A rectangular sheet of cardboard 3 feet by 5 feet will be made into an open box by cutting equal-sized squares from each corner and folding up the four edges. A diagram of the unfolded box is provided in figure, the shaded region represents the area
that was cut from the corners of the box. What is the largest volume of such a box?
Answers
Answer:
4[tex]x^{3}[/tex] - 16[tex]x^{2}[/tex] + 15x
Step-by-step explanation:
length = 5 - 2x
width = 3 - 2x
heighth = x
x(5 - 2x)(3 - 2x)
x(15 -16x + 4[tex]x^{2}[/tex])
4[tex]x^{3}[/tex] - 16[tex]x^{2}[/tex] + 15x
The largest volume of such a box is 4.345[tex]ft^{3}[/tex].
Given that,
A rectangular sheet of cardboard 3 feet by 5 feet will be made into an open box by cutting equal-sized squares from each corner and folding up the four edges.
The shaded region represents the area that was cut from the corners of the box.
We have to determine,
The largest volume of such a box.
According to the question,
The height will be x
The width will be (3 − 2 x)
And the length will be ( 5− 2 x)
.
The formula for volume will be,
[tex]Volume = Length \times Height \times Width\\\\[/tex]
Substitute the values in the formula,
[tex]Volume = x(3-2x).(5-2x)\\\\Volume = (3x-6x^{2}).(5-2x)\\\\Volume = 3x(5-2x) - 6x^{2}(5-2x)\\\\Volume = 15x - 6x^{2} - 30x^{2} + 12x^{3}\\\\Volume = 12x^{3} -36x^{2} + 15x[/tex]
Then,
To Find the derivative of the equation,
[tex]V = 12x^{3} -36x^{2} + 15x\\\\Differentiate\ with\ respect\ to\ x\ both\ sides,\\\\\dfrac{dv}{dx} = \dfrac{d(12x^{3} -36x^{2} + 15x)}{dx}\\\\V' = 36x^{2} - 72x+15[/tex]
The critical numbers by seeing where V ' = 0,
[tex]= 36x^{2} -72x +15\\\\= 3 ( 12x^{2} - 24x +5 )\\[/tex]
By using the quadratic formula or your calculator to solve for
x = 0.23, and 1.6
x = 1.6 is not in the domain since that would make one of our side lengths less than zero. x = 0.23
Plug x back into the equations to get the dimensions,
[tex]3-2x = 3- 2 \times -0.23 = 3+0.46 = 3.46\\5-2x = 5 - 2 \times -0.23 = 5+0.46 = 5.46[/tex]
Therefore, the dimension are 0.23 ft x 3.46 ft x 5.46 ft.
Hence, The largest volume of such a box is 4.345[tex]ft^{3}[/tex].
To know more about Dimension click the link given below.
https://brainly.com/question/23288467
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Please help I can’t fail this
Answers
Answer:
B
Step-by-step explanation:
I plugged it into a graphing calculator but if you use "rise over run" you'll get your answer without a phone
En un parque de forma circular de 700 m de radio hay situada una fuente,
tambien de forma circular, de 5 m de radio. Calcula el área de la zona de
paseo.
Answers
área del parque
A=Pi . R^2
A=Pi (700m^2)
A=3.1416 x 490000m^2
A= 1539380.4 m ^2
área de la fuente
a= Pi. r^2
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a=3.1416 x 25cm^2
a= 78.54 cm^2
Luego lo que hacemos que al area grande le restamos la pequeña.
pero antes que nada convertiremos los metros a centimetros.
A= 1539380.4 m^2
1539380.4 m^2 (100cm/1m)
eliminaras los metros y te quedara asi
1539380.4 ( 100 cm/ 1)
153,938,040 cm^2
luego restamos A-a
153,938,040 cm^2 - 78.54cm^2
R/ el area de la zona de paseo es de 153937961.5 cm^2 !!
I need help with this one. Please. thanks!
Answers
Explanation:
Get x by itself therefore subtract 6 from both sides
24 = 4x
Divide both sides by 4
6=x
Hope this helps ;)
Answer:
x=6
Step-by-step explanation:
30=6+4x
you have to combine the number that are the same, like 2 and 4 or 3x and 4x
30-6=4x (you should always remember when you move a number if it was - it will turn +)
30-6=4x
24=4x
x=24/4
x=6
The set of life spans of an appliance is normally distributed with a mean Mu = 48 months and a standard deviation Sigma = 8 months. What is the z-score of an appliance that stopped working at 64 months?
Group of answer choices
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-1
2
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Answers
Answer:
D.2
Step-by-step explanation:
The z-score of an appliance that stopped working at 64 months is 2
What is z score?Standard score or z score in statistics is defined as the number of standard deviations by which that the value of a score is above or below the mean value.
The formula to find the z score of a data is,
z = (x - μ) / σ
Here x is the observed value, μ is the mean and σ is the standard deviation.
Given that,
Mean = 48 months
Standard deviation = 8 months
x = 64 months
Substituting in the formula,
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Hence the z score of the appliance is 2.
Learn more about Z Score here :
https://brainly.com/question/15016913
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
radius is half of the diameter
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Answers
Answer:
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Step-by-step explanation:
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11. One term, about 700 Statistics 2 students at the University of California, Berkeley, were asked how many college mathematics courses they had taken, other than Statistics 2. The average number of courses was about 1.1; the SD was about 1.5. Would the histogram for the data look like (i), (ii), or (iii)? Why?
Answers
Answer:
(i)
Step-by-step explanation:
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Answers
Answer:
18/5
Step-by-step explanation:
12+17+20+8+13 =70
70/5 = 14 which is the mean
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2 3 6 6 1
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18/5
A local hamburger shop sold a combined total of 596 hamburgers and cheeseburgers on Saturday. There were 54 fewer cheeseburgers sold than hamburgers.
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Answers
Answer:
542
Step-by-step explanation:
I believe it is 542, because 596 and 54 are the only numbers available in this equation, so you would subtract 54 from 596
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Answers
Answer:
4%
Step-by-step explanation:
Given data
The total sales= $8900
Donated amount=$356
Hence the percent donated is
=Donated amount/Total Sales *100
= 356/8900*100
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Answers
Which choice is equivalent to the quotient below shown here when x>0?
Answers
Answer:
B
Step-by-step explanation:
step 1 - rationalize the denominator to get:
[tex]\sqrt{35x^5}[/tex] ÷ [tex]\sqrt{7x^3}[/tex] = ([tex]\sqrt{245}[/tex] ·x^5/2·x^3/2) ÷ 7x³
= ([tex]\sqrt{5}[/tex][tex]\sqrt{7}[/tex][tex]\sqrt{7}[/tex]·x^4) ÷ 7x³
= 7[tex]\sqrt{5}[/tex]·x^4 ÷ 7x³
= [tex]\sqrt{5}[/tex]x
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Answers
Answer:
false
Step-by-step explanation:
False
5(9)(3.2)
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Look at the Example. How do you know that (-3/4)(-8a)+(-3/4)(-12) is equivalent to both -3/4(-8a-12) and 6a+9?
PLEASE HELP I WILL GIVE BRAINLIEST.
Answers
Step-by-step explanation:
To solve the problem [tex]-\frac{3}{4} (-8a-12)[/tex]
we first use the distributive property, which means to multiply everything on the inside with the outside number on the left.
so [tex]-\frac{3}{4} * -8a, -\frac{3}{4} *-12[/tex]
This would equal
[tex]6a+9[/tex]
its pretty simple.
what may be confusing is the fraciton multiplication
to solve this we convert the -8 and -12 into a fraction. This would be
[tex]-\frac{8}{1} and-\frac{12}{1}[/tex]
and multiplying fractions is easy, u just do it straight across.
so 3 times 8 is 24 so this would be 24/4
and 24/4 simplified is 6
and 3 times 12 is 36
so it would be 36/4
this would equal 9 simplified
and since we are just multiplying all negative numbers here they all turn out to be positive numbers because you should know. a negative times a negative equals a positive.
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x (4 - 20)
2 (2x - 10)
4(x - 20)
4(x - 5)
Answers
Answer:
4(x-5)= 4x-20
so the equivalent equation is 4(x-5)
Answer:
I don't actually know sorry
Step-by-step explanation:
I don't know
2. The mean weight of the students on the
Trail Middle School wrestling team is 150
pounds with a mean absolute deviation of
10 pounds. The mean weight of the
students on the Burlington Middle School
wrestling team is 130 pounds with a mean
absolute deviation of 10 pounds. By how
many pounds is the mean weight of the
students on Trail's team greater than the
mean weight of the students on
Burlington's team?
Answers
Answer:
The mean of Trail Middle School wrestling team is greater by 20 pounds as compared to that of Burlington Middle School wrestling team
Step-by-step explanation:
Since the value of absolute deviation in case of Trail Middle School wrestling team and Burlington Middle School wrestling team is same. Hence, there will be no impact of it while determining the difference in mean deviation of both the team.
Thus, the difference in mean deviation is [tex]150-130 = 20[/tex]
The mean of Trail Middle School wrestling team is greater by 20 pounds as compared to that of Burlington Middle School wrestling team
What is the slope of the line that passes through the points (-8, -6)(−8,−6) and (-18, 6) ?(−18,6)? Write your answer in simplest form.
Answers
We can find the rise over run by solving for and simplifying:-6-6/-8-(-18)=-12/10=-6/5
Find the area of a circle with a circumference of 31.4 units.
Answers
Answer:
area = 78.46
Step-by-step explanation:
31.4 = 2pi * r
divide 31.4 by 2 and get 15.7
15.7 = pi * r
divide 15.7 by pi and get
4.997 = r
(4.997^2) * pi = 78.46
Answer:
I agree with you. that is what I got too