Elena is making an open-top box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 inches long, and then folding up the sides. If the side lengths of her square cutouts are inches, then the volume of the box is given by V(x)=x(11-2x)(17-2x)
Answers
Answer:
Step-by-step explanation:
Refer the attached picture for complete question
a) V(x)=x(11-2x)(17-2x)
B(x)=140
Side and volume cannot be negative
So, x> 0
11-2x>0 and 17-2x>0
[tex]x<\frac{11}{2}[/tex] and [tex]x< \frac{17}{2}[/tex]
Domain for V(x) :[tex]0<x<\frac{11}{2}[/tex]
b)For finding the greatest Volume
[tex]\frac{dV}{dx}=0[/tex]
[tex]V(x)=x(11-2x)(17-2x)=4x^3-56x^2+187x[/tex]
[tex]\frac{dV}{dx}=12x^2-112x+187=0\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{112\pm\sqrt{(112)^2-4(12)(187)}}{2(12)}[/tex]
x=7.155 , 2.177
Consider the graph
So, Volume at 7.155 is negative
Thus x≈2 gives the greatest volume
c)
Consider the graph .
It is increasing from [tex]-1 \leq x \leq 2[/tex] and [tex]x \geq 7[/tex]
So, Graph increasing interval is [-1,2] ∪[7,∞)
d)
At the point of intersection, both graph has the same value .
Related Questions
Find the value of each variable.
Answers
Answer:
19. x = 65
20. x = 12
21. x = 35, y = 85
Step-by-step explanation:
19. 2x -10 = 120
2x (-10 + 10) = (120 +10)
2x/2 = 130/2
x = 65
20. 2x + 4x + 108 = 180
6x + (108 - 108) = (180 - 108)
6x/6 = 72/6
x = 12
21. 2x + 25 = 3x - 10
2x + (25 - 25) = 3x (- 10 - 25)
(2x - 3x) = (3x - 3x) - 35
-x/-1 = -35/-1
x = 35
3x - 10 + y = 180
3(35) - 10 + y = 180
105 - 10 + y = 180
(95 - 95) + y = (180 - 95)
y = 85
Calculate the unit rate for each option of Takis, explain which option is better,
and why?
Answers
(1st explanation is the left bag and the 2nd in the right bag)
Explanation: If the bag is $1.68 for 4oz of takis and you want to find the unit rate you do 1.68 divided by 4 which equals $0.42 per oz of takis.
2nd Explanation: If its $4.42 for 20 oz of takis do 4.42 divided by 20 which equals $0.22.
Explanation for the teacher (I saw the worst words ever, "why?": The right bag of takis are the best value since the left bag is a little bit less than twice the right bag.
Answer:
they are better because they are cheeper than the other
PLZ HELP ME HELP PLZ
Answers
Answer:
2000
Step-by-step explanation:
that i the answer becuase you multply
Irma is just learning to play the Happy Fairies video game. In the game, players gain and lose points based on how well they take care of the fairies in their fairy gardens. Irma had a total of – 5 points. Then, her fairy house fell over in the wind and she got – 3 points. How many total points does Irma have now?
Answers
Answer: -8 points
Step-by-step explanation:
From the question, we are informed that Irma is just learning to play the Happy Fairies video game and that in the game, players gain and lose points based on how well they take care of the fairies in their fairy gardens.
We are told that Irma had a total of –5 points, then, her fairy house fell over in the wind and she got –3 points.
Her total points now will be the addition of -5 and -3. This will be:
= -5 + (-3)
= -5 - 3
= -8
Note that minus multiplied by plus is minus.
Answer: -8
Step-by-step explanation:
6 lumberjacks can cut down 15 mahogany trees in 2 hours. How much longer will
it take 8 lumberjacks to cut down 35 mahogany trees working at the same rate?
B. 1}hr
c.hr
A. 3hr
D. 21hr
Answers
9514 1404 393
Answer:
3.5 hr
Step-by-step explanation:
We assume that "the same rate" means effort per tree is a constant. "Effort" is measured as the product of lumberjacks and hours. Then ...
(lumberjacks)(hours)/trees = (6)(2)/15 = (8)(t)/35
Multiplying by 35/8, we have ...
(35/8)(12/15) = t = (3·4·5·7)/(2·3·4·5) = 7/2 = 3.5
It will take 8 lumberjacks 3.5 hours to cut down 35 trees.
can someone help me I need a quick answer. If a base of 5 has an exponent of 2 and is subtracted from a base of 4 that hs an exponent of 3, what is the remaining number?
Answers
Answer:
39
Step-by-step explanation:
4^3 equals 64, and 5^2 equals 25. 64 - 25 = 39.
HELP PLEASE ASAP
Which of the following are irrational numbers?
55
53
✓20
71
Submit
Answers
Answer: √20
Step-by-step explanation:
4.47213595 (the 5 repeats)
−38÷7/12 another math question.
Answers
Answer:
-0.45238095238
Step-by-step explanation:
-38 divided by 7/12= -0.45238095238
4) Tony pays $245 for a PS4. He decides to sell the PS4 with a 30%
markup. How much is Tony selling the PS4 for?
Answers
Answer:
175
Step-by-step explanation:
trust me .
Answer:
318.5
Step-by-step explanation:
30% of 245 is 73.5
245 + 73.5 = 318.5
Corliss earns an hourly wage, as well as tips, each day he works. His daily earned income, m, after h hours can be represented by the inequality m>11h+35.
He makes at most $11 per hour plus $35 in tips.
He makes more than $11 per hour plus $35 in tips.
He makes at least $11 per hour plus $35 in tips.
He makes less than $11 per hour plus $35 in tips.
Answers
Answer:
He makes more than $11 per hour plus $35 in tips
Step-by-step explanation:
First, you should always look at the sign and identify whether it's greater than, less than, greater than or equal to, or less than or equal to. In this inequality, the sign being shown is greater than: represented by m>11h+3
Here are inequality key words to help better understand the signs:
> : Greater Than, More Than
≥ : More Than or Equal To, At Least, No Less Than, A Minimum of
< : Less Than, Fewer Than
≤ : Less Than or Equal To, At Most, No More Than, A Maximum of
Plz help do questions 9 and 10 I will give brainlest
Answers
Answer:
9. B.) c=28h
10. C.) 5x=45y
Step-by-step explanation:
1. 84 cards in three hours 84/3 = 28 cards per hour
2. 2x=18y which means x=9y, x 5 = 5x = 45y
What is the mean height of Bella's corn stalks?
A 69cm
B 75cm
C 78cm
D 80cm
E 81cm
Answers
Answer:
C. 78
Step-by-step explanation:
Add all of them together, then divide by 5 because there are 5 different plants.
What the equation of the line that is perpendicular to the line y = −3x + 5 that goes through point D (9, 2)?
Answers
Answer:
y=1/3-1 ...............
Part A: If (6^2)^x = 1, what is the value of x? Explain your answer.
Part B: If (6^0)^x = 1, what are the possible values of x? Explain your answer.
Answers
Step-by-step explanation:
A.
[tex](6^2)^x=1\\\\36^x=1\\\\36^x=36^0\Rightarrow x=0[/tex]
Every number to the power of 0 gives us 1
[tex]a^0=1\ \text{for}\ a\in\mathbb{R}[/tex]
B.
[tex](6^0)^x=1\\\\1^x=1\\\\x\in\mathbb{R}[/tex]
1 to the any power gives us 1.
[tex]1^n=1\ \text{for}\ n\in\mathbb{R}[/tex]
Can someone send me the answer to the question in the photo? (with solutions)
Answers
Answer:
This is so easy question .
I can do.
a line is perpendicular to y - 5 = -1/4(x + 8) and goes through the point (-1,2). What is the lines y-intercept?
Answers
Answer:
y = 4x + 6
Step-by-step explanation:
Turn the equation we are given into slope-intercept form.
y - 5 = -1/4(x + 8)
y - 5 = -1/4x - 2
y = -1/4x + 3
The slope of a perpendicular line is the opposite reciprocal of the original line.
-1/4 -> 4/1 -> 4
Find the new y-intercept using the point given.
y = 4x + b
2 = 4(-1) + b
2 = -4 + b
6 = b
Fill in everything we solved for.
y = 4x + 6
Best of Luck!
Which of the following can be concluded given Z1 a ZT?
4
3/2
5
a
Answers
Mr. Leto plans to save money to buy a carpet. If he saves $50 each week for 30 weeks, he will have saved the exact amount of money needed to buy the carpet. If Mr. Leto instead saves $75 each week, how many weeks will it take him to save the same amount of money?
Answers
Answer:
Number of new weeks = 20 week
Step-by-step explanation:
Total money saves = $50 x 30
Total money saves = $1,500
Find:
Number of new week
Computation:
Total money saves = Number of money save per week x Number of new weeks
1,500 = 75 x Number of new weeks
Number of new weeks = 20 week
I need helpppp?!!!
What is the slope of the line??
Please give right answer
Answers
Answer: -1/2
Step-by-step explanation:
Slope=rise/run
Up 1 and to the left 2 which makes it a negative
to find this, take two points from the graph. I used (0,3) and (2,2). Then find the difference between the y coordinates and x coordinates. So in this case, the difference between 3 and 2 is 1. And the difference between 0 and 2 is two. And remember it is rise over run so that makes it 1/2. And lastly, you know it's negative because the graph is decreasing. hope this helpsss
Kathy ran the 400-meter dash in 60.48 seconds. She ran the 200 meter dash in 28.9 seconds.If she divided her 400-meter dash time in 8 equal time segments, how long would it take cathy to run one of these segments Please HELPPP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answers
Answer:
Kathy would take 7.56 seconds to run each of the 8-time segments of the 400-meter dash.
Step-by-step explanation:
Kathy ran the 400-meter dash in 60.48 seconds, so if she now divided that time into 8 equal time segments we have:
[tex] t = 60.48 s [/tex]
By dividing the above equation into 8:
[tex] t = \frac{60.48 s}{8} = 7.56 s [/tex]
Hence, she would take 7.56 seconds to run each of the 8-time segments of the 400-meter dash.
I hope it helps you!
An equilateral triangle with side length 4cm is shown in the diagram, work out the area of the triangle.
Give your answer rounded to 1 DP.
Answers
Answer:
4√3cm^2
Step-by-step explanation:
we know that the area of equilateral triangle is √3/4a^2
write an equation of a line passing through point p(-2, 6) that is parallel to the line x= -5
Answers
Answer:
x= -2
Step-by-step explanation:
x = -5 is a vertical line, so a line parallel would also have to be a vertical line
It goes through the point ( -2,6)
The x coordinate -2
So a line parallel would be x= -2
Answer:
x= -2
Step-by-step explanation:
Tammy rents an apartment close to her school campus. The amount that she spends on rent is given by the equation r = 355m, where r is the amount spent on rent and m is the number of months she stays in the apartment. What is the constant of proportionality (r to m) for this proportional relationship?
A.
B.
C.
177.5
D.
355
Answers
answer is c because if it's not a and b then the only answers will be c and d and d is the same as the number so it's c
The post office is selling 7 cent stamps and 9 cent stamps. If a package requires 43 cents to mail, how many 9 cent stamps will you need?
Answers
If a package requires 43 cents to mail, the number of 9 cent stamps that will be needed is 41cent is the value needed.
What is meant by mathematical equation?Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
Identify the question that is being asked. Write the pertinent details in straightforward statements. Give values that need to be discovered symbols. Find the mathematical connections between the assertions.
The most well-known equation in the entire universe is E=mc2. Just like that. It is succinct, elegant, and expresses a phenomenon that is so important that everyone should be aware of it.
Given,
The equation will be:
7x + 9y = 43
7(2) + 9(3) =41
14+ 27 = 41
Since the value that's is gotten not equal to 43
Therefore The value is 41 cent is needed to 9 cent stamps
To learn more about mathematical equation refer to:
https://brainly.com/question/2972832
#SPJ2
338 points in 16 games. how many points did they make per game?
Answers
just divide 338 by 16.
-hope this helps
PLEASE HELP!! MATH FINAL, NO EXPLANATION NEEDED :))
Answers
Answer:
B.
Step-by-step explanation:
When you move right or left it's inside the parentheses and the opposite so right is - and left is + when you move up or down its the same so up is + and down is -.
Answer:
B
Step-by-step explanation:
It's asking for moving right 3 and down 2. To move right three, you have to subtract 3 (It's switched up). This goes inside the parenthesis, because if it was outside of the parenthesis, it would be going up or down. Now, to go down 2, you have to subtract 2 outside of the parenthesis (It's normal). That leaves you with f(x-3)-2. Therefore, the answer is B.
Expand & simplify 4(t+2)+6(t-4)
Answers
Answer:
10t - 16
Step-by-step explanation:
4(t + 2)+ 6(t - 4)
4t + 8 + 6t -24
10t - 16
Now expand the second bracket: 6t - 24
4t + 8 + 6t - 24
Add all like terms together: 10t - 16
Tara has 3/4 cup of ice cream. How many 1/5 -cup servings are in 3/4 cup of ice cream?
Answers
Answer:
4/15
Step-by-step explanation:
because 1/5÷3/4=4/15
can a triangle have an exterior angle that is obtuse at two vertices? Explain
Answers
Answer:
Yes
Step-by-step explanation:
An obtuse triangle will have two obtuse angle at its exterior.
Take for instance, the angles in the triangle are 100, 40 and 40.
The exteriors would be 80, 140, 140 (this is gotten by subtracting each interior angles from 180).
So, using the above analysis, we can conclude that the statement is possible.
Solve for f 7a - 3d + 6f = 5
Answers
Answer:
f = 5/6 - 7a/6 + d/2
Step-by-step explanation: