The dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
The given parameters are:
Volume = 480m^3Cost: $5 per square meter for the bottom, and $3 per square meter for the sides.Assume the dimensions of the container are: x, y and z.
The volume (V) would be:
[tex]V = xyz[/tex]
Substitute 480 for V
[tex]xyz =480[/tex]
And the objective cost function would be:
[tex]C =8xy + 6xz + 6yz[/tex]
Differentiate the cost function using Lagrange multipliers
[tex]8x + 6z = \lambda xz[/tex]
[tex]8y + 6z = \lambda yz[/tex]
[tex]6x + 6y = \lambda xy[/tex]
Divide equation (1) by (2)
[tex]\frac{8x + 6z}{8y + 6z} = \frac{\lambda xz}{\lambda yz}[/tex]
[tex]\frac{8x + 6z}{8y + 6z} = \frac{x}{y}[/tex]
Factor out 2
[tex]\frac{4x + 3z}{4y + 3z} = \frac{x}{y}[/tex]
Cross multiply
[tex]4xy + 3yz = 4xy + 3xz[/tex]
Evaluate the like terms
[tex]3yz = 3xz[/tex]
Divide both sides by 3z
[tex]y = x[/tex]
Divide the first equation by the third
[tex]\frac{8y + 6z}{6x + 6y} = \frac{\lambda yz}{\lambda xy}[/tex]
[tex]\frac{8y + 6z}{6x + 6y} = \frac{z}{x}[/tex]
Factor out 2
[tex]\frac{4y + 3z}{3x + 3y} = \frac{z}{x}[/tex]
Cross multiply
[tex]4xy+3xz = 3xz + 3yz[/tex]
Cancel out the common terms
[tex]4xy = 3yz[/tex]
Divide both sides by y
[tex]4x = 3z[/tex]
Make z the subject
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
Recall that:
[tex]xyz =480[/tex]
Substitute [tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
[tex]x \times x \times \frac 43x = 480[/tex]
So, we have:
[tex]\frac 43x^3 = 480[/tex]
Multiply both sides by 3/4
[tex]x^3 = 360[/tex]
Take the cube roots of both sides
[tex]x = \sqrt[3]{360}[/tex]
Recall that:
[tex]y = x[/tex]
So, we have:
[tex]y = \sqrt[3]{360}[/tex]
Also, we have:
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Hence, the dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
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If log x+y/5 = 1/2(log x + log y) the find the value of x/y + y/x ?
Given that
log (x+y)/5 =( 1/2) {log x+logy}
We know that
log a+ log b = log ab
⇛log (x+y)/5 =( 1/2) log(xy)
We know that log a^m = m log a
⇛log (x+y)/5 = log (xy)^1/2
⇛log (x+y)/5 = log√(xy)
⇛(x+y)/5 = √(xy)
On squaring both sides then
⇛{ (x+y)/5}^2 = {√(xy)}^2
⇛(x+y)^2/5^2 = xy
⇛(x^2+y^2+2xy)/25 = xy
⇛x^2+y^2+2xy = 25xy
⇛x^2+y^2 = 25xy-2xy
⇛x^2+y^2 = 23xy
⇛( x^2+y^2)/xy = 23
⇛(x^2/xy) +(y^2/xy) = 23
⇛{(x×x)/xy} +{(y×y)/xy} = 23
⇛(x/y)+(y/x) = 23
Therefore, (x/y)+(y/x) = 23
Hence, the value of (x/y)+(y/x) is 23.
How do I find the percentage of two column data table?
Answer this .i will make you brainliest
[tex]\huge{\underline{\underline{\boxed{\sf{\purple{ǫᴜᴇsᴛɪᴏɴ}}}}}}[/tex]
(8) An aeroplane takes off from Dubai located in the +4 time zone at 13:00. It arrives in Manila in Philippines, located in the +8 time zone at 20:00.(1) Find the time in Manila when the aeroplane departsfrom Dubai.(ii) Find the time duration of the flight.(iii) What is the time in Dubai when the aeroplane arrives in Manila?[tex]\huge{\underline{\underline{\boxed{\sf{\ref{Answer}}}}}}[/tex]
(i)17.00(ii)3 hours(iii) 16.00[tex]\large\huge\green{\sf{♥ Explanation♥}}[/tex]
Dubai located +4 zone, takes off at 13.00,∴Hence, at standard it is 13.00-4 =99.00 STD talk
off reached at Manila +8 Zone at 20.00
∴Hence at standard & 2000 -8
reached.⇒ 12.00 STD
Hence time of flight was = 3 hours.(i) Time at Manila, whicle Plane de parts
12-3+8 ⇒9+8 → 17.00
(ii) duration = 3 hours.
(iii) in dubai 13.00 + 3 = 16,00
_____________________
Ans
i)17.0.0 (ii) 3 hours (iii) 16.00
________________________
♕ hence we done:) xD
Bryce wrote the linear regression equation y = 1. 123 x minus 6. 443 to predict the armspan, y, of a person who is x inches tall. Riley has an armspan of 67. 5 inches. Which is the best prediction of Riley’s height? 54. 36 inches 65. 84 inches 66. 55 inches 69. 36 inches.
The best prediction of Riley’s height is 65.84 inches and it can be determined by using the linear regression equation.
Given that,Bryce wrote the linear regression equation,
[tex]\rm y=1.123x-6.443[/tex]
To predict the arm span, y, of a person who is x inches tall.
Riley has an arm span of 67.5 inches.
We have to find,Which is the best prediction of Riley’s height?
According to the question,To predict the arm span, y, of a person who is x inches tall.
Riley has an arm span of 67.5 inches.
The linear regression equation is,[tex]\rm y=1.123x-6.443[/tex]
Where the arm span, y, of a person who is x inches tall.
Riley has an arm span of 67.5 inches,
Then,
The best prediction of Riley’s height is,
[tex]\rm 67.5 = 1.123x -6.443\\\\67.5+6.443=1.123x\\\\ 73.943 = 1.123x\\\\ x = \dfrac{73.943}{1.123}\\\\ x = 65.84 \ inches[/tex]
Hence, The best prediction of Riley’s height is 65.84 inches.
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A dress which costs $180 is being sold at a discount of 10%. The amount of the discount is
$1.80
$10.00
$18.00
$170.00
Answer:
The discount is 18 dollars
Step-by-step explanation:
The three solids below have the same height. The cross-sections of the parallel planes have equal areas,
Which solid has the greatest volume?
It should be noted that all the solids have the same volume.
What is volume?Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. It should be noted that the definition of length is interrelated with volume.
Here, the three solids below have the same height. The cross-sections of the parallel planes have equal areas. They all have same volume.
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Anna saved $20 in a jar each month for 2 1/2
years. She spent 75% of her savings on a computer. How much money did Anna have left in the jar?
Answer:
20*2.5=50
50*0.75=37.5
Hope This Helps!!!
Answer:270
Step-by-step explanation:
8x7= something x0.1
please help me
let something = x
[tex]8 \times 7=x \times 0.1 \\ x = \frac{8 \times 7}{0.1} \\ x = \frac{8 \times 7 \times 10}{1} \\ x = 560[/tex]
therefore, something = 560
correct answer:-8x7= 560 x0.1What is the equation of the line that passes through the point (-2, 1) and has a
slope of 3/2?
Answer:
Step-by-step explanation:
Given:
x1 = -2
y1 = 1
slope (m) = 3/2
Solution:
y - y1 = m ( x - x1 )
y - 1 = 3/2 ( x - (-2) )
y - 1 = 3/2 ( x + 2 )
y - 1 = 3/2x + 3
y = 3/2x + 3 + 1
y = 3/2x + 4
Find the area of each figure
Answer:
18
Step-by-step explanation:
6*6/2
Rachel is 10 years older than her sister, Renee. In six years from now, the sum of their ages will be 40. How old is each girl?
(Systems of Equations Word Problem)
Answer: I say the answer is 20 years old, 30 years old
Step-by-step explanation: If rachel is 10 years old than her sister in six years from now, the sum of their ages will be 40. So rachel is 10 years older than her sister so the younger sister has to be 20 years old and and rachel is 30 years old.
if x is reduced by 25%. the result will be
[tex]\huge\color{skyblue}\boxed{\colorbox{black}{Answer♡}}[/tex]
[tex]a \: number \: x \: is \: reduced \: by \: 25\%[/tex]
[tex]25\% \: of \: x \: means \: ( \frac{25}{100} )(x) = 0.25x \\ \\=> x - 0.25x \\ = > 0.75x[/tex]
hope helpful~
The reduced quantity if x is reduced by 25% is 0.75x.
What is percentage?A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.
Given:
x is reduced by 25%,
Calculate the 25% of x as shown below,
25 / 100 × x
0.25x
Calculate the reduced quantity,
Reduced quantity = x - 0.25x
Reduced quantity = x(1 - 0.25)
Reduced quantity = 0.75x
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PLEASEE HELP ME ITS EAZY
If its easy, why don’t you do it yourself??
Lalit got 50% in Hindi,75% in English and 90 marks in maths. The maximum marks in each subject were 100,140 and 160 respectively. Find his aggregate percentage
Answer:
61%Step-by-step explanation:
MARKS
% Max Actual
Hindi 50% 100 50
English 75% 140 105
Math 160 90
400 245 61%(245/400)
Which equation is perpendicular to y=4x-6 and passes through point (B, 12)
Answer:
asdasd
Step-by-step explanation:
asdasdasd
Evaluate c√+b(a−3)^3, when a = 5, b = 2, and c = 49.
a.84
b.72
c.54
d.23
(will mark brainliest if correct)
Answer:
D). 23Step-by-step explanation:
I just did this question and it is 100% correct
The perimeter of a rectangular piece of land is 280m. People divide the land into two small pieces: a square, a rectangle. The total perimeter of the two small plots is 390m. Calculate the area of the original piece of land.
Step-by-step explanation:
Length of the Rectangular piece of the land = 12 + 1/2 m = 25/2 m
Breadth of the Rectangular piece of the land = 5 + 1/5 m = 26/5 m
If 4 small square flower bed of side length 1 m are made at center.
To find: Area of the rectangular land , Perimeter of the rectangle and Area of land left when flower bed are mad.
Perimeter of the rectangle = 2 × ( length + breadth )
= 2 × ( 25/2 + 26/5 )
= 2 × ( 177/10 )
= 177/5 m
= 35.4 m
Area of the rectangular land = Length × Breadth
= 25/2 × 26/5
= 5 × 13
= 65 m²
Area of a flower bed = side × side = 1 × 1 = 1 m²
Area of 4 flower bed= 4 × 1 = 4 m²
Area left in the land = 65 - 4 = 61 m²
Therefore, Perimeter of the land is 35.4 m
Area of land is 65 m²
Area of the land left after flower beds is 61 m²
Please help me solve this problem ASAP
Answer:
28?
Step-by-step explanation:
4x=2x+56 (equal angles)
2x=56 (divide both sides by 2)
x=28 (angle)
Answer:
∠B = 112°
Step-by-step explanation:
1) ∠B and ∠D are congruent because they are alternate interior angles (same side interior) so they equal the same
2) Set the two expressions equal to each other:
2x+56 = 4x
56 = 2x
x=28
3) Plug 28 in for x in the expression (2x+56) and get 112°
Work out the size of angle x.
Answer:
65°
Step-by-step explanation:
x=180°-40°-75°
x=65°
Write an equation that represent the line
Rita’s earnings are based on how many hours she works. Rita worked 22 hours and earned $379.50. What would Rita earn for working 52 hours?
Rita will earn $897 for working 52 hours.
Word problems in mathematics are mathematical operations that are applied to solve real life cases.
From the information given:
Rita's earnings are dependent on the hours she worksIf Rita worked for 22 hours, she earns $379.50
Now, if Rita worked for 52 hours, the amount Rita will earn can be expressed by using the relation:
[tex]\mathbf{= \dfrac{52 \ hours \times \$379.50}{22 \ hours} }[/tex]
= $897
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I need help putting these together in the correct place
Answer:
whats do you mean by that whats the question ❓
The diagram shows a triangle.
What is the value of b?
37
143
90
30
Answer:
37
Step-by-step explanation:
All angles of a triangle have to add up to 180 degrees
180 - 113 - 30 = 37
37+113+30 = 180
Find the value of x, y, and z, in the rhombus below.
Answer:
x = 19, y = -7, z = -18
Step-by-step explanation:
Since its a rhombus and 1 side = 29, all sides = 29. Just solve each side.
2x - 9 = 29
2x = 38
x = 19
-3y + 8 = 29
-3y = 21
y = -7
-2z - 7 = 29
-2z = 36
z = -18
The value of the variables x, y, and z will be 19, -7, and -18, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
All the sides of the rhombus are congruent with each other.
Then the equations are given below.
2x - 9 = 29
-3y + 8 = 29
-2z - 7 = 29
Simplify the first equation, then we have
2x - 9 = 29
2x = 38
x = 19
Simplify the second equation, then we have
-3y + 8 = 29
3y = - 21
y = -7
Simplify the third equation, then we have
-2z - 7 = 29
2z = - 36
z = - 18
The value of the variables x, y, and z will be 19, -7, and -18, respectively.
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ankita and her three friends are going to share a three bedroom apartment if the total rent is Rp.r, what is ankitas share
Using proportions, it is found that Ankita's share is of [tex]\frac{x}{4}[/tex], considering that the total rent is of x Rp.r.
This question is solved by proportions, using a rule of three.Considering that there are 4 people and the rent is of x Rp.r, 4 people pay x, how much does Ankita, which is one person, pay?The rule of three is:
4 people - x
1 people - a
Applying cross multiplication:
[tex]4a = x[/tex]
[tex]a = \frac{x}{4}[/tex]
Ankita's share is of [tex]\frac{x}{4}[/tex], considering that the total rent is of x Rp.r.
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Hello i need help with this one its only one.
Answer:
y=8 x+2
Step-by-step explanation:
Mike earned x dollars the first week of his new job. He earned 5% more the second week than the first week. Which expression represents the total amount of money Mike earned for both weeks?
1.50x
1.50 x
1.05x
1.05 x
2.00x
2.00 x
2.05x
Answer:
1.05x I think
show that 12n cannot end with the digit 0 or 5 for any natural number
Answer:
Step-by-step explanation:
It can end with a 0.
For example 12 * 5 = 60.
Given the equations x^2 + 8x + 12 = 0 and 3x + 6 = 0, what is the common
solution?
[tex] {x}^{2} + 8x + 12 = 0 \\ = > {x}^{2} + 6x + 2x + 12 = 0 \\ = > x(x + 6) + 2(x + 6) = 0 \\ = > (x + 2)(x + 6) = 0 \\ = > x = - 2 \: \: or \: \: - 6[/tex]
[tex]3x + 6 = 0 \\ = > 3x = - 6 \\ = > x = \frac{ - 6}{3} \\ = > x = - 2[/tex]
Here, the common solution is -2.
Answer:
x = -2.
Hope you could get an idea from here.
Doubt clarification - use comment section.
Matthew spent 2/3 of his birthday on books and 1/4 of his birthday money on snacks. He says he spent 3/7 of his birthday money.
Which statement is most accurate?
*Disclaimer* show work
Answer:
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] + [tex]\frac{1}{4}[/tex] = [tex]\frac{8+3}{12}[/tex] = [tex]\frac{11}{12}[/tex] ≈ 1
The correct answer is the last one (C)