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]
The Madison's son Dwayne
A restaurant manager classifies customers as regular, occasional, or new
Answer:
Step-by-step explanation:
I am sorry but please give detailed question
Dennis mowed his next door neighbors lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. How many of each coin did he earn
Answer:
28 nickels and 52 dimes
Step-by-step explanation:
.05x 28 + .10 x 52 = 6.60
1.40 + 5.20 = 6.60
^28 + ^52 = ^80
Ashley has sold 70% of the 20 candy bars she is supposed to sell for her softball team. How many candy bars does she have left to sell?
Answer:
70/100=x/20 cross multiply you get 1400/100=14
If Ashley sold 70% of her candy bars it means she has 30% left to sell
of means times
30%=.30
20 x .30= 6 candy bars to sell
Step-by-step explanation:
give brainliest please :)
Answer:
6
Step-by-step explanation:
70% of 20 is 14
20-14=6
let me know if im wrong
What did Physics say to History when they are arguing?
Answer:
Hey!
Here's your answer!!
➡️Don't change the subject⬅️
Why do they even exist!?
Gotta study those experiments which we never perform and those people who are long gone xD
Do you wants to buy a bike for $180 he has $40 Dave mows lawns for $10 per lawn Write in equation that can be used to find eggs the number of lawns Dave needs mow to have enough money to the to buy his bike
Answer:
Dave needs to mow 14 lawns to have enough money to buy a bike.
Step-by-step explanation:
180-40=140, 140/10=14. Dave needs to mow 14 lawns to have enough to buy a bike.
can you help me on this question
they are the same but one of the is a bad pic
used to parallel lines cut by transversal below to answer the question. which statement is not a true statement will mark brainest
Answer:
B
Step-by-step explanation:
there is no angle e unless i am reading this incorrectly, but i double-checked all the other answer choices and they are all correct, so B is the answer:)
Answer:
see attached
Step-by-step explanation:
student schoolitycom/students/common/index
Cow
CCM! Payne New
Henry, Ladaris
DISTRICT SWI CA GRADE 6 MATH 20-21
D3101 2. P N →
Eat Test
4
BO
In a TV contest show, Thomas has 280 points. To determine his final score in the game, Thomas will spin the spinner shown below, and multiply his current number of points by the
fraction the spinner lands on
Which statement correctly describes the effect of multiplying his current score by the fractions shown on the spinner?
A Multiplying by will decrease his score
B Multiplying by will decrease his score.
Copyright 2020 laminate Education, Inc. All Rights Reserved
US 2:41
Answer:
Step-by-step explanation:
this is due today help
Answer:
Sunday: 50 Monday: 60 Tuesday: 50 Wednesday: 50 Friday: 40 Saturday: 40
Step-by-step explanation:
That's If Its To The Nearest Tenth If This Is What U Wanted I'm Just Doing What The Instructions Told Me
Given a linear equation with a slope of - 13/4, determine the slope of a line that is perpendicular. Enter the answer as a fraction.
Answer:
4/13
Step-by-step explanation:
To find the perpendicular slope, find the negative reciprocal, which is 4/13 in this case. All you do is flip the numerator and denominator, and change the sign.
Answer:
4/13 should be the answer as it is the reciprocal.
Step-by-step explanation:
I learned this like 2 or 3 years ago so im a bit rusty but im pretty sure thats the answer
Monica works in a mailroom for 18 hours
each week. How many hours does she work in
52 weeks?
Answer:
936
Step-by-step explanation:
Because 18 times 52= 936
When do we use inequalities?
Answer: In math but if u mean “irl” they use it in business like how much is in there inventory (stock) and the price stock they can make to get an profit and etc.
Step-by-step explanation:
What is a better credit score?
Select the correct answer below:
A lower number
An even number
An odd number
O A higher number
Answer:
A higher number.
Step-by-step explanation:
You don't want your credit to be low, and a higher number beats all of them.
You want high credit.
Not low.
Answer:
definately you want a higher number
A test contains two multiple-choice questions. If a student makes a random guess to answer each question. (Hint: Consider two outcomes for each question—either the answer is correct or it is wrong.) 2.2.1 How many outcomes are possible?
Answer: 2
Step-by-step explanation: he could ethier get t right or get it wrong
Enter the slope-intercept equation for the image of line ℓ after a clockwise rotation of 90°. (Hint: To find the image of line ℓ, choose two or more points on the line and find the images of the points.)
Answer:
y = -2x - 2
Step-by-step explanation:
From the graph attached,
If the line 'l' passes through two points A(0, -1) and B(4, 1).
Rule for the rotation of any point (x, y), 90° clockwise about the origin is,
(x, y) → (y, -x)
By this rule,
A(0, -1) → A'(-1, 0)
B(4, 1) → B'(1, -4)
Let the equation of the line A'B' is,
y - y' = m(x - x')
where m = slope of the line A'B'
And (x', y') is a point lying on the line.
Slope of the line passing through A' and B' will be,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{0+4}{-1-1}[/tex]
m = -2
Therefore, equation of the line passing through (-1, 0) and slope = -2,
y - 0 = (-2)(x + 1)
y = -2x - 2
So the equation of the line after rotation of lie 'l' by 90° clockwise will be,
y = -2x - 2
Need help ASAP !!! I am failing MATH
Answer:
i think it is D
Step-by-step explanation:
Suppose you have information about average heights of a random sample of airline passengers. The mode is 65 inches, the median is 72 inches, and the mean is 70 inches. To convert the data into centimeters, multiply each data value by 2.54. What are the values of the mode, median, and mean in centimeters?
Answer: mode = 165.10 cm, median = 182.88 cm, mean = 177.80 cm
Step-by-step explanation:
mode = 65*2.54 = 165.10 cm
median = 72*2.54 = 182.88 cm
mean = 70*2.54 = 177.80 cm
The values in cm are:
Mode = 162.56 cm
Median = 182.88 cm
Mean = 177.8 cm
Given,
The mode is 65 inches, the median is 72 inches, and the mean is 70 inches.
We need to convert the data into centimeters by multiplying each data value by 2.54 and find the values of the mode, median, and mean in centimeters.
How many cm in one inch?There is 2.54 cm in one inch.
Example:
If we want to find cm in 4 inches.
We just multiply 4 with 2.54 cm.
2.54 cm = 1 inch
4 x 2.54 cm = 4 x 1 inch
10.16 cm = 4 inches
We have,
We know that,
1 inch = 2.54 cm
Mode = 65 inches
1 inch = 2.54 cm
64 inches = 64 x 2.54 cm = 162.56 cm
Median = 72 inches
72 inches = 72 x 2.54 cm = 182.88 cm
Mean = 70 inches
70 inches = 70 x 2.54 cm = 177.8 cm
Thus the values in cm are:
Mode = 162.56 cm
Median = 182.88 cm
Mean = 177.8 cm
Learn more about the conversion of inches to cm here:
https://brainly.com/question/14881622
#SPJ2
The quantities and are proportional
9514 1404 393
Answer:
r = 1
Step-by-step explanation:
Solving the equation for r gives ...
r = y/x
Using the first line of the table, we find r to be ...
r = 5.8/5.8 = 1
The constant of proportionality is r = 1.
Alice is completing the table so that it is a function. Which values can she NOT use to complete
the table? Explain.
What is the sum of the fractions? Use the number line to help find the answer.
3/5 plus -7/5
Answer:
-4/5
Step-by-step explanation:
Answer:
The answer is -4/5
Step-by-step explanation:
Hope this helps!:)
A dolphin jumped from 5 feet below the surface of the sea. Jane wrote −5 to represent the depth from which the dolphin jumped. What does 0 represent in this situation?
Answer:
it represents the surface of the sea
Step-by-step explanation:
i did the test lol :)
2) Martha cut three pieces of rope that are 5 1/4 inches each from a rope that is 20 inches
long. What is the length of the remaining part of the rope?
Help me please
Answer:
Step-by-step explanation:
Total length of the rope = 20 inches.
Martha cuts 3 pieces of rope that is 5 1/4 inches each.
Find the total length of the 3 pieces of rope:
Total of 3 pieces of rope = 5 1/4 + 5 1/4 + 5 1/4 = 15.75
Since we know the total rope length is 20 inches, if you subtract the total length of the 3 pieces of rope you will get the remaining length of rope.
Remaining length = 20 - 15.75
= 4.25 inches of rope
What is the slope of the line that passes through the points (1, 1) and (7, 5)?
Answer:
The slope of the line is
[tex] \frac{2}{3} [/tex]
HELP ASAPPPP
What is the equation of this graphed line? If the line passes through (-6,-3) and (6,-7)
Answer:
y= -1/3x - 5
Step-by-step explanation:
Answer:
The answer would be y=-1/3x-7.
Step-by-step explanation:
Using the formula y2-y1/x2-x1 to find the slope of the line, plug in the numbers and you will get a slope of -1/3. Now using the the formula y-y1=m(x-x1) and plug in the numbers, and you will get the equation y=-1/3x-7.
The width of a rectangle is 50% more than the length. The perimeter is 65. Find both dimensions.
Answer:
Step-by-step explanation:
Perimeter of rectangle = 2 times width + 2 times length
P= 2W + 2L
Let's say W = width , L= length
We are told the width is 50% more than the length.
width = 0.5 + L
W = 0.5 + L
From here we can say
Perimeter = 2W + 2L so,
P = 2(0.5 + L) + 2L
P = 1 + 2L + 2L
P = 1 + 4L
We are also told perimeter is 65 (P=65)
65 = 1 + 4L
Subtract 1 from both sides
64 = 4L
Divide 64 by 4 to find L
L = 64/4 = 16
Now since we know L= 16, this means
W = 0.5 + L is the same as
W = 0.5 + 16 = 16.5
Therefore Length = 16, width = 16.5
A family buys 8 tickets to a show. They also pay a $5
parking fee. They spend $61 to see the show.
What is the solution to the story?
13.80
10.60
07.00
8.25
Answer:
C. $7.00
Step-by-step explanation:
8 times 7 is 56 + 5 = 61
If Coach Smith has 12 players and each player needs three uniforms, three shin guards, two balls, and three pairs of cleats. How much will he end up spending on his equipment for the entire soccer team?
you can't do that. there isn't enough detail. we don't know how much each item costs
4(a + 2) + 2 = 4 - 2(-2a - 3)
Answer:
0=0
Step-by-step explanation:
4(a + 2) + 2 = 4 - 2(-2a - 3)
4a + 8 + 2 = 4 + 4a + 6
4a + 10 = 10 + 4a
0 = 0
find three ratios that are equivalent to 20:25
Answer:
4/5 , 40/50, 80/100
Step-by-step explanation: