The pool dimensions that will minimize the cost of construction are length of square bottom = 20 ft and height of pool = 5 ft
Let l be the length of side of the square bottom of the pool and h be the height of the pool.
Its volume V = l²h
Now, the total surface area of the pool equal the area of its sides plus the area of its base.
The area of its 4 sides is 4lh.
Since the cost of the side of the pool is $80 per square foot, the total cost for the sides of the pool is C = $80 × 4lh = $ 320lh
Also, The area of its square bottom is l².
Since the cost of the side of the pool is $40 per square foot, the total cost for the square bottom of the pool is C' = $40 × l² = $ 40l²
So, the total cost of the pool is C" = C + C' = 320lh + 40l²
C" = 320lh + 40l²
Since the volume equals 2000 ft³, V = l²h
2000 = l²h
h = 2000/l²
Substituting h into C", we have
C" = 320lh + 40l²
C" = 320l × 2000/l² + 40l²
C" = 640000/l + 40l²
To find the value of l which makes C" minimum, we differentiate C" with respect to l and equate it to zero.
So, dC"/dl = d(640000/l + 40l²)/dl
dC"/dl = d(640000/l)/dl + d(40l²)/dl
dC"/dl = -640000/l² + 80l
Equating dC"/dl to zero, we have
-640000/l² + 80l = 0
-640000/l² = -80l
Cross-multiplying, we have
640000 = 80l³
Dividing through by 80, we have
l³ = 640000/80
l³ = 8000
Taking cube root of both sides, we have
l = ∛8000
l = 20 ft
We differentiate C" twice to determine if this value of l gives a minimum for C".
So, d²C"/dl² = d(-640000/l² + 80l)/dl
d²C"/dl² = d(-640000/l²)/dl + d(80l)/dl
d²C"/dl² = 640000/l³ + 80
Substituting l = 20, we have
d²C"/dl² = 640000/l³ + 80
d²C"/dl² = 640000/20³ + 80
d²C"/dl² = 640000/8000 + 80
d²C"/dl² = 80 + 80
d²C"/dl² = 160 > 0
Since d²C"/dl² = 160 > 0. So, l = 20 ft gives a minimum for C".
Since h = 2000/l²
Substituting l = 20 into the equation, we have
h = 2000/l²
h = 2000/20²
h = 2000/400
h = 5 ft
So, the pool dimensions that will minimize the cost of construction are length of square bottom = 20 ft and height of pool = 5 ft
Learn more about dimensions of a pool here:
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The price of the trail mix at the health food store is $7.50 per pound at this rate what is total cost of 8 ounces bags of trail mix
Answer:
Below
Step-by-step explanation:
1 pound = 16 ounces
Therefore if you're looking for 8 ounces, divide $7.50 in half.
You get $3.75
Answer:
At this rate, the total cost of 8 ounce bag of trail mix would be $3.75.
Step-by-step explanation:
So first I found that for 1 LB (pound), there is 16 ounces so 8 oz is half of 16. If we know that, we have to divide 7.5 by 2 to get 3.75.
Mrs. Coulter has 3 / 5 yard of ribbon to tie on balloons for the festival. Each balloon will need 3 / 10 yard of ribbon. How many balloons can Mrs. Coulter tie with ribbon
Answer:
I know they are not the same name but they have the same question they are the same answerStep-by-step explanation:
#hope it helps you #happy learningI need help i have no clue what to do!
Answer:
Step-by-step explanation:
-6x-2y= -26
3(-6x-2y)= -26*3
-18x-6y= -78
(subtract this from the first equation)
(-2x-6y)-(-18x-6y)= -14+78
16x=64
x=4
Now that we know x= 4 we can plug that into an equation and solve for y
-2(4)-6y= -14
-8-6y= -14
-6= -6y
y= 1
x=4
y= 1
(4,1)
find x if mi = 3x - 5 and mj = x + 5
A line passing through the point(-10,-5) and has a slope of -1/2
What is the value of x?
(picture attached)
x= 48
P/s: sorry. I cant explain
ok done.thank to me :>
If f(x)=6, what is x?
Answer:so: 6=6/5-x^3
6=6(5-x^3)
6=30-6x^3
-6x^3=6-30
-6x^3=-24
-6x^3+24=0
6x^3-24=0
6(x^3-4)=0
x^3-4=0
x^3=4
x=cube root 4
x=1.5874
Step-by-step explanation:
A beach ball has a radius of 3 inches calculate volume
Answer:
113.1 in.³
Step-by-step explanation:
V = (4/3)πr³
V = (4/3) × 3.14159 × (3 in.)³
V = 113.1 in.³
who is in 6th grade or 7th?
cause I swear hrw.com is horrible
Answer college
Step-by-step explanation:
help me can you help with the second part
Answer:
12 packages with 2 toothbrushes and 3 soaps each
Step-by-step explanation:
Plzzzzz help meeeeeeee plzzzzz
Answer:
1) The profit made is $560.
2) Don't know sorry!!
3) A student will pay $1134 for a calculator.
Step-by-step explanation:
14. They are symbols that denote silence and give the performer time to relax. * O a. notes O b.rests O c. time signatures
Answer:
b.rests
Step-by-step explanation:
HOPE IT'S HELP
#PHILIPPINES
PLEASE HELP ME INSTANTLY I WILL GIVE A BRAINLY AND A THANKS
Answer:
1.the first one is the distance from home
2. is 91
3.increases by 91 i belive tht should be correct
Step-by-step explanation:
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!9
Answer:
letter D
thank me later....
I borrow $5 from Luis and $ 8 from Stephanie.
How do I show my debt with integers.
Answer:
-5 + -8 = -13
Step-by-step explanation:
-5 + -8 = -13
in total you owe $13 but seperat it’s $5 and $8.
also you show a debt with Integers by using negative numbers.
In Jackie’s math class, there are 51 students and one-third of the class is boys. How many girls are there in Jackie’s math class?
Answer:
34 boys
Step-by-step explanation:
you divide 51 by 3 which gets yOU 17 and then you subtract 17 by 51 which gets you 34
x + 12 = 20 i really need help
Hello! :)
x+12=20
Move all numbers to the right, using the opposite operation:
x=20-12
x=8
Therefore, x=8
Hope it helps. Enjoy your day! :)
Do ask me if you have any question.
~An excited gal
[tex]MagicalNature[/tex] here to help
Graph y=-6 please please please
Answer:
Step-by-step explanation: Y=6 is 36 if u subtract from 6 and add 20 plus 7
maria has $100 dollars to spend. she wants to buy a sweater for $30 and a pair of jeans for $42. she would like to spend the rest of her money on t-shirts that cost $4 each. how many can she buy?
Answer:
7 T-Shirts
Step-by-step explanation:
Given:
100 Dollar
30 = sweater
42 = Jeans
4 each = t-shirts
Solution:
30+42 = 72
100-72 = 28
28/4=7
Therefore she can buy 7 T-Shirts.
Answer:
7 shirts
Step-by-step explanation:
100 (total) - 30 (sweater) - 42 (jeans) = 28 (for shirts)
28 (money) / 4 (shirt cost) = 7 (shirts)
Assuming no tax and stuff, Maria should be able to by 7 shirts on top of her other items.
hey i need all three boxes solved please
giving 12 points
Answer:
it says 6 points not 12 points
Step-by-step explanation:
Coordinate plane .........
Answer:
The answer is the blue dot
Step-by-step explanation:
You should remember that the x goes first in (x,y).
What is the topic of a piece of informational writing? (100 point)
A. the meanings of words
B. the way the writer feels about the subject
C. the subject or focus
D. the way information is grouped
Answer:
the topic of a piece of informational writing: C. the subject or focus
The topic of an informative piece is the writer's feelings about the subject which is the correct answer that would be an option (B).
What is information writing?Informational writing is a piece of writing that is truthful and aims to educate or explain a topic to the reader. This teaches primary school students how to write realistic, insightful essays on a variety of topics.
It gives the reader fundamental information about a certain issue, which serves to inform the reader. Informational writing, unlike other types of writing, does not aim to influence the reader's opinion or inspire them to take action.
The informational writing is straightforward and succinct. It does not include any superfluous words, flamboyant notions that might confuse the readers or too detailed terminology.
Therefore, the correct answer would be option (B).
Learn more about the Information writing to click here:
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#SPJ5
1) x + x + 8x + 12 =
x + x + 8x + 12 = ...
= 2x + 8x + 12
= 10x + 12
~aljabar
x + x + 8x + 12
= 1x + 1x + 8 + 12
= (1 + 1 + 8)x + 12
= 10x + 12 ✔️
:)
In which quadrant is the number –14 – 5i located on the complex plane?
I
II
III
IV
In which quadrant is the number –14 – 5i located on the complex plane? I II III IV
Answer:
III
Step-by-step explanation:
go 14 left and 5 down, and you're in the third quadrant
Answer:
III (Third quadrant)
Step-by-step explanation:
Okay, in terms of complex numbers, the x axis is the imaginary scale while the y axis is the real scale. And this works just like a normal x and y axis! We can break down -14-5i into -5i and -14, and -5i is the imaginary number on the x axis, so we move five units to the left from the origin. -14 is the real number, so we then move down 14 units, and we end up with a coordinate that is in the III, or third, quadrant. Hope this helps! :)
find equation of a line containing (3,-4) and having a slope of -2. if this line contains the points(a, 8) and (5,b) find a and b
i will give brainlest for the best answers with best explanation
Answer:
a = - 3, b = - 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 2 , then
y = - 2x + c ← is the partial equation
To find c substitute (3, - 4 ) into the partial equation
- 4 = - 6 + c ⇒ c = - 4 + 6 = 2
y = - 2x + 2 ← equation of line
------------------------------------------------------------------
Substitute (a, 8 ) into the equation and solve for a
8 = - 2a + 2 ( subtract 2 from both sides )
6 = - 2a ( divide both sides by - 2 )
- 3 = a
Substitute (5, b ) into the equation and solve for b
b = - 2(5) + 2 = - 10 + 2 = - 8
Please help!!!!!!!!!!!
Answer:
10. right triangle 11. obtuse triangle 12. right triangle 13. right triangle
Step-by-step explanation:
Find the sum of 382 - 8 - 10 and 1042 +2 - 10.
Answer:
364 and 1034
Step-by-step explanation:
One side of a regular hexagon ABCDEF forms the side of a regular polygon with n sides.
Angle GAF = 105°. Work out the value of n.
Answer:
n = 8.
Step-by-step explanation:
The interior angle of a regular hexagon = 120 degrees.
So m < GAB = 360 - 120 - 105
= 135 degrees so the regular polygon has a total of 135n degrees.
Using the formula for the sum of interior angles of a polygon,
For the polygon with n sides:
Sum of interior angles = 180(n - 2)
135n = 180(n - 2)
135n = 180n - 360
45n = 360
n = 360/45 = 8.
15 liters increased by 60% is ___ liters
[tex]15 \times (1 + .6) = 24 \: \: \: liters[/tex]
it's 24 littershope it helps
What is the value of y?
09
O 18
O 3
Answer:
The answer is 9
Step-by-step explanation:
First looking at the triangle with the 90 degree sign in it we know that the other angles in that triangle will have to add with 90 to equal 180
So doing the easier way replace 9 with y and do this for the other numbers 3 and 18 to see if the result of (2y+18) and 4y will equal the same number
[tex](2(9)+18)=36 \\4(9)=36[/tex]
[tex](2(3)+18)=24 \\4(3)=12[/tex]
[tex](2(18)+18)=54 \\4(18)=72[/tex]
and because the lines on each triangle represent that those sides are congruent
I hope this because I am only using what I remember from geometry but please let me know if I am wrong