Answer:
No. Since the value of the ratio
is not the same for each pair of values, the relationship is not proportional. So, an equation cannot be written for the situation. its c
Step-by-step explanation:
The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials. (Let x, y, and z be the dimensions of the aquarium. Enter your answer in terms of V.)
Answer:
The dimensions of the aquarium that minimize the cost of the materials:
[tex]x=y=\sqrt[3]{\frac{2V}{5}}\\z=\sqrt[3]{\frac{25V}{4}}[/tex]
Step-by-step explanation:
Let x, y and z be the dimensions of aquarium .
Surface area of an aquarium = xy+2yz+2xz
Volume of aquarium V=[tex]Length \times Breadth \times Height=xyz[/tex] ----A
We are given that slate costs five times as much (per unit area) as glass
So, Cost function : C=5xy+2yz+2xz
Now we will use langrage multiplier to find the dimensions of the aquarium that minimize the cost of the materials.
[tex]\nabla C =\lambda \nabla V[/tex]
[tex](\frac{\partial C}{\partial x},\frac{\partial C}{\partial y},\frac{\partial C}{\partial z})= \lambda (\frac{\partial V}{\partial x},\frac{\partial V}{\partial y},\frac{\partial V}{\partial z})[/tex]
[tex](5y+2z,5x+2z,2y+2x)=\lambda(yz,xz,xy)[/tex]
So,
[tex]5y+2z=\lambda yz[/tex] ----1
[tex]5x+2z=\lambda xz[/tex] -----2
[tex]2y+2x=\lambda xy[/tex] ----3
Multiply 1 ,2 and 3 by x,y and z respectively.
[tex]5xy+2xz=\lambda xyz[/tex] ----4
[tex]5xy+2yz=\lambda xyz[/tex] -----5
[tex]2yz+2xz=\lambda xyz[/tex] ----6
Now equate 4 and 5
5xy+2xz=5xy+2yz
x=y
Substitute y=x in 5 and 6 and equate them
[tex]5x(x)+2(x)z=2(x)z+2xz\\5x^2=2xz\\5x=2z\\\frac{5}{2}x=z[/tex]
Substitute the values in A
[tex]V = xyz = x \times x \times \frac{5}{2}xV=\frac{5}{2}x^3\\\sqrt[3]{\frac{2}{5}V}=x\\x=y=\sqrt[3]{\frac{2}{5}V}\\z=\frac{5}{2}x=\frac{5}{2}(\sqrt[3]{\frac{2}{5}})=\sqrt[3]{\frac{25V}{4}}[/tex]
Hence,
The dimensions of the aquarium that minimize the cost of the materials:
[tex]x=y=\sqrt[3]{\frac{2V}{5}}\\z=\sqrt[3]{\frac{25V}{4}}[/tex]
Here are recipes for two mixtures of salt and water that taste different. Mixture A: salt (teaspoons) water (cups) 4 5 7 8 3/4 9 11 1/4 Mixture B is defined by the equation y=2.5x , where x is the number of teaspoons of salt and y is the number of cups of water. Respond to the following questions: 1. If you used 10 cups of water, which mixture would use more salt? How much more? Explain or show your reasoning. 2. Which mixture tastes saltier? Explain how you know.
Answer:
1.) Mixture A will use more salt.
Mixture A will require 4 more spoons of salt than mixture B of 10 cups of water is used.
2.) Mixture A
Step-by-step explanation:
Given the daya:
MIXTURE A
___Salt A(teaspoons _____water (Cups)
___4 _____________5
___7 _____________8 3/4
___9 _____________ 11 1/4
Mixture B is defined by the equation'
y = 2.5x ;
x = number of teaspoons of salt ;
y = number of cups of water
Respond to the following questions:
1.) If you used 10 cups of water, which mixture would use more salt? How much more? Explain or show your reasoning.
For mixture B:
If number of cups of water, y = 10
y = 2.5x ; 10 = 2.5x
10/2.5 = x
x = 4 ; 4 teaspoons of salt
Let's write an equation in terms of y and x to represent mixture A.
Mixture A:
5 = k4
k = 5/4
k = 1.25
Equation for mixture A:
y = 1.25x
10 = 1.25x
10/1.25 = x
x = 8 ; 8 teaspoons of salt
Mixture A will use more salt.
Mixture A will require 4 more spoons of salt than mixture B of 10 cups of water is used.
2. Which mixture tastes saltier? Explain how you know.
Mixture A is saltier as it makes use of more teaspoons of salt for the same amount of water.
1. Mixture A will use 4 more teaspoon of salt
2. The mixture that makes use of more teaspoon of salt (4 teaspoon) for the same quantity of water (10 cups) will taste saltier, which is: Mixture A.
Recall:
A proportionate relation is defined by the formula: y = kxk is the constant of proportionality or unit rate between two variables.From the information given:
x = quantity of salt (teaspoons)y = quantity of water (cups)Therefore, k = y/x
Equation for mixture B is given as: y = 2.5x
Using a pair of values from the table for mixture A, let's find the constant of proportionality and the equation that defines Mixture A.
Using (4, 5):
k = y/4 = 5/4 = 1.25Thus, substitute k = 1.25 into y = kxEquation for Mixture A is: y = 1.25x
1. Let's find the mixture that will have more salt if y = 10 (cups of water).
Substitute y = 10 in each equation that defines each mixturesMixture A: y = 1.25x
10 = 1.25x
Divide both sides by 1.258 = x
x = 8
Amount of salt you will have in mixture A is you use 10 cups of water is 8 teaspoonsMixture B: y = 2.5x
10 = 2.5x
Divide both sides by 2.54 = x
x = 4
Amount of salt you will have in mixture A is you use 10 cups of water is 4 teaspoonsThus, Mixture A will use 4 more teaspoon of salt.
2. The mixture that makes use of more teaspoon of salt (4 teaspoon) for the same quantity of water (10 cups) will taste saltier, which is: Mixture A.
Learn more here:
https://brainly.com/question/25211140
what is the product of 2(-4)
Answer:
-8
Step-by-step explanation:
First, write it out in standard form:
2 x (-4)
Then multiply!
Answer:
-8
Step-by-step explanation:
it is basically 2 x -4 and a negative times a positive is a negative which makes it -8
What is the distance between -50 and 12 on a number line?
Answer:
The distance is 62
Step-by-step explanation:
Take the second number and subtract the first number
12 - ( -50)
12 + 50
62
The distance is 62
a softball team wants to sell $8,500 worth of tickets for its upcoming season. if each ticket cost $18 how many tickets will the team have to sell to reach their goal?
Answer:
473 tickets
Step-by-step explanation:
8,500/18=472.2222222 but, since you can’t sell only part of a ticket, you’ll round up to get 473 tickets.
Is 4:5 equivalent to 8:10 as radios?
Suppose you want to put sprinkles on cupcakes. You have 2/3 of a bag of sprinkles and you only need 1/9 of the bag per batch how many batches can you cover with sprinkles?
Answer:
i think 6
Step-by-step explanation:
2/3 divided by 1/9 then , 2 times 9 then. 3 times 9 = 18/3 if you simplifying the answer is 6
order the numbers from least to greatest please help
Answer:
-2,-7/4, 1/2, square root of 5, 2.4
Step-by-step explanation:
Answer:
-2, -1.75, 1/2, [tex]\sqrt{5}[/tex], 2.4
Step-by-step explanation:
1/2
-2
√5≈2.24
-1.75
2.4
-2, -1.75, 1/2, [tex]\sqrt{5}[/tex], 2.4
Choose a true statement.
g(x) is not a function because f(x) is not a
function.
O g(x) is not a function because f(x) is not one-
to-one.
O g(x) is a function because f(x) is one-to-one.
O g(x) is a function because f(x) is not one-to-
one.
Answer: c
Step-by-step explanation:
The correct statement is that g(x) is a function because f(x) is one-to-one.
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
We know a function f(x) has its inverse g(x) if and only if f(x) is a one-to-one function.
From the given statements the only true statement is, g(x) is a function because f(x) is one-to-one.
learn more about inverse functions here :
https://brainly.com/question/14627458
#SPJ6
Mr. Ortiz is a driving instructor. Of his students, 23 have taken the driver's test and 17 of them have passed
on the first attempt. Mr. Ortiz earns a $300 bonus if 80% of his students pass the test on the first attempt.
How many consecutive students must pass on the first attempt in order for Mr. Ortiz to earn the bonus
Answer:7
Step-by-step explanation:
Plz solve for brainlistMarlene runs 4 km in 30 min. At this rate,
can Marlene run 6 km in 45 min?
Complete the following calculation an
d
explanation. Use the Communication
Checklist.
Answer:
comparing rates.. use the formula d = r * t where d= distance , r = rate or speed and t = time ofc. :)
Step-by-step explanation:
we know the distance and the time but not the rate.. find that r ....
d/t = r 4/30 = r = 0.13333333333 this is in Km per minute, b/c the 4 is Km and the 30 is in minutes. Units are not to important other than keeping track of what they are.
Now we can answer the question can Marlene run 6 Km in 45 mins. b/c we know her rate , or speed, so at her rate of 0.133333333 Km/min and using that d = r * t formula what is her distance in 45 minutes.. so multiply 45 * 0.133333= 6 so she runs exactly 6 Km in 45 minutes.. so the math answer is yes
A bride is choosing a dress for her bridesmaids. If there are 4 styles, 7 colors, and 5 fabrics, in how many ways can she select the bridesmaids' dress?
Answer: 60
Step-by-step explanation: multiply 4,7,and 5
She can select the bridesmaids' dress in 140 possible ways.
What is Permutation?Permutation represents each of the several possible ways in which a set or number of things can be ordered or arranged.
Given is a bride who is choosing a dress for her bridesmaids which are available in 4 styles, 7 colors, and 5 fabrics.
Now, for every possible style there exist a dress for that color. So, with 4 styles and 7 colors, the total number of possible dresses will be = 7 x 4 = 28. Now, for these 28 dresses, their are 5 different fabric available, so the total number of possible ways or dresses from which she can select the dress are = 28 x 5 = 140
Therefore, she can select the bridesmaids' dress in 140 possible ways.
To solve more questions on Arrangements and selections, visit the link below-
https://brainly.com/question/16721336
#SPJ2
RECO
Which expression is equivalent to 3x – 1/2y+2 2/3y-5/6x
Answer:
13 ( x + y ) / 6
Simplify square root -200
Answer:
10 i sqrt 2
Step-by-step explanation:
i indicates that it is an imaginary number. this is because 200 is negative.
The simplified form of the given square root number is 10i√2. Therefore, the correct answer is option D.
The given square root number is √-200.
The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.
Here, 200 = 2×2×2×5×5
Thus, √-200=√-2×2×2×5×5
=2×5×i√2
= 10i√2
Therefore, the correct answer is option D.
To learn more about the square root of a number visit:
https://brainly.com/question/8971086.
#SPJ6
Charles walked on a treadmill 16 3/4 miles over 4 days. How many miles did he walk per day?
Find the quotient below. Write the answer as a fraction in the simplest form 7 1/2 divided 5/6
Answer:
9
Step-by-step explanation:
steps for dividing mixed numbers.
Change every mixed number to an improper fraction.
Multiply the reciprocal of the divisor, simplifying if possible.
Put answer in lowest terms (or simpliest form)
Check to be sure the answer makes sense.
can someone solve, the answer is in the double form something
Answer:
See Below
Step-by-step explanation:
(x-3)-2 ≤ 1 (x-3)-2 ≥ -1
+2 +2 +2 +2
x-3 ≤ 3 x-3 ≥ 1
+3 +3 +3 +3
x ≤ 6 and x ≥ 4
The distance (d) in meters that an ant can travel varies directly with the amount of time (t) in hours it spends walking. assume that an ants constant off proportionality is 18.write the equation to the represent the proportional relationship between d and t using the information given. What does the constant of proportionality represent in this problem?
The constant is 18
To find distance (d) you would multiply the constant by the time(t).
D = 18t
Distance is speed x time, so the given constant would be the speed of the ant.
6x4x8x5=
that is the
what is the value of the expression below (4 * 7) - [(10 * 2 ) - 1 ]
Answer:
9
Step-by-step explanation:
According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11? Plus-or-minus one-eleventh, plus-or-minus five-elevenths, plus-or-minus 1, plus-or-minus5 Plus-or-minus one-fifth, plus-or-minus1, plus-or-minus eleven-fifths, plus-or-minus11 Plus-or-minus one-eleventh, plus-or-minus one-fifth, Plus-or-minus five-elevenths, Plus-or-minus 1, Plus-or-minus eleven-fifths, Plus-or-minus5, Plus-or-minus11 0, Plus-or-minus one-eleventh, Plus-or-minus one-fifth, Plus-or-minus five-elevenths, Plus-or-minus 1, Plus-or-minus eleven-fifths, Plus-or-minus5, Plus-or-minus11
Answer:
Plus-or-minus one-fifth, plus-or-minus1, plus-or-minus eleven-fifths, plus-or-minus11
Step-by-step explanation:
According to the Rational Root Theorem, the potential roots of f(x) = 5x² – 7x + 11 are; Plus-or-minus one-fifth, plus-or-minus1, plus-or-minus eleven-fifths, plus-or-minus11.
Rational Root Theorem:The given function is; f(x) = 5x² – 7x + 11
On this note; Using the rational Root Theorem while determining the root; we have;
f(x) = 0 = x² -7/5x + 11/5.
The possible roots are therefore the factors of the constant, 11/5 and are as follows;
±11/5±1±11±1/5.Read more on Rational Root Theorem;
https://brainly.com/question/4251786
A line passes through the point (-10, – 7) and has a slope of 5/2
Write an equation in slope-intercept form for this line.
I need help is anyone is out there and knows how to do this help.
HELP ASAP
Answer:
Sorry i have no idea hahha
Step-by-step explanation:
Good luck
Snow is falling steadily in Syracuse, New York. After 2 hours, 4 inches of snow has fallen.
Write an equation that gives the amount of snow that has fallen after x hours at this rate.
Answer:
y = 2x
Step-by-step explanation:
y-int = 0
slope = 2
32 Over 8 = 28 Over x
a. x = 4
c. x = 8
b. x = 28
d. x = 7
Answer:
d. x = 7
Step-by-step explanation:
32/8 = 28/x
simplify the fraction
4/1 = 28/x
cross multiply:
4x = 28
divide both sides by 4:
x = 7
2(x-5)=4x+7
solve for x
Answer:
x=-6
Step-by-step explanation:
What is-1 5/6 times 6 1/2
Answer:
-11.9166666667
Step-by-step explanation:
Answer:
-11.9166666667
Step-by-step explanation: I just seached it up
Can some please tell me what this is?
Step-by-step explanation:
This is mean domain is all real numbers
What is the quotient of : 4.652/.3
Answer:
15.51
Step-by-step explanation:
Mr. Hernandez found salmon on sale at HEB for $6.99 per pound. How much would it cost if Mr. Hernandez bought 3.2 pounds of salmon? Round your answer to the nearest cents.
Answer:
$22.37
Step-by-step explanation:
Answer:
$22.37
Step-by-step explanation:
6.99(3.2)