The cut-out from each corner that maximizes the volume is 3 inches.
The dimensions are given as:
[tex]\mathbf{Length = 15}[/tex]
[tex]\mathbf{Width = 24}[/tex]
Assume the cut-out is x.
So, the dimension of the board is:
[tex]\mathbf{Length = 15 - 2x}[/tex]
[tex]\mathbf{Width = 24 - 2x}[/tex]
[tex]\mathbf{Height = x}[/tex]
The volume (V) is calculated as:
[tex]\mathbf{V = Length \times Width \times Height}[/tex]
So, we have:
[tex]\mathbf{V = (15 - 2x) \times (24 - 2x) \times x}[/tex]
Expand
[tex]\mathbf{V = 360x - 78x^2 + 4x^3}[/tex]
Differentiate
[tex]\mathbf{V' = 360 - 156x + 12x^2}[/tex]
Set to 0
[tex]\mathbf{ 360 - 156x + 12x^2 = 0}[/tex]
Divide through by 12
[tex]\mathbf{ 30 - 13x + x^2 = 0}[/tex]
Rewrite as:
[tex]\mathbf{ x^2 - 13x + 30 = 0}[/tex]
Using a calculator, we have:
[tex]\mathbf{x = \{3, 10\}}[/tex]
The value of x = 10 is greater than the dimensions of the box.
So, we have:
[tex]\mathbf{x = 3}[/tex]
Hence, the cut-out from each corner that maximizes the volume is 3 inches.
Read more about maximum volumes at:
https://brainly.com/question/7063268
HELP PLEASE please somebody help
Answer:
right triangle
Step-by-step explanation:
gl
Lola's pet turtle walked 10 feet, and then half that length again.
Lola's baby brother walked 3 feet, and then half that length again.
Lola's hamster walked 6.5 feet, and then half that length again.
Lola's mom walked x feet, and then half that length again.
11.
(7x-23)
49°
(3x)
(11y- 1)
Answer:7x−23=7x−23
49°=7x−23
3x=3x
11y−1=11y−1
Step-by-step explanation:
help plz ill give brainliest Which expression is equivalent to 4(3y + 7) + 5y?
28y + 17
17y + 28
8y + 28
17y + 7
Answer:
17y+28
Step-by-step explanation:
First, distribute the 4 to 3y+7. This would get you 12y+28. Then add the 5y to the 12y+28. This would bring you to your answer of 17y+28
Answer:
4(3y+7)+5y= 12y+28+5y=17y+28
The two lines represent the amount of water bottles filled ( in gallons) over time in two different factories. Which factory is filling more quickly? Explain how you know?
Ryan and clarie are solving the equation -3x+7=-14.Ryan says the answer is x=7.Claire says the answeris x=-7.Who do you agree with andwhy
Which of the following is a rational number?
a
A) ✓2.5
B) - ✓64
C) 4✓5
D) ✓ 14.4
i think it’s D but i don’t know for sure
Answer:
A. is the right answer
Step-by-step explanation:
D is not right because it is not a perfect square. A is the only perfect square optional, which makes it rational. Hope this helps :)
Translate the sentence into an equation.
Three less than the product of 2 and a number is equal to 6.
Use the variable x for the unknown number.
Answer:
2x - 3 = 6
Step-by-step explanation:
solve for 'x':
2x - 3 = 6
2x = 9
x = 9/2 or 4 1/2
Check:
2(9/2) - 3 = 6
9 - 3 = 6
6 = 6
Solve for x: 1/9 x what = 2 1/8
Answer:
x=1/8
Step-by-step explanation:
pickpeuhahaahahaha
Answer:
1/9 x 21/8 = 7/24
Step-by-step explanation:
Can someone help please?
Answer:
Step-by-step explanation:
You multiply the bottom number
and keep the top one like it is
answer this questions plz and if you do i will mark u the brainliest
A gardener is planting sunflowers around the sides of the square - shaped garden. What will be the length of the garden if the gardener covered 24 m covering around the garden?
Answer:
96 m
Step-by-step explanation:
a farm has almond trees and walnut trees. the number of almond trees is 2 third of the number of walnut trees. there are almost 120 almond trees.
how many walnut trees are there
Find the value of x and y in each parallelogram shown below.
Answer:
x= 12
y= 4
Step-by-step explanation:
x
15+ 9= 24
24÷ 2= 12
x= 12
y
21- 1= 20
20÷ 5= 4
y= 4
I need help quick plssss
go extra 90 ang taya mo the n adto ang iya mga manok mga 50 my karapatan b pre ung mga anak nya kc kasal dw cla ng tube and
Answer:
The rate of change is -3. The y-intercept (0,1). The equation of this linear function is y = -3x + 1
EXPLANATION: It is (0,1) because 0 is the x-intercept and 1 is the y-intercept. (x,y)
Sandy walks 26 miles in a month. If she were consistent in her walking for 2 years, how many miles will she have walked?
Answer:
624 miles
Step-by-step explanation:
there are 12 months in a year.
meaning, 24 months in two years.
if she is able to walk 26 miles a month, for 24 months
(multiply 26x24)
she will walk 624 miles.
Before: 42 dogs
Now: 35 dogs
What is the percentage decrease?
Answer:
16.7% (to 3sf)
Step-by-step explanation:
Percentage decrease
= [tex]\frac{42-35}{42}[/tex] × 100%
= [tex]\frac{7}{42}[/tex] × 100%
= [tex]\frac{1}{6}[/tex] × 100%
= 16.7% (to 3sf)
(-7,1) and (-7,-5) on the coordinate
plane?
Answer:
(-7,1) lies on the 2nd quadrant
(-7,-5) lies on the 3rd quadrant
Hope it helps:)
rearrange the word theet
Answer: The word rearranged could be teeth.
:)
Answer:
teeth
Step-by-step explanation:
6a+3a+8b+a−5b
3b+6a3 b plus 6 A
3b+9a3 b plus 9 A
3b+10a3 b plus 10 A
13b+9a
ASAP PLEASE
Answer:
all 5
Step-by-step explanation:
6a+3a+8b+a-5b = 10a+3b
3b+6a+3b+6a = 9b+6a
3b+9a+3b+9a = 6b+18a
3b+10a+3b+10a = 6b+20a
13b+9a = 13b+9a
Can anyone help me with this???
Answer:
A and C are both solutions to the equation.
8.
Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y= 2/3x + 9; (–6, 5)
A. y= 2/3x + 9
B. y= -2/3x + 1
C. y= -3/2x - 4
D. y= -3/2x + 3/2
Answer:
B
Step-by-step explanation:
I had this question before
Answer:
C. y= -3/2x - 4
Step-by-step explanation:
Option 2, y=-3/2x-4
Step-by-step explanation:
Solve with the point-slope formula: y-y1=m(x-x1). The line is perpendicular, meaning the slope of the new equation will be the oppposite reciprocal of the original slope.
First, we need to rewrite the original equation into standard form.
2x-3y=13
-3y=13-2x
y=-13/3+2/3x
From this, we can see that the slope here is 2/3. Since the line we're looking for is perpendicular, the opposite reciprocal of that slope is -3/2.
Now, we can plug in the coordinates we have into the formula (-6, 5), along with our slope (-3/2).
y-(5)=-3/2(x+6)
y-5=-3/2x-9
y=-3/2x-4
And to check, we can just plug the coordinates into our new equation:
Check:
(5)=-3/2(-6)-4
5=9-4
5=5
(x+3)(x-3)-x(x+4)=15
Find MP.
Segment addition
Answer:
MP = 29
Step-by-step explanation:
MP = 5y + 9
MP = MN + NP
MP = 17 + 3y
Step 1 - As both equations are equal to MP:
3y + 17 = 5y + 9
Step 2 - Subtract 9 from both sides to isolate the 5y:
3y + 17 - 9 = 5y + 9 - 9
3y + 8 = 5y
Step 3 - Subtract 3y from both sides:
3y + 8 - 3y = 5y - 3y
8 = 2y
Step 4 - Divide both sides of the equation by 2:
[tex]\frac{8}{2} = \frac{2y}{2}\\4 = y[/tex]Step 5 - Plug known variable y back into the equation:
5y + 9 = MP
5(4) + 9 = MP
20 + 9 = MP
MP = 29
Hope this helps!What is one difference between a pre-owned car and new car?
- Both have less repairs.
✅Pre-owned cars are cheaper.
- New cars depreciate less rapidly.
- They both have lifetime warranties.
Answer:
Pre-owned cars are cheaper.
Step-by-step explanation:
Which equation can be used to describe the relationship between x and y shown in the table below?
Answer:
y = 3x/2 + 24
Step-by-step explanation:
y = ax + b
⇒ 6 = -12a + b
9 = -10a + b
⇒ 2a = 3, a = 3/2
⇒ b = 24
⇒ y = 3x/2 + 24
Yes I will Mark Brainlist
Answer:
D = 3.5t
Step-by-step explanation:
Distance = Speed · Time
Plug in the numbers and you get D = 3.5t
Hope this helps!
PLS SOLVE THIS ASAP IM IN CLASS
5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13
Answer:
no solution
Step-by-step explanation:
-5(-3x-2)-(x-3)=-4(4x+5)+13
-15x-10-x+5=-16x-20+13
-16x-5=-16x-7
-5=-7
1. Which value of x is the solution of the equation
5 = 2(x – 8) - x
-
1) – 21
2) 3
3) -3
4) 21
Answer:
21
Step-by-step explanation:
5 = 2(x - 8) -x
5 = 2x - 16 -x
5 = x - 16
16 + 5 = x
21 = x
Answer:
= 2 1 /2
hope it helps you! :D
Find the value of x.
Answer:
-2
Step-by-step explanation:
The two angle are internal alternate relative to the two parallels, so they have the same measure.
[tex]-8x+8 = -6x+20\\-2x=12 \rightarrow x = -2[/tex]
Answer:
x = -6
Step-by-step explanation:
The two angles given are alternate angles - this means they are equal. Therefore:
-8x + 8 = -6x + 20
We can solve this by first putting all the x's on one side and the numbers on the other side:
-8x + 6x = 20 - 8
Now we can simplify both sides down:
-2x = 12
Finally divide both sides by -2 to get x on its own:
x = -6
Hope this helps!
