If the surface area of the rectangular box is 4 m² then the dimensions that maximize its volume is (2/√3 , 2/√3 , 1/√3) .
In the question ,
let length of rectangular box be = l
let width of rectangular box be = b and
let height of rectangular box be = h .
Since the box has no top ,
So , the surface area is = lb + 2bh + 2hl = 4
we get h = (4-lb)/(2l + 2b) .
The volume of the box is given as V = l×b×h .
Substituting the value of h from above in the volume formula , we get ,
V = lb(4-lb)/(2l + 2b)
differentiating it with respect to l ,
we get ,
dV/dl = [((2l+2b)(4b-2lb²)-lb(4-lb).2)/(2l+2b)²] = 0
Simplifying further ,
we get ,
2l² + 4lb - 8 = 0 ....equation(1)
Differentiating volume with respect to "b" .
dV/db = [((2l+2b)(4l-2l²b)-lb(4-lb).2)/(2l+2b)²] = 0
simplifying further ,
we get ,
2b² + 4lb - 8 = 0 ...equation(2) .
Simplifying equation(1) and (2) , we get
l = b ,
Substituting l = b in equation(1) ,
we get ,
2l² + 4l² = 8
l = 2/√
and b = 2/√3 .
Substituting the values in h ,
we get ,
h = (4-lb)/(2l + 2b)
h = 1/√3 .
Therefore , the dimensions of the box is (2/√3 , 2/√3 , 1/√3) .
The given question is incomplete , the complete question is
A rectangular box with no top is to have a surface area of 4 m². find the dimensions (in m) that maximize its volume.
Learn more about Volume here
https://brainly.com/question/15025419
#SPJ4
Timmy and Johnny's parents are very unfair. This year, Timmy received 5 Christmas presents, but his brother received 19. Their parents say that each year, Timmy will receive one more present than he did the last year, and Johnny will receive one less present that he did the last year. How many years will it take for them to receive the same amount of presents
Answer:
7 Years
Step-by-step explanation:
1 Year: 6,18
2 Years: 7,17
3 Years: 8,16
4 Years: 9,15
5 Years: 10,14
6 Years: 11,13
7 Years: 12,12
solving systems by Substitution
x-4y=15=3x-12y=12
Answer:
There is no solution
Step-by-step explanation:
x - 4y = 15
3x -12y = 12
Times the first equation by -3
-3x +12y = -45
3x - 12y = 12
0 = -33
So, there is no solution.
The Oakland Tigers are having team shirts made. One option is to pay Susan's Tees a $34 setup fee and then buy the shirts for $10 each. Another option is to go to City Printing, paying $23 for a setup fee and an additional $11 per shirt. The team parent in charge of the project notices that, with a certain number of shirts, the two options have the same cost. What is the cost? How many shirts is that?
To find the cost of the shirts, we need to set up a system of equations. Let x be the number of shirts.
Option 1: 34 + 10x = Option 2: 23 + 11x
We can solve this system of equations by subtracting the equations:
34 + 10x - 23 - 11x = 0
11x - 23 = 0
11x = 23
x = 23 / 11
Therefore, the cost is the same when the team orders 23/11 = 2 shirts.
point) The number of Drosophila fruit flies in controlled experiment assumes the following growth pattern when the food source is limited: 600 N(t) 1+ Me-0.3t where measured in days. A. How many fruit files were there in the beginning? What is the limiting number of fruit flies 600 C.At what time was the population increasing most rapidly? D. At what rate is the number of fruit flies increasing after days? 600/(1+11e
time was the population increasing most rapidly. At rate is the number of fruit flies increasing after days A. 600 B. 600 C. t=0 D. 0.09
The equation 600/(1+Me-0.3t) is a model for the population of Drosophila fruit flies, with time representing the number of days the experiment has gone on for. A. The population of fruit flies in the beginning is given by the equation as 600. B. The limiting number of fruit flies is also given by the equation as 600. C. The population is increasing most rapidly when t=0. D. After days, the number of fruit flies is increasing at a rate of 0.09, which can be calculated by taking the derivative of the equation with respect to t.
Learn more about time here
https://brainly.com/question/28050940
#SPJ4
if antonella has 3 more quarters than nickels and they have a combined value of 225 cents, how many of each coin does she have?
Antonella have a number of coins of quaters and nickels whose total value is 250.
The number of coins of nickel is 10 and the number of coins of quarters is 7.
Nickel and quarters are the coin based form of currency in the United States. The value of one nickel is 5 cents, while that of one quarter is 25 cents. We have given that
Antonella has 3 more quaters than nickles.
Let she has "x" number of quaters and "y" be number of nickels .
According to question,
y = 3+ x ---(1)
Combined value of all is 225 cents .
i.e 25 × x + y× 5 = 225 cents
plug the value of y from equation (1) to equation(2) we get,
25 x + 5(3+x) = 225
solve the equation
=> 25x + 15 + 5x = 225
=> 30x = 210
=> x = 7
put the value of x in equation (1)
y = x + 3 = 10
Hence, the number of nickels coins is 10 and numbers of quaters are 7.
To learn more about quaters and nickle, refer:
https://brainly.com/question/17127685
#SPJ4
how much do national football league players weigh on aerage in a random sample of 50 nfl players the average weight is 244.4 pounds
This statistic is based on an average of all players in the NFL. The average weight of a random sample of 50 NFL players may be slightly different.
This statistic is based on an average of all players in the NFL. It is not possible to accurately estimate the average weight of a random sample of 50 NFL players without actually measuring the weight of each individual player. The average weight of a random sample of 50 NFL players may be slightly different due to the randomness of the sample and individual player physical characteristics.
In order to accurately determine the average weight of a random sample of 50 NFL players, the weight of each individual player must be measured. The sample size of 50 players is relatively small, and the results may be significantly affected by the inclusion or exclusion of a single player. Additionally, the average weight of the sample may vary due to individual player physical characteristics such as height, body composition, and muscle mass. Furthermore, the average weight could be affected by the age and experience level of the players in the sample. All of these factors should be taken into consideration when attempting to determine the average weight of a random sample of NFL players.
Learn more about statistic here
https://brainly.com/question/14128303
#SPJ4
What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 54
Step-by-step explanation:
The 2 angles shown are vertical angles, so they are equal.
2x + 2 = 3x - 52
2x - 3x = -52 - 2
-x = -54
x = 54
They are 110° angles
Answer: x = -10
Step-by-step explanation:
1: Add: 2x+2 3x-52 = 5x -50
2: Divide both sides by the same factor: 5x - 50
------------
5 5
3: Level: x= -10
Find the sales tax. Sales Tax Selling Price Rate of Sales Tax Sales Tax
$40.00
8%
The sales tax is $
The sales tax on the good based on the selling price that is given will be $3.20.
How to calculate the sales tax?It should be noted that the sales tax simply means the tax that's levied on the goods and services that are sold by.
Based on the information given, the following can be deduced:
Sales tax Percentage = 8%
Price of good = $40
In this situation, in order to calculate the sales tax, we will have to multiply the sales tax percentage by the amount of the good which is the selling price. This will be:
Sales tax = Sales tax percentage × Price
Sales tax = 8% × $40
Sales tax = 0.08 × $40
Sale tax = $3.20
Therefore, the sales tax is $3.20.
Learn more about tax on:
brainly.com/question/25783927
#SPJ1
X over 100 = 100
What is X?
Answer:
x is 1000
Step-by-step explanation:
hope this helps
lagrange multiplier what are the points on the intersection of the ellipsoid with the plane that are respectively closest and furthest from the origin?
The points on the intersection of the ellipsoid with the plane that are respectively closest and furthest from the origin are
(2–√,−2–√,2−22–√)
(−2–√,2–√,2+22–√)
Using Lagrange multipliers we attempt to find the extrema of f(x,y,z)=x2+y2+z2 given that g(x,y,z)=x−y+z−2=0 and that h(x,y,z)=x2+y2−4=0.
Given,
∇f=⟨2x,2y,2z⟩
∇g=⟨1,−1,1⟩
∇h=⟨2x,2y,0⟩
Extrema satisfy the condition that ∇f=μ∇g+λ∇h for some λ,μ∈R.
This is to say,
2x=2λx+μ
2y=2λy−μ
2z=μ
If λ=1 then μ=0 and so z=0, the g constraint tells us that x=y+2, and the h constraint tells us that y2+(y+2)2=4, meaning that either y=0 or y=2. This provides us with two crucial points in addition to the g constraint:
(2,0,0)
(0,−2,0)
Now assume λ≠1, and so
x=μ2−2λ
y=−μ2−2λ=−x
Since x=−y, we have that x=±2–√, y=∓2–√. Using the g constraint, our two critical points are
(2–√,−2–√,2−22–√)
(−2–√,2–√,2+22–√)
And then it's east to determine which is the max and which is the min out of these four critical points.
To learn more about Lagrange multiplier
https://brainly.com/question/4609414
#SPJ4
the nth term of this sequence: 1/2,4/3,9/4,16/5
URGENT
Answer: [tex]\frac{n^{2} }{n+1}[/tex]
Step-by-step explanation:
The numerator (top digit) are squares. For example,
1 is [tex]1^{2}[/tex]
4 is [tex]2^{2}[/tex]
9 is [tex]3^{2}[/tex]
and so on.
The bottom digit increases by one.
Therefore, the Nth term would be that number (N) squared on the numerator, and n+1 on the denominator.
4700 people attended a football game. If 2% of the people who attended were
teenagers, how many teenagers attended the game?
Insert the values given in the problem then scale up or
down to find the missing value.
attendees
percent
100
The number of teenagers in the game are 94.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, 4700 people attended a football game.
Here, 2% of the people who attended were teenagers
So, the number of teenagers are
2% of 4700
= 0.02×4700
= 94
Therefore, there are 94 teenagers attended the game.
To learn more about the percentage visit:
brainly.com/question/24159063.
#SPJ1
Thomas increased the amount of water she gives her plants from 2 cups to 2 1/2 cups. By what percentage did Thomas increase the amount of water?
What is the answer to the picture I put below
The domain of the function y = √x + 4 is
0 ≤ x < ∞ How to find the domainAll of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.
The domain of a function are all possible values that will give output
For the function y = √x + 4
the domain are all positive real numbers which is shown by option C which is 0 ≤ x < ∞
these are numbers from zero to infinity. infinity is denoted by the symbol ∞
Hence the domain is 0 ≤ x < ∞
Learn more about range and domain at:
https://brainly.com/question/30068593
#SPJ1
help please i need it
Answer:
since a || b
<A = <ABb = 60°
in a triangle the sum of all angles is 180°
so,
30 + 60 + x = 180
x= 180-90
x= 90
LOT OF POINTS!!
PLEASE NEED ANSWERS QUICKLY!!
By using the properties of angle,
The proof of ∠1 ≅ ∠3 has been given below
What is angle?
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle
1. ∠2 ≅ ∠4 [Given]
2. m∠2= m∠4 [Angle Congruence Postulate]
3. ∠2 and ∠3 are supplementary [Given]
4. m∠2+m∠3 = 180° [Definition of Supplementary angles]
5. ∠1 and ∠4 are supplementary [Angle on a straight line]
6. m∠1+m∠4 = 180° [Definition of supplementary angles]
7. m∠1+m∠4 = m∠2+ m∠3 [ Substitution from 4 and 6]
8. m∠1+m∠4 = m∠4+m∠3 [Substitution from 2]
9. m∠1=m∠3 [Cancellation property]
10. ∠1 ≅ ∠3 [Converse of angle congruence theorem]
To learn more about angles, refer to the link-
https://brainly.com/question/25716982
#SPJ1
write an equation in point-slope form of each line that passes through the given points. (4, 1), (-2, 7)
Step-by-step explanation:
40 times 3453 divided by 24=
Answer:
Step-by-step explanation:
57,555
Answer:5755
Step-by-step explanation: 40 X 3453 = 138,120
138,120 / 24 = 5755
Differentiate 3x² over x³ +3
Answer:
[tex] \displaystyle{y' = \dfrac{ - 3x( {x}^{3} + 6) }{( {x}^{3} + 3)^{2} }}[/tex]
Step-by-step explanation:
We can use the quotient rule:
[tex] \displaystyle{y = \frac{u}{v} \to y '= \dfrac{u'v - uv'}{ {v}^{2} }}[/tex]
In this case, u and v both are functions. By applying formula above, we will have:
[tex] \displaystyle{y' = \dfrac{(3 {x}^{2})' ( {x}^{3} + 3) - (3 {x}^{2} )( {x}^{3} + 3)' }{( {x}^{3} + 3)^{2} }}[/tex]
Then apply power rule to derive functions, we have to know that:
[tex] \displaystyle{y = {x}^{n} \to y' = n {x}^{n - 1} } \\ \\ \displaystyle{y = c \to y' = 0 \: \: \: (c \in \mathbb{R})}[/tex]
Therefore, we will have:
[tex] \displaystyle{y' = \dfrac{6x ( {x}^{3} + 3) - (3 {x}^{2} )3 {x}^{2} }{( {x}^{3} + 3)^{2} }}[/tex]
Expand the terms in:
[tex] \displaystyle{y' = \dfrac{6 {x}^{4} + 18x - 9 {x}^{4} }{( {x}^{3} + 3)^{2} }} \\ \\ \displaystyle{y' = \dfrac{ - 3 {x}^{4} + 18x }{( {x}^{3} + 3)^{2} }} \\ \\ \displaystyle{y' = \dfrac{ - 3x( {x}^{3} + 6) }{( {x}^{3} + 3)^{2} }}[/tex]
Hence, that's the answer. You can keep in unfactored form or factored form as you desire!
ten students are arranged in a row. every minute, a new student is inserted in the row (which can occur in the front and in the back as well, hence 11 possible places) with a uniform 1 11 probability of each location. then, either the frontmost or the backmost student is removed from the row (each with a 1 2 probability). suppose you are the eighth in the line from the front. what is probability that you exit the row from the front rather than the back?
The probability that you exit the row from the front rather than the back is 1/2.
How do you determine probability?The probability is calculated by dividing the total number of outcomes by the number of possible ways the event could occur. Probability and odds are two separate ideas. Odds are the possibility of something happening divided by the likelihood that it won't happen.
What is fundamental probability in math?A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ4
15) Translate 4 units down, and then reflect over the y-axis. Pre-image: (5, 15) (4, 12) (2, 18) mage: I need help
The image of the transformation is (-5, 11) (-4, 8) (-2, 14)
How to determine the image of the transformationFrom the question, we have the following parameters that can be used in our computation:
Pre-image: (5, 15) (4, 12) (2, 18)
Transformation: Translate 4 units down, and then reflect over the y-axis.
Mathematically, this can be expressed as
(x, y) = (-x, y - 4)
Substitute the known values in the above equation, so, we have the following representation
(5, 15) (4, 12) (2, 18) = (-5, 11) (-4, 8) (-2, 14)
Hence, the image is (-5, 11) (-4, 8) (-2, 14)
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
Given that f(x) = x² + 3, work out the value of:
a) f(6)
b) f(-6)
The value of f(x) = x² + 3 at
(a) f(6) = 39
(b) f(-6) = 39
To work with these functions, we just need to put the value of x in the given function f(x) = x² + 3 i.e. substituting 6 and -6 into the equation per variable, then solving and simplifying as needed, to get the answer
(a) f(x) = x² + 3
f(6) = [tex]6^{2}[/tex] + 3
= 39
Hence, f(6) = 39
(b) f(x) = x² + 3
f(-6) = [tex](-6)^{2}[/tex] + 3
= 39
Therefore, the value of function f(x) = x² + 3 at f(6) and f(-6) is the same that is 39.
To learn more about functions:
brainly.com/question/2284360
Nevach and Michael are helping their friend Nabhitha move. If Nevaeh can
move 6 boxes for every 24 boxes that Michael moves, then how many boxes
can Michael move for every box that Nevaeh moves?
Michael boxes
24
Answer:
For every 1 box Naveah moves, Michael moves 4 boxes
if all sales are made on account, the only piece of information you would need to calculate the cash received from customers during the period is the net change in accounts receivable. State True or False your answer:
a. True
b. False
If all sales are made on account, the only piece of information you would need to calculate the cash received from customers during the period is the net change in accounts receivable.
It is False.
Information available from the question,
In the question:
If all sales are made on account, the only piece of information you would need to calculate the cash received from customers during the period is the net change in accounts receivable.
The answer in TRUE/FALSE
Now, According to the question:
Accounting for cash transactions:
Daily cash sheet: If cash transactions are a significant part of your business, you should also prepare a daily cash sheet to reconcile your cash received and paid out for the day. If you use a daily cash sheet, you can reconcile your cash receipts with your daily deposit into your bank account.
So, The given statement is False.
Learn more about Accounts at:
https://brainly.com/question/14643061
#SPJ4
Marcus has x songs downloaded on his phone. He downloads 20 more songs to his phone.
Enter an expression in the box to represent the number of songs Marcus now has on his phone.
Answer:
x + 20 = y
Step-by-step explanation:
x + 20 = y
where x= number of songs
y = total songs marcus has
Elizabeth rents a home for $1,200 a month. The security deposit she paid is one months' rent. Renters insurance will cost $120 for the year. Elizabeth expects utilities to average $164 a month. What will be the total cost of renting the home for the first year (prior to any refund of her security deposit)? PLEASE SHOW WORK
Answer:
$17,688.00
Step-by-step explanation:
(1200 x 13) + 120 + (164 x 12)
17688
give the equation of the line that goes through the point (5, -2) and has a slope of 0.
When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b). B stands in for the y value of the y-intercept point in the formula.
How to calculated the slope intercept?Determine the equation of the line with a slope of 2/3 and a y intercept of (0, 4).
Solution
Step 1: Replace the provided in the formula.
Provided that the slope, m, is given as 2/3 and the y intercept, (0, 4), b = 4.
y = mx + b
y = 2 3 x + 4
2 /3 x – y = - 4
(Note: You must multiply this by the LCD of 3 to fix this since the conventional form does not support fractional numbers.)
3( 2 /3x – y) = (- 4) (- 4)
3/2x – 3y = - 12
This is the line's determined equation.
Verify is the second step.
Utilizing the formula, plot two points. In this example, y1 = 2 and Y2 = -6. 2x - 3y = - 12 2x – 3y = - 12
Let y = 2 Let y = - 6
2x – 3(2) = - 12 2x – 3(-6) = - 12
2x – 6 = - 12 2x + 18 = - 12
2x = - 6 2x = - 30 \sx = - 3 x = - 15
P1 therefore equals (-3, 2) and P2 equals (-15, -6).
To Learn more About slope intercept refer to:
https://brainly.com/question/25826868
#SPJ4
Write an equation in slope-intercept form for the line that contains the point (1, -1) and is parallel to y = 3x - 2.
Considering the definition of parallel line, the line that contains the point (1, -1) and is parallel to y = 3x - 2 is y= 3x -4.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Parallel lineParallel lines are two lines that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts.
Equation of parallel line in this caseIn this case, the line is y= 3x -2
where:
the slope is 3.the ordinate to the origin is -2.Two lines are parallel if they have the same slope. So, the parallel line has a slope of 3.
The line passes through the point (1, -1). Replacing in the expression for a line:
-1= 3× 1 + b
-1= 3 + b
-1-3 = b
-4 = b
Finally, the equation of parallel line is y= 3x -4.
Learn more about parallel line:
brainly.com/question/7197064
brainly.com/question/11470863
brainly.com/question/7280013
#SPJ1
Find the slope of every line that is perpendicular to this one.
Answer:
-4/7
Step-by-step explanation:
The slope of the given line is [tex]\frac{3-(-4)}{4-0}=\frac{7}{4}[/tex].
Perpendicular lines have slopes that are negative reciprocals of each other, so the answer is [tex]-4/7[/tex].
The slope of every line perpendicular to the line passing through (4, -3) and (0, -4) is -4.
We have,
Let's first find the slope of the given line passing through (4, -3) and
(0, -4):
slope = (change in y) / (change in x)
= (-4 - (-3)) / (0 - 4)
= (-4 + 3) / (-4)
= -1 / (-4)
= 1/4
The slope of the given line is 1/4.
Now, to find the slope of a line perpendicular to this line, we take the negative reciprocal of the slope:
[tex]slope_{perpendicular} = -1 / slope[/tex]
= -1 / (1/4)
= -4
Therefore,
The slope of every line perpendicular to the line passing through (4, -3) and (0, -4) is -4.
Learn more about the equation of a line here:
https://brainly.com/question/23087740
#SPJ4
whats the probabilty that a randomly selected dorm room has a tv but no refridgerator
Using the provided percentages, it is discovered that:
a) A randomly chosen dorm room has a 31% chance of having a TV but no refrigerator.
b) A randomly chosen dorm room has a 48% chance of having either a television or a refrigerator, but not both.
c) There is a 31% chance that a randomly chosen dorm room lacks both a refrigerator and a television.
How to find the Calculation?Item a:
TVs were owned by 52% of people.
21% of them had a refrigerator as well.
52 - 21 = 31
A randomly chosen dorm room has a 31% chance of having a TV but no refrigerator.
Item b:
31% just have a TV.
Only 17% of people—38—have a refrigerator.
31 + 17 = 48
A randomly chosen dorm room has a 48% chance of having either a television or a refrigerator, but not both.
Item c:
The likelihood that at least one exists is:
P(A∪B) = P(A) + P(B) - P(A∩B)
Hence:
P(A∪B) = 0.52 + 0.38 - 21 = 0.69.
1 - 0.69 = 0.31
There is a 31% chance that a randomly chosen dorm room lacks a refrigerator or a television.
The Complete Question.
To Learn more About percentages refer to:
https://brainly.com/question/24877689
#SPJ4
Answer:
The probability that a randomly selected dorm room has a TV but no refrigerator is 0.31
What is Probability?
Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.
According to question
The probability that a randomly selected dorm room has a TV but no refrigerator
Solution :
Suppose
A = event of having refrigerators,
B = event of having a TV,
We have,
P(A) = 34% = 0.34,
P(B) = 51% = 0.51,
P(A∩B) = 21% = 0.21
Therefore:
Probability of a TV but no refrigerator = P(A∩B')
= P(A) - P(A∩B)
= 0.34 - 0.21
= 0.31
To Learn more About Probability, Check out: https://brainly.com/question/11234923
#SPJ4
