating fruit, then you are not eating a banana. If you are not eating food, then you are not eating fruit.
If you are not eating food, then you are not eating a banana.
The second conclusion is the contrapositive of the first conclusion.
d.If you are eating food, then you are eating a banana.
If you are not eating fruit, then you are not eating a banana. If you are not eating food, then you are not eating fruit.
If you are not eating food, then you are not eating a banana.
The second conclusion is the contrapositive of the first conclusion.
Answer:
c is the answer
Step-by-step explan ation:
Margo borrows $1000, agreeing to pay it back with 5% annual interest after 15 months. How much interest will she pay?
2(v-h)/k=r
Solve equation for v in terms of all other variables involved
For the given expression, the equation for v in terms of all other variables involved will be v=(r·k)/2+h.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the given expression is 2(v-h)/k=r
We have to solve the expression in the term v as,
2(v-h)/k=r
Open the brackets and multiply 2 in the bracket as
(2v-2h)/k=r
Apply the cross-multiplication operation as
2v-2h=r·k
Rearrange the equation as
2v=r·k+2h
The equation for v in terms of all other variables involved is obtained as,
v=(r·k)/2+h
Thus, for the given expression, the equation for v in terms of all other variables involved will be v=(r·k)/2+h.
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(X-3)(x+2) = 0 what is the answer to this ?
Determine the interval on which f(x) = the square root of the quantity of x plus 2 is integrable.
(−∞, 2)
[−2, ∞)
(−∞,−2) U (−2, ∞)
All reals
The interval on which f(x) is integrable is:
[-2, ∞)
Step-by-step explanation:We are given a function f(x) as:
[tex]f(x)=\sqrt{x+2}[/tex]
We know that a function is integrable over a given interval if it is continuous over a given interval.
Now, we know that the square root function is well defined if the function under the square root sign is positive.
This means here the function is well defined if:
[tex]x+2\geq 0[/tex]
i.e.
[tex]x\geq -2[/tex]
Also, the square root function is continuous over it's domain.
and hence it is integrable over it's domain.
This means that the function is integrable over:
[-2,∞)
Simplify the fraction
what is 16 over 38
Algebra 1A unit 4 lesson 2 Answers please help ?!!
Which distance is longer? 1 mile 1000 meters 10000 centimeters?
Which polygon is always regular