Answers
Answer:
(25 -5√7)/3 ≈ 3.924 inches
Step-by-step explanation:
After removing squares from the corners and folding up the sides, the open-top box will have dimensions ...
x × (20 -2x) × (30 -2x)
The maximum value for this cubic expression in the domain 0 < x < 10 is found easily by a graphing calculator to be at x = 3.924 inches.
__
You can solve this by expanding the cubic and finding the solution that makes its derivative equal to 0.
V(x) = 4x^3 -100x^2 +600x
The derivative is ...
V'(x) = 12x^2 -200x +600 = 0
Dividing by 12, we have ...
x^2 -50/3x +50 = 0
Completing the square, we get the form ...
(x -25/3)^2 = -50 +(25/3)^2 = (-450 +625)/9 = 175/9
Taking the square root gives ...
x -25/3 = ±(5√7)/3
The solution in the desired range is ...
x = (25 -5√7)/3 ≈ 3.924 . . . inches
_____
Additional comment
We limit the value of x to half the width of the cardboard material, as any longer cuts would overlap to create a negative box dimension. The graph shows the maximum volume to be about 1056.3 cubic inches. Box dimensions would be 3.924 in deep by 12.153 in by 22.153 in.
__
The generic solution can be found using a similar procedure. For cardboard dimensions a×b, it will be ...
x = ((a +b) -√((a -b)² +ab))/6
Related Questions
1. Approximately fourteen 20-ounce plastic drink bottles must be recycled to produce 1 square foot of carpet. Write an expression for the number of bottles needed to make c square feet of carpet.
Answers
please hurry and help ill give brainy
The ratio of skiers to snowboarders is 5 to 2. If 210 skiers rode the chairlift in the last hour, how many snowboarders rode the chairlift during that same time?
[A] Write a proportion that is defined by this situation.
[B] Explain how the cross product is used to solve the problem.
[C] Answer the question.
Answers
Answer:
84
Step-by-step explanation:
5/2 for every 2.5 skiers one snowboarder rides
[A] 2.5 skiers to one snowboarder
[B] [tex]\frac{1}{2.5} = \frac{?}{210}[/tex]
210=2.5*x divide both sides by 2.5
x=84
[C] 84 snowboarders rode at the same time as 210 skiers
In a city the distance between the libary and the police station is 3 miles less than than the distance between the police station and fire station the distance between the libary and police station is 5 miles how far apart are the police station and the fire station
Answers
Answer:
8 miles
Step-by-step explanation:
Given
Represent the police station with P, Library with L; Fire station with F
The first statement can be represented as:
[tex]L - P = P - F - 3[/tex]
The second can be represented as:
[tex]L - P = 5[/tex]
Required
Determine the distance between the police station and the fire station (P - F)
[tex]L - P = P - F - 3[/tex] --- (1)
[tex]L - P = 5[/tex] --- (2)
Substitute 5 for L - P in (1)
[tex]5 = P - F - 3[/tex]
Add 3 to both sides
[tex]3 +5 = P - F - 3 + 3[/tex]
[tex]3 +5 = P - F[/tex]
[tex]8= P - F[/tex]
[tex]P - F = 8[/tex]
f(x) = 10x - 2x2
find f(4)
A 24
B -22
C. -24
D. -8
Answers
Answer:
maybe try A
Step-by-step explanation:
please help with the problem above
Answers
Answer:
The answer would be -9x^2+x-8
Can someone help me out please ?
Answers
Answer:
i think its option 1
Step-by-step explanation:
can someone help me please, please hurry. I may mark brainiest
Answers
A rectangle that is 2 inches by 3 inches has been scaled by a factor of 7. 1.What are the side lengths of the scaled copy? 2. Suppose you want to scale the copy back to its original size. What scale factor should you use?
Answers
Solve for the value of s.
HELP PLS NOW 20 POINTS
Answers
Answer:
15
Step-by-step explanation:
82 + (7s - 7) = 180
- subtract 82 from both sides
7s - 7 = 98
- add 7 to both sides
7s = 105
- divide both sides by 7
s = 15
combine like terms 10a-10a+1
Answers
Answer:
1
Step-by-step explanation:
10a and -10a would combine and cancel eachother out leaving you with 1
Evaluate each function over the set of real numbers.
If f(x) = |x-3|, f (3) =
-3
0
1
3
Undefined
Answers
Answer:
1.) 0
2.) undefined
3.) undefined
Step-by-step explanation:
2020EDGE
The value of function f(x) = |x-3| at x=3:
f(3) = 0
Given,
f(x) = |x-3|
Now,
Here the function f(x) is modulus function . Thus the values coming out of the function will be positive .
So,
f(x) = |x-3|
Now we have to substitute the value of x in the function.
f(3) = |3 - 3|
f(3) = |0|
f(3) = 0
Thus the value of function at x = 3 is 0 .
Know more about modulus function,
https://brainly.com/question/30241426
#SPJ2
How has our national anthem helped to promote unity in diversity?
Answers
Answer:
Nepal's national anthem really promotes diversity
Step-by-step explanation:
There are all sorts of words used that display diversity
HELP ME PLZZ I NEED HELP WITH THIS!!!
Answers
Answer:
D because you're adding to negatives and you get a postive
-2(x - 5) = -14 PLEASEEEEE HELPPPPPP
Answers
Need help with these bad
Answers
A figure has side lengths 5, 7, and 13. Could the figure be a triangle?
Answers
Answer: no
Step-by-step explanation:
round the nearest tenth 11.34? A:11.3 B:12.34 C:12 SOMEONE PLZ HELP
Answers
Answer:
B is the asnwer
Step-by-step explanation:
Answer:
Your answer is A. 11.3
Step-by-step explanation:
To round to the nearest tenth of 11.34, you will be using the 4 to determine if the 3 (in the tenth place) will be rounded up or stay the same. Since 4 is under 5, the 3 will remain the same.
(1 point) .
What is the equation, in standard form, of a parabola that models the values in the table?
х -2 0 4
f(x) 0 -6 78
a.) y= 6x² + 5x - 4
b.) y=-4x2–5x + 6
c.) y=5x2 + 4x = 6
d.) y=4x² + 5x- 6
please helpppp
Answers
Answer:
Correct answer D. y = 4x2 + 5x – 6
Step-by-step explanation:
just took the test
Plz help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
6: no
7: no
-9: yes
-2: no
What type of slope does (-7,8) and (-7,0) have?
Answers
Answer:
Undefined slope
Step-by-step explanation:
any number divided by 0 is undefined
-8/0
Answer: m=12/7
Step-by-step explanation:
I looked it up for you bro
You’d like to see how many baseball and soccer games you can attend this spring. Travel time for basketball games is 2 hours and soccer games is 1 hour. You would like to spend no more than 15 hours traveling to the games. In total, you would like to attend at least 8 games.
Answers
We have to attend 7 basketball games and 1 soccer game.
Given, we had two types of game namely basketball and soccer.
Travel time for basketball games is 2 hours and soccer games is 1 hour.
Let no. of basketball games be x and no of soccer games be y.
According to the question we would like to attend at least 8 games, so we have the inequality [tex]x+y\geq 8[/tex]
And we would spend no more than 15 hours traveling to the game, so [tex]2x+1y\leq 15[/tex].
[tex]x+y=8\\[/tex]
[tex]2x+1y=15\\[/tex]
On solving we get [tex]x=7[/tex] and [tex]y= 1[/tex].
Hence we have to attend 7 basketball games and 1 soccer game.
For more details on Equation follow the link:
https://brainly.com/question/10824691
why do math exist in school?
Answers
Answer: I have no idea
Step-by-step explanation:
pwease help thank you
Answers
So, first off, judging from the h(x) graph, h(x)=-2x–1
So this is compositions or something like that; it’s been a year since I’ve done calculus but here we go:
First, you must find f(6) by replacing every x in that function by 6
f(6) = (1/2)(6) – 4
f(6) = (6/2) – 4
f(6) = 3 – 4
f(6) = -1
Now, since you’ve found f(6), now to find h(-1) (since f is -1 and h( f(6) ) is h(-1) )
h(-1) = 2(-1) – 1
h(-1) = -2 – 1
h(-1) = -3
So, the answer is -3
The sides of a rectangle have a length of x + 4 units and a width of 2x + 5 units. Which of the following represents the perimeter of the rectangle? Someone please help. I need it
Answers
Answer:
B. 6x+18
Hope this helps!
Step-by-step explanation:
The answer is 55. You need to use the rules above to find the actual measure for angle b
Answers
Step-by-step explanation:
A circle is 360 degrees
209 is part of the circle so find the difference between 360 and 209
360 - 209 = 151
If the two angles are equivalent to 151, then we find the difference between 151 and 96 to get the measurement for angle b
151 - 96 = 55
I read now that it says use the rules above, but I'm not seeing any rules in the picture so hopefully my steps are the rules you're referring to
what is an equation of the line in, point slope form, that passes through the given point and has the given slope?
point: (8,-8); slope: 3
Answers
Answer:
I hope this helps
Step-by-step explanation:
The answer is 3.453
Answer:
y + 8 = 3(x - 8)
Step-by-step explanation:
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex]) Use point-slope form.
y - (-8) = 3(x - 8) Substitute [tex]y_{1}[/tex]for -8, m for 3, and [tex]x_{1}[/tex] for 8.
y + 8 = 3(x - 8) is the equation.
(I'd appreciate a brainliest! thanks)
The image of trapezoid PQRS after a reflection across Line W Y is trapezoid P'Q'R'S'.
2 trapezoids are shown. Line W Y is the line of reflection. Line segment R R prime has a midpoint at point Z. Line segment S S prime has a midpoint at point X.
What is the relationship between RR' and SS'?
Answers
Answer:
The answer is C. RR' || SS'
Step-by-step explanation:
Answer:
The answer is C. RR' || SS'
pls help me...
A. y is all real numbers
B. y>0
C.-6</=x </=6
D.0 </=y </=8
Answers
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[tex]0 \leqslant y \leqslant 8[/tex]
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Thus the correct answer is (( D )) .
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The atomic number of an element is equal to the number protons in the atoms of that element
True or false
Answers
Answer:
True
Step-by-step explanation:
Answer:
It is true
Step-by-step explanation:
Hope I Helped....✌
3a+ 6 = 15, 3a = 9, a+ 2= 5, 1/3a =1
are any of these equation equivalent to one another if so, which ones? Explain tou reason
Answers
Given parameters:
Find if any of the equations are the equivalent;
3a+ 6 = 15
3a = 9
a+ 2= 5
[tex]\frac{1}{3a}[/tex] =1
To find which of the equations are equivalent to one another, let us solve them first. The ones with the same solution are definitely equivalent.
(i) 3a+ 6 = 15
3a = 15 - 6
3a = 9
a = 3
(II) 3a = 9
a = 3
(III) a+ 2= 5
a = 5-2
a = 3
(IV) [tex]\frac{1}{3a}[/tex] =1
1 = 3a
a = [tex]\frac{1}{3}[/tex]
We clearly see that the first three equations are equivalent.