Dimensions of the rectangular box with largest volume if the total surface area is given as 4 cm² : (√2/3 , √2/3 ,√2/3)
Given, rectangular box with largest volume.
Let f(x , y , z) = xyz
Ф ≡ xy + yz + xz - 2 = 0
[tex]F =[/tex] [tex]f + \lambda[/tex][tex]\phi[/tex]
[tex]F = xyz + \lambda (xy + yz + xz - 2)[/tex]
[tex]F_x = 0\\yz + \lambda(y + z) = 0......1\\\\F_y = 0\\xz + \lambda(x+z)= 0......2\\\\F_z = 0\\xy + \lambda(x + y) = 0..........3[/tex]
xy + yz + xz - 2 = 0........4
Solving the above 4 equations,
[tex]yz + \lambda(y + z) = 0\\\lambda = -yz/(y+z)\\\\xz + \lambda(x + z) = 0\\\lambda = -xz / (x+z)[/tex]
Evaluating the lambda values,
x = y
Similarly, y = z
Therefore, x² + x² + x² - 2 = 0
x = √2/3
y = √2/3
z = √2/3
Hence, Dimensions : (x , y , z) = (√2/3 , √2/3 ,√2/3)
Know more about rectangle,
https://brainly.com/question/31663437
#SPJ4
5d+1/2=d-4 section 2.04
Answer: d = -9/8
Steps: 5d + ½ = d - 4
Subtract ½ from both sides: 5d + ½ - ½ = d - 4 - ½
Simplify: 5d = d - 9/2
Subtract d from both sides: 5d - d = d - 9/2 - d
Simplify: 4d = -9/2 ÷ 4
Simplify: d = -9/8
PLz mark brainliest:)
-3/7 % -1/2 =??
What is the answer to this equation
Answer:
-0.21428571428
What is the slope and y-intercept of the linear equation y = 5x − 4?
m =
b =
Answer:
I got it right on edge 2020/2021
Step-by-step explanation:
m=5
b=-4
Can any one help me?
I need help with Number 7 please!!!
Answer:
8.06 ft or [tex]\sqrt{65}[/tex] ft
Step-by-step explanation:
Since Rebecca bought a square table and squares have equal sides, you can take the square root of the area of the table, which gives you [tex]\sqrt{65}[/tex] ft per side. This can be approximated to 8.06 ft.
what is /4 of 3/4 =
What is 1/4 of 3/4
Answer:
3/16
Step-by-step explanation:
1/4 of 3/4 is just another way of saying (1/4)*(3/4). When multiplying fractions, you must multiply the numerators and denominators to get the product so the numerator of the products is 1*3 and the denominator is 4*4 to get:
3/16
Answer:
3/16
Step-by-step explanation:
1/4 of 3/4
= 1/4 × 3/4
you multipy the numerators together and then multiply both denominators
ie. 1×3 divided by 4×4
= 3/16
How can you use the order of operation to explain why you cannot combine the variable terms before using the distributive property when solving the equation 7(x+5)-x=42
Answer:
Step-by-step explanation:
The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.
This standard is critical to simplifying and solving different algebra problems. Without it, two different people may interpret an equation or expression in different ways and come up with different answers. The Order of Operations is shown below.
Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.
Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.
Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.
Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.
Before we begin simplifying problems using the Order of Operations, let's examine how failure to use the Order of Operations can result in a wrong answer to a problem.
Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways
We cannot combine the variable terms before using the distributive property when solving the equation as it will results in wrong answer.
What is distributive property of multiplication over addition ?
If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.
Here the expression given is :
7(x+5)-x=42
The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.
Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.
Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.
Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.
Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.
Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways.
Read more about property of multiplication here :
https://brainly.com/question/14391436
#SPJ2
LUCILLE'S PENCIL POUCH WOULD HOLD 3/8
OF THE 48 PENCILS THAT SHE PURCHASED AT
THE BEGINNING OF THE NEW SCHOOL YEAR. How many pencils will fit in her pouch
HOW MANY PENCILS WILL FIT IN HER POUCH?
Answer:
The pouch would be able to hold 12.8 pencils :)
Step-by-step explanation:
because 3/8 is 37.5 and if you do that divided by 48 and add a decimal infront of the eight you will get your answer
4(3x + 1)
What is the answer to 4(3x + 1)
Answer:
Answer is 12x+4. Hope that helped.
Determine the quotient of 2 over 5 divided by 3 over 4
Answer:
8/15
Step-by-step explanation:
what is the sale tax on a $14,500 truck if the tax rate is 9%
Answer:
$15, 805.00
Step-by-step explanation:
Tax is based on the state you live in.
M/x =n-p, x for p ??
Answer:
the answer is A) X=m/n-p
Step-by-step explanation:
m/x=n-p
n-p=m/X
(n-p)×x=m
X=m/n-p
For a certain type of sand, 1 cubic foot weighs 80 pounds. The sand goes in a container that weighs 40 pounds. Use the Ray tool to make a graph that shows the total weight of the container and sand, w, filled with n cubic feet of this sand. I need the coordinates for the graph please.
Answer:
First, let's write our equation in a general way.
We know that:
1 cubic foot weighs 80 pounds.
The container weighs 40 pounds.
Then, if i put n cubic feet of sand in the container, the total mass will be one time the mass of the container plus n times the mass of one cubic foot of sand.
We can write this as:
w(n) = 40lb + n*80lb
This is a linear equation, where the y-axis will represent the mass in pounds and the x-axis will be the number of cubic feet of sand in the container in units, a graph of this is shown below.
You can see that it is really steep, this is because for really small increments in n, the weight increases a lot.
Answer
ok, Just plot the points at (0,40) and (2,200) :))
ANSWER PLEASE NEED HELP ASAP
Answer: 43 should be divided into 0.37 to find “x”.
Step-by-step explanation:
For a certain product we obtained a regression line equation Y = 10 - 0.8 X, where X is price (in $) and Y is sales (in $1,000). The slope of the line (- 0.8) represents:___---.
A. If the price were $10, expected sales would be $8,000.B. If the price were zero, expected sales would $800.C. If the price increases by $1, sales will decrease by $800, on average.D. Sales are maximized when the price is $0.8.
E. None of the other answers are correct.
Answer:
C. If the price increases by $1, sales will decrease by $800, on average
Step-by-step explanation:
Slope of regression equation represents the increase/decrease in dependent variable Y due to unit change in independent variable X. Here, independent variable is X is price and dependent variable Y is sales. The slope negative sign represent decrease in dependent variable due to unit increase in independent variable. Sales is given in ($1000) So, (0.8*1000)=800. It means that due to unit dollar increase in price the sales will decrease by $800. Thus, If the price increases by $1, sales will decrease by $800, on average is the correct interpretation.
Evaluate 12x−3y when x=−14 and y=3.
Answer:
-177
Step-by-step explanation:
12(-14) -3(3)
-168-9
-177
Answer:
-177
Step-by-step explanation:
Plug in -14 for x and 3 for y:
12(-14) - 3(3)
Note that when you multiply a positive and a negative number, your answer will be negative.
Multiply:
12 * -14 = -168
-3 * 3 = -9
Combine the terms:
-168 + (-9) = -168 - 9 = -177
-177 is your answer.
~
question 10 I mark as brainliest
Answer:
134 is the answer
Answer: 134
Step-by-step explanation:
54+ (48+72) x 2/3
54+120x2/3=134
Jason delivers newspapers on Saturdays and Sundays only. Each newspaper weighs about 1 pound 5 ounces. If he delivers 15 newspapers each day, how much do the two days' worth of newspapers weigh in pounds and ounces?
Answer:
39pounds 6oz
Step-by-step explanation:
15x2=30
1x30=30pounds
5x30=150oz
30p+150oz=39.37500
37500p=6oz
39pounds and 6 oz
Equivalent Expressions
Warm-Up
Active
Evaluating an Expression
Complete the statements.
Evaluate (15 - 4x) + 5 when x = 3.
Substitute the given value for the
Evaluate within
parentheses.
to simplify.
Use the
inside the
Evaluate exponents.
First, complete the
parentheses.
Next, complete the
parentheses.
Last, complete the addition.
inside the
Multiply and divide
from left to right.
The value is
Add and subtract
from left to right.
Answer:
Complete the statements.
Substitute the given value for the
✔ variable
.
Use the
✔ order of operations
to simplify.
First, complete the
✔ multiplication
inside the parentheses.
Next, complete the
✔ subtraction
inside the parentheses.
Last, complete the addition.
The value is
✔ 8
.
Step-by-step explanation:
Plz give me brainlest
Answer:
Variable, order of operations, multiplication, subtraction, 8.
Step-by-step explanation:
Got it right Edge2021
Riley and Rhoda plan to buy several bags of dog food and a dog collar. Each bag of dog food costs $7, and the dog collar cost $5
Answer:
2bags= $14 + $5
3bags= $21+ $5
4bags= $28 + $5
5bags= $35 + $5
6bags= $42 + $5
multiply # of bags by 7
and add $5
Multiply: -12y(y - 6) Enter the correct answer.
Which is true 0.45>0.5
0.45<0.5
4.05=0.45
4.05 <0.45
Answer:
4.05 is greater than 0.45
Is this a function or not a function? (Picture)
Answer:
Not a Function
Step-by-step explanation:
A family is purchasing 17 tickets for a downtown walking tour. Adult tickets are $10, child tickets are $7, and senior tickets are $8.50. The total
cost of the tickets is $141.50, and they are purchasing 2 more senior tickets than adult tickets.
Create and solve a system of linear equations to represent this situation. Then select the true statement.
А. The solution to this system is nonviable because it results in a fractional number of tickets.
B. The solution to this system is no viable because it results in a negative number of tickets.
C. The solution to this system is viable.
D. The solution to this system is nonviable because it results in a fractional amount of money.
Answer:
А. The solution to this system is nonviable because it results in a fractional number of tickets.
Step-by-step explanation:
Let x represent the number of adult tickets, y represent the number of child ticket and z represent the number of senior ticket.
Since the number of purchased ticket is 17, hence:
x + y + z = 17 (1)
The total cost of tickets is $141.50, hence:
10x + 7y + 8.5z = 141.5 (2)
they are purchasing 2 more senior tickets than adult tickets, therefore:
x = z + 2 (3)
Solving equation 1 2 and 3 simultaneously gives:
x =17/3, y = 23/3, z = 11/3
Therefore the solution to this system is nonviable because it results in a fractional number of tickets.
Answer:
А.The solution to this system is nonviable because it results in a fractional number of tickets
Step-by-step explanation:
took the test on edmentum and got it correct
Kai is making a chessboard using pieces of wood that measure 1 square inch.
When he finishes, the chessboard will have an area of 64 square inches.
How many pieces of wood should he put along each side?
A cube has a volume of 125 cubic inches. What is the length of each edge?
Answer:
The correct option will be: c. 8 pieces of wood.Step-by-step
M is the midpoint of line segment PQ. MQ = 5x + 8 and PQ = 6x + 65, find x
Answer:
freeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
trump 20202020202020020202020
Geometric Sequence♡
5, -2, 4/5
the common ratio was 2/5
find the 10th term
An oilfield contains 6 wells that produce a total of 1,800 barrels of oil per day. For each additional well that is drilled, the average production per well decreases by 25 barrels per day.
Required:
How many additional wells should be drilled to obtain the maximum amount of oil per day?
Answer:
The additional wells for maximum amount of oil per day is 3 wells.
Step-by-step explanation:
Given;
initial number of wells, n = 6
total production, T = 1800
average production per well, = 1800/6 = 300 barrels per day
Let the additional well = y
total number of wells after optimization = 6 + y
new production per well = 300 - 25y
new total production = (6+y)(300-25y)
t = 1800 - 150y + 300y - 25y²
t = 1800 + 150y - 25y²
dt / dy = 150 -50y
for maximum value, dt/dy = 0
150 - 50y = 0
50y = 150
y = 150 / 50
y = 3
Therefore, the additional wells for maximum amount of oil per day is 3 wells.
33 additional wells should be drilled, reaching 39 wells, to obtain the maximum amount of oil per day.
Given that an oilfield contains 6 wells that produce a total of 1,800 barrels of oil per day, and for each additional well that is drilled, the average production per well decreases by 25 barrels per day, to determine how many additional wells should be drilled to to obtain the maximum amount of oil per day, the following calculation must be performed:
1800 x 6 = 10800 1200 x 30 = 36000 1000 x 38 = 38000 950 x 40 = 38000 900 x 42 = 37800 975 x 39 = 38025
Therefore, 33 additional wells should be drilled, reaching 39 wells, to obtain the maximum amount of oil per day.
Learn more in https://brainly.com/question/13581736
A diver swims 5.875 feet up to the surface of the water. Which number represents the diver’s position in relation to the surface before swimming to the top?
-5.9 feet
Negative 5 and three-fourthsfeet
-58 feet
Negative 5 and StartFraction 7 over 8 EndFractionfeet
Answer:
Negative 5 and 7 over 8
Step-by-step explanation:
Answer:
Negative 5 and StartFraction 7 over 8
Step-by-step explanation:
Sub to SZ Lexrn if that does not show search up shiyo on vr and first vid is them please help out , thx bye . If you do it cmt and ill make a post for yall for 100 points, so my friends won't amke fun of me
Answer:
If it counts as a question, lol sure, I'd love to help