Answer:
191.016 in²
Step-by-step explanation:
Let the volume of the cube be V = lwh where l = length of box, w = width of box and h = height of box.
Now l = 3w.
So, V = lwh = (3w)wh = 3w²h
h = V/3w²
Since the rectangular box is open at the top, its total surface area is A = lw + 2lh + 2wh
substituting l = 3w, we have
= (3w)w + 2h(l + w)
= 3w + 2h(3w + w)
= 3w² + 2h(4w)
= 3w² + 8wh
substituting h = V/3w²
= 3w² + 8w(V/3w²)
A = 3w² + 8V/3w
Differentiating A with respect to w and equating it to zero, we have
dA/dw = d[3w² + 8V/3w]dw
dA/dw = d3w²/dw + d(8V/3w)/dw
dA/dw = 6w - 8V/3w²
dA/dw = 0
6w - 8V/3w² = 0
6w = 8V/3w²
6w³ = 8V/3
w³ = 8V/(3 × 6)
w³ = 4V/9
w = ∛(4V/9)
substituting V = 220 in³, we find the minimum value for the width
w = ∛(4 × 220 in³/9)
w = ∛97.7778
w = 4.607 in
To determine if this is a minimum value of width which gives minimum area, we take the second derivative of A. So,
d²A/dw² = d(6w - 8V/3w²)/dw
= 6 + 16V/3w³
substituting w³ = 4V/9, we have
d²A/dw² = 6 + 16V/3(4V/9)
= 6 + (16 × 9)/(3 × 4)
= 6 + 4 × 3
= 6 + 12
= 18
Since d²A/dw² = 18 > 0 , w = ∛(4V/9) = 4.607 in gives a minimum for the surface area.
So, we calculate this area by substituting w = 4.608 in. So,
A = 3w² + 8V/3w
= 3 × (4.607 in)² + (8 × 220 in³)/(3 × 4.607 in)
= 63.6733 in² + 1,760 in³/13.821 in
= 63.6733 in² + 127.3424 in²
= 191.0157 in²
≅ 191.016 in² to three decimal places.
Which expression is equivalent to 4 – (-7)
a 7+ 4
b 4 - 7
c-7 - 4
d -4 + 7
Answer:
A. 7 +4
Step-by-step explanation:
4 -( - 7 )
4 + 7
7 + 4
Answer:
a
Step-by-step explanation:
4 + 7 = 11. subtracting a negative number is the same as adding
Solve for xxx.
Your answer must be simplified.
x/-6 ≥ -20
[tex] \mathsf{Hey \: there}[/tex]
[tex] \mathsf{\dfrac{x}{ - 6} \geq - 20}[/tex]
We can substitute the greater or equal to sign as a "equal" sign (for now)[tex] \mathsf{\dfrac{x}{ - 6} = - 20}[/tex]
Multiply both of your sides by ⬇[tex] \mathsf{ \dfrac{6}{-1}}[/tex]
Like[tex] \frac{6}{-1} \times \frac{ -1}{6} \mathsf{x} = \frac{6}{-1} \times - 20[/tex]
[tex] \mathsf{Cancel \: out: \dfrac{6}{ -1} \times \dfrac{ - 1}{6} \: because \: it \: you \: 1 }[/tex]
[tex] \mathsf{Keep:{\dfrac{6}{-1} \times \: -20} \: because \: it \: helps \: solve \: for \: your \: equation}[/tex]
[tex] \mathsf{x = 120}[/tex]
We do the same for your equation but a tad bit different![tex] \boxed{ \mathsf{your \: answer: \boxed{ \mathsf{ \huge\bf{x \leq120}}}}} \checkmark[/tex]
- ITS AN OPENED CIRCLE SHADED TO THE LEFT GOOD LUCK ON YOUR ASSIGNMENT AND ENJOY YOUR DAY!~
[tex] \dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]
Answer:
hehe <120 i thinkkkkkkkkk
Step-by-step explanation:
What is the greatest place value in this number, 189?
Answer:
the 1 cause it's a 100
Step-by-step explanation:
100 + 80 + 9
In a recent year, 0.57 of those registered to vote in the United States voted in an election.
Write 0.57 as a percent.
Answer:
57%? I think.
Step-by-step explanation:
Answer: 57% iḿ sure.
Step-by-step explanation:
which inequality is true?
Answer:
the answer is B
Step-by-step explanation:
For which inequality is x = 5 a solution ?
Answer:
C
Step-by-step explanation:
because x<2 is ... -1,0,1
x>9 is 100,11,12...
but x<18 is 17,16.. 6,5,4
x>42 is more than 42 so 43,44,45...
Find the point-slope equation of the line contains (-2,-3) and having slope m=4
Answer:
y + 3 = 4 x (x + 2)
Step-by-step explanation:
point slope formula is y-y1 = m(x-x1)
slope intercept form is y = 4x + 5
y=mx +b
m=4
Find the prime factorization of 32. Write in exponential form.
A. 2 × 2 × 2 × 2 × 2
B. 26
C. 2 × 2 × 2 × 2
D. 25
Answer:
find the prime factorization of 32. write in exponential form.
option A is correct
Two people are driving to work at different constant speeds. The graph below shows the distance traveled over time by driver 1.
The table (no graph included just the table) below shows the distance traveled over time by driver 2.
What is the difference between the speeds of the two drivers in mph?
Answer:
5 mph
Step-by-sep explanation:
To find of out the difference between the speed of the two drivers in miles per hour (not in miles per minute), first, calculate the unit rate or speed of driver 1 using the graph, and driver 2 using the table given.
Unit rate/speed = distance travelled/time = y/x.
Speed of Driver 1/unit rate:
The graph shows 1.5 miles (y) is travelled in 2 minutes (x).
Convert the 2 minutes to hour, you will have:
[tex] \frac{2}{60} = \frac{1}{30} hr [/tex]
Speed in mph = [tex] \frac{y}{x} = \frac{1.5}{\frac{1}{30}} = 1.5*\frac{30}{1} = 45 [/tex]
Speed of Driver 1 in mph = 45 mph
Speed of Driver 2/unit rate:
The table shows 2.5 miles (y) is travelled in 3 minutes (x).
Convert the 3 minutes to hour, you will have:
[tex] \frac{3}{60} = \frac{1}{20} hr [/tex]
Speed in mph = [tex] \frac{y}{x} = \frac{2.5}{\frac{1}{20}} = 2.5*\frac{20}{1} = 50 [/tex]
Speed of Driver 2 in mph = 50 mph
Difference between the speed of the two drivers = 50 - 45 = 5 mph
describe the prime factorization of 180
Answer:
5 x 2 x 2 x 3 x 3 = 180Step-by-step explanation:
HOPE THIS HELPS’
PLZZ MARK BRAINLIEST
choose the correct solution and graph
z+9≤6
Answer:
z ≤ -3
Step-by-step explanation:
z + 9 ≤ 6
z ≤ -3
are the triangles congruent ?
Answer:
yes its sss
Step-by-step explanation:
Answer:
SSS BECAUSE THE TRIANGLE IS GOING UP AND DOWN SO 5% of it so SSS
Which graph is this?
I need help with this
Answer:
120 students
Step-by-step explanation:
so divide 300 by 10 = 30
then multiply it by 4 = 120
I WILL GIVE BRAINLIEST AND POINTS PLEASE GIVE ME THE ANSWER OF THIS FAST PLEASE!!!!!
what is 52.03 squared?
Answer:
It is 2707.1209
Step-by-step explanation:
15% of the students in the class
did not complete their homework. If there
are 20 students in the class, how many didn't do their homework?
Answer:
3
Step-by-step explanation:
15% of 20 Is 3.
Jenny cut a wire into 4 equal pieces. The wire was originally 7.92 meters long. How long is each piece?
Answer:
1.98 meters
Step-by-step explanation:
divide 7.92 by 4
(7.92)/4
1.98
why does 4^3 equal 64 and not 12
Answer:
because 4.4.4.4
Step-by-step explanation:
Use the distributive property to remove the parentheses. Simplify your answer as much as possible.
1/2(4w-5)
please help i need answers asap
Answer:
2w - 2 1/2
Step-by-step explanation:
you need to multiply the faction by each one of the numbers. multiplying them by 1/2 is going to be the same was dividing them by 2
4w (1/2) - 5 (1/2)
2w - 2 1/2
hope this helps!
How do you do this question?
Answer:
z = -ln│5eᵗ + C│
Step-by-step explanation:
dz/dt + 5eᵗ⁺ᶻ = 0
dz/dt = -5eᵗ⁺ᶻ
dz/dt = -5eᵗeᶻ
-e⁻ᶻ dz = 5eᵗ dt
e⁻ᶻ = 5eᵗ + C
-z = ln│5eᵗ + C│
z = -ln│5eᵗ + C│
The Tigers, a football team, must gain 10 yards in the next four plays to keep possession of the ball. The Tigers lose 24 yards, gain 4 yards, and lose 10 yards. How many yards do they need to keep possession?
40
20
-20
-8
Answer:
B. The must gain 20 yards to keep possessionStep-by-step explanation:
Let the number of yards gained be positive
Let the number of yards lost be negative
Since the total that must be gained in the next four games is 10, hence the total is +10
If The Tigers lose 24 yards, gain 4 yards, and lose 10 yards in the first three rounds with x being the number of yards in the fourth round, this is expressed as;
-24 + 4 - 10 + x = 10
-20 - 10 + x = 10
-30 + x = -10
x = -10 + 30
x = 20
Hence they need 20 yards in the last round to keep possession
HELP ASAP RN 10 POINTS AND BRAINLIEST TO WHOEVER DOES IT CORECTLY The cost to rent a bicycle at Freewheels is $10 plus an hourly rate for each hour the bicycle is rented. The graph represents the linear relationship between the cost, in dollars, to rent a bicycle and the
number of hours rented.
Based on the graph, which statement is true?
Freewheels charges a $4 initial fee and $10 per hour.
Freewheels charges a $10 initial fee and $4 per hour.
Freewheels charges an $8 initial fee and $42 per hour.
Freewheels charges a $42 initial fee and $8 per hour.
Answer:
Freewheels charges a $10 initial fee and $4 per hour.
that is the correct answer! hope this helped!
The coordinates from the graph.
(0, 10) and the rate of change is 4.
Freewheels charge a $10 initial fee and $4 per hour.
Option B is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
From the graph, we have the following coordinates.
(0, 10)
(1, 14)
(2, 18)
(3, 22)
(4, 26)
(5, 30)
(6, 34)
Now,
The coordinates (0, 10) mean that there is an initial fee of $10.
Rate of change between two points.
= (18 - 14) / (2 - 1)
= 4/1
= 4
This means there is a charge of $4 per hour.
From the graph, we see that,
Freewheels charge a $10 initial fee and $4 per hour.
Option B is the correct answer.
Thus,
The coordinates from the graph.
(0, 10) and the rate of change is 4.
Freewheels charge a $10 initial fee and $4 per hour.
Option B is the correct answer.
Learn more about coordinates here:
https://brainly.com/question/13118993
#SPJ2
There are 105 members in a marching band. They are traveling on buses. Each bus holds 35 members. How many buses are needed to carry the band members?
Answer:
3 buses i'm pretty sure :))
Mai has 4 CDs that she is going to give away. She lets her best friend choose 3 of the 4 CDs. How many different groups of 3 CDs are possible?
A party planner estimates a party will cost $200 plus $8 for each person attending. What is the y-intercept of the graph of the linear function representing the total cost of the party?
Answer:
The y intercept is 200
Step-by-step explanation:
Given
Base Cost = 200
Per person =8
Required
Determine the y intercept
First, we need to determine the equation.
The total amount (y) for x persons can be calculated using:
y = Base Cost + Amount per person * x.
This gives
y = 200 + 8 * x
y = 200 + 8x
The general expression of a linear equation is:
y = mx + b
Where b = y intercept
By comparison,
b = 200
Hence, the y intercept is 200
Which shows the best use of associative and commutative properties to make simplifying 3/4 - 5 + 9 -2/4 + 2 easier?
Answer:
(-5) + 9 + 2 + 3/4 + (-2/4)
NEED HELP ASSSAAPPP
Choose the correct slope of the line that passes through the points (-4, 8) and (-8,8).
O slope = undefined
O slope = -1
O slope = 1
O slope = 0
Answer:
0
Step-by-step explanation:
Find f(-5) If f(x) = lx+ 1l.
I need the correct answer not the wrong answer or the I don’t know answer CORRECT..
Answer:
6 un
Step-by-step explanation:
2 22= 6
Answer:
1
Step-by-step explanation:
2devided
by 2 =1