Answer:
The maximum volume of such box is 32m^3
V = x×y×z = 32 m^3
Step-by-step explanation:
Given;
Total surface area S = 48m^2
Volume of a rectangular box V = length×width×height
V = xyz ......1
Total surface area of a rectangular box without a lid is
S = xy + 2xz + 2yz = 48 .....2
To be able to maximize the volume, we need to reduce the number of variables.
Let assume the rectangular box has a square base,that means; length = width
x = y
Substituting y with x in equation 1 and 2;
V = x^2(z) ....3
x^2 + 4xz = 48 .....4
Making z the subject of formula in equation 4
4xz = 48 - x^2
z = (48 - x^2)/4x .......5
To be able to maximize V, we need to reduce the number of variables to 1, by substituting equation 5 into equation 3
V = x^2 × (48 - x^2)/4x
V = (48x - x^3)/4
differentiating V with respect to x;
V' = (48 - 3x^2)/4
At the maximum point V' = 0
V' = (48 - 3x^2)/4 = 0
Solving for x;
3x^2 = 48
x = √(48/3)
x = √(16)
x = 4
Since x = y
y = 4
From equation 5;
z = (48 - x^2)/4x
z = (48 - 4^2)/4(4)
z = 32/16
z = 2
The maximum volume can be derived by substituting x,y,z into equation 1;
V = xyz = 4×4×2 = 32 m^3
x|y
-2|2
1|5
3|7
---- ----
A. y = x + 4
B. y = -x
C. y = x - 4
D. y = 4 - x
Answer:
y = x + 4
Step-by-step explanation:
y = mx + b (m = slope; b = y-intercept)
I used 2 points (-2 , 2) and (1 , 5) to calculate the slope of the line
m= (y₂ - y₁)/(x₂ - x₁)
(5-2)/(1--2) = 3/3= 1
y = 1x + b
using point (1, 5)
5 = 1(1) + b
5 = 1 + b
b = 5-1
b=4
y= 1x + 4 or simply y= x + 4
Answer:
A y = x + 4
yeh i did the test
Step-by-step explanation:
B) cos(C)
C) sin(B)
D) sin(C)
Answer:
C).
Step-by-step explanation:
Since angles A and B are complementary, their cofunctions are equal. So, cos(A) = sin(B).
2. 245.00
3. 246.08
Answer:
246.000
Step-by-step explanation:
Well If you take it and Line it up like this,
(A)Amy; 58.75
(J)Jeremy; A+23.25
(O)Oscar; A+23.25= ?x3
This is an easy way to find out what it is you need to do, So A+23.25 is 58.75+23.2 which should give you the value of 82, which brings you to the next step of A+23.25= ?x3 which in this you only wanna focus on the ?x3, we now know ?= 82 so this brings it to 82 times 3 which gives you a value of 246. Thus giving you your answer.
Hope this helps.
The population in California is 50 times greater than the population in South Dakota.
To find out how many times greater the population in California is than in South Dakota, you can divide the population of California by the population of South Dakota:
Population of California = 4 * 10⁷
Population of South Dakota = 8 * 10⁵
Population ratio = (Population of California) / (Population of South Dakota)
Population ratio = (4 * 10⁷) / (8 * 10⁵)
Population ratio = 50
Therefore the population in California is 50 times greater than the population in South Dakota.
Learn more on calculating ratio here brainly.com/question/2328454
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Question
California Has A Populatio Of Approximately 4*10^(7)People And South Dakota Has Populatio Of Approximately 8*10^(5) People. How Many Times Greater Is The Population In California Than In South Dakota
california has a populatio of approximately 4*10^(7)people and south dakota has populatio of approximately 8*10^(5) people. how many times greater is the population in california than in south dakota
Answer:
40000000 800000
Step-by-step explanation:
whats the question here?
9514 1404 393
Answer:
$200
Step-by-step explanation:
The interest is given by ...
I = Prt
I = ($4000)(0.05)(1) = $200
The simple interest owed is $200.
Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.
David says he has 2/3 of a line length left, while Wear says he has 11/16 of a length left.
Convert the fraction numbers 2/3 and 11/16 into the decimal number. Then we have
2/3 = 0.6667
11/16 = 0.6875
The decimal number 0.6875 is greater than 0.6667. Then the fraction number 11/16 is greater than the fraction number 2/3.
Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.
More about the Algebra link is given below.
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Answer:
Don
Step-by-step explanation:
1. We make the fractions have common denominators so it is easier to compare them. We can do this buy multiplying 2/3 by a factor of 16, so it becomes 32/48. For 11/16, we multiply by a factor of 3 so it becomes 33/48. It is now apparent that Don has the longer pipe.