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,
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Does anyone know this question?
You are buying fruit to make fruit baskets. Apples come in bags of 20. Oranges come in bags of 16, and bananas come in bags of 32. You have one bag of each fruit. Each fruit basket must be identical. What is the greatest number of fruit baskets that you can make using all of the fruit? *
Answer:
4 fruit baskets.
Step-by-step explanation:
Use GCF to find the answer. 20 divided by 4 is 5, 16 divided by 4 is 4, and 32 divided by 4 is 8.
Solve the following system of equations for X..
3x – 2y = 8
2x + 2y = 7
Help
A)3
B)-3
C)15
D)1
Answer:
x = 3
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
this is really easy promise
Answer:
A.) slope= 4 and y intercept= 3
Step-by-step explanation:
y = x4+3
Answer:
y = x4+3
Step-by-step explanation:
look at answer
Simplify the expression 4x+3(5y+x
Answer:
Step-by-step explanation:
4x + 3(5y + x)
= 4x (5y + x) + 3 (5y + x)
= 20xy + 4x² + 15y + 3x
Please select the word from the list that best fits the definition
energy obtained from heat within the earth
Answer:
geothermal
Step-by-step explanation:
energy obtained from heat within the earth-geothermal
What is the leading coefficient of a third degree polynomial function that has an output of 1,272 when x=2, and has zeros of −6, 7i, and −7i?
Answer:
The leading coefficient is 3
Step-by-step explanation:
Polynomials
Given the roots of a polynomial x1,x2,x3, it can be expressed as:
[tex]p(x)=a(x-x1)(x-x2)(x-x3)[/tex]
Where a is the leading coefficient.
We are given the roots x1=-6, x2=7i, x3=-7i, thus:
[tex]p(x)=a(x+6)(x-7i)(x+7i)[/tex]
Operating the product of the conjugated imaginary roots:
[tex]p(x)=a(x+6)(x^2+49)[/tex]
Knowing p(2)=1,272 we can find the value of a
[tex]p(2)=a(2+6)(4+49)=1,272[/tex]
Operating:
[tex]a(8)(53)=1,272[/tex]
[tex]424a=1,272[/tex]
Solving:
[tex]a=1,272/424[/tex]
a=3
The leading coefficient is 3
Answer:
3
Step-by-step explanation:
f(x) = x2. What is g(x)?
Answer:
B. g(x)=(2x)^2
Step-by-step explanation:
this is right
What does reflecting over each axis do to a function algebra 2
How do you check if a number is rational?
How do you check if a number is irrational?
Thanks!
P.S. 50 points & brainiest to whoever answer first!
Answer:
well it's really simple
Step-by-step explanation:
So the quick and dirty tip for checking whether a number is rational or irrational is to write it in decimal form. If the decimal goes on and on forever and never stops or begins to repeat predictably, it’s irrational. If the decimal stops after a finite number of digits or begins to repeat predictably, it’s rational.
Any number that is able to be written down as a fraction/ratio is a ration number.
An irational number is a number hat has a decimal, but can't be written as a fraction. Ex: Pi/π
On average, Carson saves about 53% of his allowance each month. When creating a circle graph of what Carson does
with his money, which of the following fractions would be the best to represent how much he saves?
1/2 1/4 3/10. 3/4
Answer:
1/2
Step-by-step explanation:
1/2 would be the best fraction to represent how much he saves.
Find the value of x.
Answer:
12
Step-by-step explanation:
1. the rule: 3:6=6:x;
2. if 3/6=6/x, then x=12.
The number of students in a chess club decreased from 16 to 12. What is the percent decrease ? Round to the nearest percent.
Answer:
25% decrease
- Trust me it's right
I NEED THIS ANSWER QUICK PLEASE!!!!!!!!!!
During the first hour of a snowstorm, 1 2/8 inches of snow fell. In the next hour, 4 3/8 inches fell. In the third hour, the snow stopped and 1 inch of snow melted. How much snow was on the ground at the end of the third hour?
Answer:
1 + 4 = 5
4/8 +3/8 = 7/8
5 7/8 - 7/8 = 5 inches left on the ground after 3 hours
Step-by-step explanation:
The value of n is a distance of 3 units from 1 an 1/2 on a number line click on the number line to the possible values of n
Answer:
3
Step-by-step explanation:
Given the question :
The value of n is a distance of 3 units from 1 an 1/2 on a number line click on the number line to the possible values of n
From the context of the expression:
n is the distance which exists between 1 1/2 and 3 units from it;
Which may be ;
1 1/2 - - - - (1 1/2 + 3) = 4 1/2
1 1/2 - - - - - (3 - 1 1/2)
Either way, there exists a distance of 3 units between 1 1/2 and 3 units from it.
Hence, n = 3
Answer:
1 and 3 would both be correct
Given the graph of h.
Solve for x: h(x) = -2 .
Answer:
{-3, -1}
Step-by-step explanation:
We want to find the value of x when the value of the graph is -2
h(x) = -2 when x=1 and x = -3
{-3, -1}
Which number has the lowest value?
A1/5B0.25C0.21D1/3
Answer:
A
Step-by-step explanation:
Answer:1/3 is bigger
Step-by-step explanation:
Which equation represents a line that is perpendicular to the line on the graph ? O y = - 4x + 3 O O y = - 1/4 * x + 1 y = 1/4 * x - 2 O O y = 4x + 4
Answer:
D
Step-by-step explanation:
Answer
Its C notD!!!!!!
Step-by-step explanation:
The other person is wrong im right
HURRY PLEASE 2020 2021 T-Math-Geo T1-CIT: Section 2 - Calculator Section
Which of these is defined as a part of a line that is bounded by two end points?
ray
angle
point
line segment
Answer:
the answer is a line segment :)
The frequency of the red eyes (p allele) in fruit flies is 63% what is the frequency of the white eye allele (9 allele)?
37%
47%
57%
23%
Answer:
[tex]q = 37\%[/tex]
Step-by-step explanation:
Given
Red Eyes
[tex]p = 63\%[/tex]
Required
Determine Frequency of White Eyes (q)
In probability;
[tex]p + q = 1[/tex]
Make q the subject
[tex]q = 1 - p[/tex]
Substitute 63% for p
[tex]q = 1 - 63\%[/tex]
[tex]q = 37\%[/tex]
Answer:
37%
Step-by-step explanation:
1.6.PS-21 Question Help Challenge A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 5 feet per second. The elevator for the miners descends 17 feet per second. One day, the equipment elevator begins to descend. After 29 seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 16 seconds? At that time, which elevator is deeper? The position of the equipment elevator relative to the surface is feet
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Equipment elevator :
Descent rate = 5 ft/s
Miner's elevator :
Descent rate = 17 ft/s
Position of elevator after 16 seconds
Total descent time of equipment elevator = (29 + 16) = 45 seconds
Position after 45 Seconds :
Descent rate * time
5ft/s * 45s = 225 ft
Descent time of Miner's elevator = 16 seconds
Position after 16 Seconds :
Descent rate * time
17ft/s * 16s = 272 fts
Miner's elevator is deeper = 272 feets > 225 fts
Position of equipment elevator relative to the surface = - 225fts
Solve -2(2x + 5) - 3 = -3(x - 1).
The solution for the equation -2(2x + 5) - 3 = -3(x - 1) is x = - 16 which can be solved by the use the distributive property.
What is distributive property?Distributive Property that when we multiply a number by a group of numbers that are added together, we can multiply each value in the group separately, then add the products of the multiplications.
-2(2x + 5) - 3 = -3(x - 1)
To solve this equation, we need to first use the distributive property to expand the left side of the equation.
We have:
-4x-10-3 = -3(x - 1)
-4x-13 = -3(x - 1)
Now, we can group the like terms on the left side and the right side of the equation.
On the left side, we have -4x - 13 and on the right side, we have -3x + 3.
-4x-13 = -3x + 3
To solve for x, we can add 3x to left side of the equation and add 13 to the right side.
This results in the equation:
-4x+ 3x = 13 + 3
Now, we can add 3x with -4x of the equation to isolate the x-term.
We have:
-x = 16
x = - 16
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A bathtub can hold 30 gallons of water.
How many quarts of water can it hold?
Enter your answer as a number, like this: 42
Answer:
120 quarts
Step-by-step explanation:
1 gallon=4 quarts
30x4= 120
Point J is on line segment IK. Given JK = 2x, IJ = 5x, and IK = x + 6, determine the numerical length of JK.
Answer:
[tex]JK = 2[/tex]
Step-by-step explanation:
Given:
[tex]JK = 2x[/tex]
[tex]IJ = 5x[/tex]
[tex]IK = x + 6[/tex]
Required
Solve for JK.
Since J is on IK, we have:
[tex]IK = IJ + JK[/tex]
[tex]x + 6 = 5x + 2x[/tex]
[tex]x + 6 = 7x[/tex]
Collect Like Terms
[tex]7x - x = 6[/tex]
[tex]6x = 6[/tex]
Solve for x
[tex]x = 6/6[/tex]
[tex]x = 1[/tex]
Substitute 1 for x in [tex]JK = 2x[/tex]
[tex]JK = 2 * 1[/tex]
[tex]JK = 2[/tex]
Walter is helping to make cookies for a basketball tournament. He's made 15 cookies so far. His coach asked him to make at least 20 cookies but no more than 55. Solve the inequality and interpret the solution.
Answer:
[tex]5\leq x\leq 40[/tex]
Here, [tex]x[/tex] denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far
Step-by-step explanation:
Number of cookies made by Walter so far = 15
He is asked by his coach to make at least 20 cookies but no more than 55.
Let [tex]x[/tex] denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far.
The inequality is [tex]20\leq x+15\leq 55[/tex]
Now solve this inequality.
[tex]20\leq x+15\leq 55\\20-15\leq x\leq 55-15\\5\leq x\leq 40[/tex]
Answer: a
Step-by-step explanation: because its right
Jill has not been able to maintain the $1,000 minimum balance required to avoid fees on her checking account. She wants to switch to a different account with a fee of $0.20 per check and a $12.50 monthly maintenance fee. Jill wants to estimate the fees for her new account. Below is a summary of the checks she has written from May to August. What is the mean number of checks Jill wrote per month during the last four months? Based on the mean, estimate how much Jill expects to pay in per-check fees each month after she switches to the new account. Estimate the total monthly fees Jill will pay each month for the new checking account.
Step-by-step explanation:
Kindly find attached a summary of the checks she has written from May to August.
A. What is the mean number of checks Jill wrote per month during the last four months
mean= (14+19+23+24)/4
mean= 80/4
mean= 20 checks
B. Based on the mean, estimate how much Jill expects to pay in per-check fees each month after she switches to the new account.
the expression for the total is given as
y=12.50+0.2x
y=12.50+0.2(20)
y=12.50+4
y=16.5
=$16.5
C. Estimate the total monthly fees Jill will pay each month for the new checking account.
May= 12.50+0.2(14)
May=12.5+2.8= 15.3
June= 12.50+0.2(19)
June=12.5+3.8= 16.3
July= 12.50+0.2(23)
July=12.5+4.6= 17.1
August= 12.50+0.2(24)
August=12.5+4.8= 17.3
total will be = 15.3+16.3+17.1+17.3= $66
A:20
B:$4.00
C:$16.50
A: 14+19+23+24/4 = 20
B: 20/.2 = 4
C: 12.50+4= 16.50
How many ways can a delegation of 55 Republicans, 22 Democrats, and 33 Independents be selected from a group of 99 Republicans, 33 Democrats, and 44 Independents?
Answer:
[tex]C(99,55)\,C(33,22)\,C(44,33)[/tex]
Step-by-step explanation:
A permutation refers to arrangement of the objects or numbers in order. Combinations refers to selecting the objects or numbers from a group of objects or collection such that the order of the objects does not matter.
A delegation of 55 Republicans, 22 Democrats, and 33 Independents is selected from a group of 99 Republicans, 33 Democrats, and 44 Independents.
So,
Number of ways [tex]=C(99,55)\,C(33,22)\,C(44,33)[/tex]
Emilia wrote a total of 12 pages over 4 hours. After spending 6 hours writing this week, how
many pages will Emilia have written in total? Assume the relationship is directly proportional.
Answer:
30 pages
Step-by-step explanation:
Knowing she wrote 12 pages in 4 hours, we can do 12/4 to get 3 pages per hour. Multiply 3 pages by the 6 hours she spends writing and you get 18 pages in 6 hours. Add 12 pages and 18 pages and you have 30 pages.
Why did karen take the kids (;´༎ຶД༎ຶ`)
Wait Jimmy what are you doing here I didn't expect this
so we meet again, brother.
Answer:
Because Karen found your briefcase of $1 bills and some crusty socks.
Get over the divorce Jimmy, she doesn't like fax machines.
QUESTION 16
What is the value of m If the ratios 3:18 and m:42 are in
proportion?
Answer:
[tex]m = 7[/tex]
Step-by-step explanation:
Given
[tex]3:18 = m:42[/tex]
Required
Solve for m
[tex]3:18 = m:42[/tex]
Convert to fraction
[tex]\frac{3}{18} = \frac{m}{42}[/tex]
Multiply both sides by 42
[tex]42 * \frac{3}{18} = \frac{m}{42} * 42[/tex]
[tex]42 * \frac{3}{18} = m[/tex]
[tex]m = 42 * \frac{3}{18}[/tex]
[tex]m = \frac{42 * 3}{18}[/tex]
[tex]m = \frac{126}{18}[/tex]
[tex]m = 7[/tex]
