An open rectangular tank is made so as to contain 4.5 metres cube of liquid. The length must be twice the breadth and the amount of material used to make the tank must be minimum. Find the dimensions of the tank.
To find the dimensions of an open rectangular tank that holds 4.5 m3 of liquid with minimal material, set the length as twice the breadth and use calculus optimization to derive the breadth, length, and height.
Explanation:The student is asking for the dimensions of an open rectangular tank that can hold 4.5 m3 of liquid, where the length is twice the breadth, and the amount of material used should be minimal. To solve this, we will use optimization techniques often found in calculus.
Let the breadth be b, the length be l = 2b, and the height be h. The volume V of the tank is given by V = l \b \h = 4.5 m3. Therefore, 2b2h = 4.5.
The surface area A of the tank, which we need to minimize, is A = 2lh + 2bh + lb (since the top is open). Substituting l = 2b, we get A = 2(2b)h + 2bh + (2b)b.
From the volume equation, we can express h in terms of b, which is h = 4.5 / (2b2). Substituting this into the area equation and differentiating it with respect to b will give us a minimum. Finally, solving the equations will determine the breadth, from which we can find the length and height. By this process, we can find the dimensions with the least surface area.
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You put $500 in your bank account. With an interest rate of 5%, how long will it take the account to reach $600?
What is:
1.8 divided by ——— = 60
Fill in the blank
Plz help I need this really quick
help please ..................... and look below for full question instead of reporting me
A chef has 15 3/4 lb of beans. She packs them in freezer bags that weigh 2 1/4 lb each. How many freezer bags of beans does the chef pack?
What percent of 100 is 40
Kiera wants to increase her savings account to a balance of $1,350. Her current balance is $174 and she adds $84 a month to her savings. How many months will it take for her to reach her goal of $1,350
16 months
14 months
18 months
12 months
How many seconds equal 3.6 hours?
an electrician can wire on average 4.5 houses per week. how many months will it take her to wire 55 houses if she wires the same number each week and figures on 4.5 week per month?
Final answer:
The electrician would take approximately 3 months to wire 55 houses at a rate of 4.5 houses per week.
Explanation:
An electrician can wire 4.5 houses per week.
To wire 55 houses at a rate of 4.5 houses per week, the electrician would take 55 / 4.5 = 12.22 weeks. As there are 4.5 weeks per month, dividing the total weeks by the weeks per month gives 12.22 / 4.5 = 2.72 months, which rounds up to 3 months.
The perpendicular bisectors of ΔPQR intersect at point A as shown in the diagram. What is the radius of the circumscribed circle of ΔPQR?
how many hours is it from 12am-5am
A handyman charges fixed or r to visit a customer house in addition the handyman charges an hourly rate of H for each hour worked write a formula to represent T the total amount this handyman would charge for a job that requires N hours of work
Answer:
T = HN + r
Step-by-step explanation:
A handyman charges $H for each hour worked.
If the handyman works for N hours then the expression for the charges will be = $HN
Handyman charges a fixed amount = $r
Then the total amount charged T will be represented by
T = HN + r
Therefore, formula to calculate the total charges by handyman will be
T = HN + r
What's the sum of all the integers between √3 and √89 ?
PLEASE ANSWER!!!!! After five years of earning interest at an annual rate of 3%, an investment has earned $950 in interest. To the nearest whole dollar, determine the amount of the initial investment. Show all work for full credit.
Which graph represents the solution set of the system of inequalities?
−2x+y≤4
{
y>x+2
Answer:
Graph 2
Step-by-step explanation:
Given system of inequalities,
−2x + y ≤ 4,
y > x + 2
∵ Related equation of −2x + y ≤ 4 is,
-2x + y = 4 ⇒ y = 4 + 2x ----(1)
While, the related equation of y > x + 2 is,
y = x + 2
From equation (1),
4 + 2x = x + 2 ⇒ 4 + 2x - x = 2 ⇒ 4 + x = 2 ⇒ x = 2 - 4 ⇒ x = -2
Again by equation (1),
y = 4 + 2(-2) = 4 - 4 = 0
Hence, the intersection point of the related equation is (-2,0),
∴ Graph 1 and graph 3 can not be the graph of the given system.
Now, −2(0) + (0) ≤ 4 ( true )
That is, −2x+y ≤ 4 would contain the origin,
Also, 0 > 0 + 2 ( False )
That is, y > x + 2 does not contain the origin.
Therefore, by the above explanation it is clear that,
Grap 2 represents the solution set of the system of inequalities.
the estimated product of 20.7 and 9.18 after rounding both factors to the nearest whole number is
A robot can complete 8 tasks in 5/6 or an hour.each tasks takes the same amount .how long does it take the robot to complete one task
helppppp pleaseeeeeeee
Please help me!
x + 6 ≤ 8
What is the maximum height of a projectile, such as a rocket, called?
The function f(x) is graphed on the coordinate plane.
What is f(−4) ?
Enter your answer in the box.
f(−4) =
For this case, what you should do is observe in the graph the value of the function when x = -4.
The value of the function is observed when looking at the vertical axis.
Remember that in a function of the form y = f (x) we have:
x: independent variable
y: dependent variable.
Therefore, for x = -4 we have:
f (-4) = 4
Answer:
The value of the function evaluated at x = -4 is given by:
f (-4) = 4
The greatest common factor of 56 f^3g^2 and 70 fg^3 is 7 fg^3 .
true or false
Answer: False
Step-by-step explanation:
You can see 7*3*2*f*g is not the same as 7fg3, so the statement is false.
a theater has 4650 seats. if the theater sells all the tickets for each of its 5 shows, about how many tickets will the theater sell in all?
Plot the line for the equation on the graph. y−2=−2(x+4)
The plot of the given line is required.
The graph is shown below with two points [tex](0,-6)[/tex] and [tex](-3,0)[/tex].
The line is
[tex]y-2=-2(x+4)\\\Rightarrow y=-2x-8+2\\\Rightarrow y=-2x-6[/tex]
Let us find two points on the line
[tex]x=0[/tex]
[tex]y=-2\times0-6=-6[/tex]
[tex](0,-6)[/tex]
[tex]y=0[/tex]
[tex]0=-2x-6\\\Rightarrow x=\dfrac{6}{-2}=-3[/tex]
[tex](-3,0)[/tex]
Join the two points on the graph and the line will be constructed.
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Please solve problem # 23
What is 121,580 Rounded to the nearest thousand?
out of 40 students in billy's class, 18 are girls. what percent of the students are boys?
There are 22 boys in Billy's class of 40 students, which means that 55% of the students are boys.
Explanation:To find the percent of students that are boys in Billy's class, we can start by calculating the number of boys. There are 40 students in total and 18 are girls. Therefore, the number of boys is 40 students minus 18 girls, which is 22 boys. Now, to calculate the percentage of boys, we use the formula:
Percentage = (Number of boys / Total number of students) × 100%
By inserting the numbers we have:
Percentage = (22 / 40) × 100%
Percentage = 0.55 × 100%
Percentage = 55%
So, 55% of the students in Billy's class are boys.
What is 3/8 equivalent to
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\large\textbf{What is }\rm{\bf \dfrac{3}{8}}\large\textbf{ equivalent to?}[/tex]
[tex]\huge\textbf{Now, let's solve for the given question:}[/tex]
[tex]\mathbf{\dfrac{3}{8}}[/tex]
[tex]\mathbf{= \dfrac{3\times2}{8\times2}}[/tex]
[tex]\mathbf{\approx \dfrac{3 + 3}{8 + 8}}[/tex]
[tex]\mathbf{= \dfrac{6}{16}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\dfrac{6}{16}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]can some one help me a little hard for me