Considering the given conditions in the question, the dimensions that will minimize the cost of construction of the pool are:
base length = 10 feet
base width = 10 feet
pool depth = 20 feet
Volume of a material implies the maximum amount of substance that it can contain.
From the given question, it is expected that the pool would have the shape of a cuboid, thus its volume can be determined by:
volume of the pool = length x width x height
= base area x height
Thus, given that the volume of the pool is 2000 cubic feet, then;
2000 = base area x height
i. Let the dimensions of the square base be 10 feet, and its height 20 feet, so that;
volume = 10 x 10 x 20
= 2000 cubic feet
The cost of constructing the pool of the assumed dimensions would be:
Total area of its sides = 4 x 200
= 800 square feet
The cost of tiling the sides of the pool = $80 x 800
= $ 6400.0
Area of the base of the pool = 10 x 10
= 100 square feet
The cost of tiling the base of the pool = $40 x 100
= $4000
Total cost = $6400 + $4000
= $10400
Total cost of constructing the pool with the assumed dimensions is $10400.
ii. Let the dimensions of the square base be 20 feet, and its height 5 feet, so that;
volume = 20 x 20 x 5
= 2000 cubic feet
The cost of constructing the pool of the assumed dimensions would be:
Total area of its sides = 4 x 100
= 400 square feet
The cost of tiling the sides of the pool = $80 x 400
= $ 32000
Area of the base of the pool = 20 x 20
= 400 square feet
The cost of tiling the base of the pool = $40 x 400
= $16000
Total cost = $16000 + $32000
= $48000
Total cost of constructing the pool with the assumed dimensions is $48000.
Therefore, the dimensions that will minimize the cost of construction of the pool are:
base length = 10 feet
base width = 10 feet
pool depth = 20 feet
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The system of equations below form a line and a parabola. Select all possible solutions to this system from the answer choices below.
2+y=5
x^2+ y = 11
Answer:
no answer choices shown but solution
would be [-2.8, -∞] and [2.83, ∞]
Step-by-step explanation:
A machine paints 340 toy boats in 45 minutes. Which expression equals the unit rate per minute?
Answer:
7.55556 toy boats per minute
or
340 = 45x
Step-by-step explanation:
340 = 45x
340/45 = 45x/45
7.55556 = x
7.55556 toy boats per minute
30 POINTS:
Function f satisfies f(0) = 2 and f ′(0) = −2. Use this information to compute f^−1′(2).
Answer:
-1/2
Step-by-step explanation:
The relevant relationship is ...
f^-1'(x) = 1/f'(f^-1(x))
f^-1'(2) = 1/f'(f^-1(2)) = 1/f'(0) = 1/-2
f^-1'(2) = -1/2
_____
The attached graph shows the tangent lines at the relevant points. The red line is the tangent to f(0); the blue line is the tangent to f^-1(2).
The inverse function is the function reflected across the line y=x. So, too, for the tangent lines to the function. Each is a reflection of the other across the line y=x. For the purpose here, the tangent line is a suitable representation of the function at the point(s) of interest.
Can someone help me solve this integral plsss?
integral of (2xˆ3+3xˆ2+x)/(xˆ2+1) dx
What is the first step to solve the following equation:
n/8 = 7
Answer:
n = 56
Step-by-step explanation:
[tex]\frac{n}{8}[/tex] = 7
The first step is to multiply both sides by 8 to clear the fraction
n = 7 × 8 = 56
I need help getting the answer to this -71+blank=21
Answer:
It is Positive 92
Step-by-step explanation:
-71 + 92 = 21
Write equations for the horizontal and vertical lines passing through the point (-4,2)
Answer:
y=2
x=-4
hope this helps!
Find a value c in the interval [0,3] such that f(c) is equal to the average value.
Answer:
1.5
Step-by-step explanation:
Numbers in the interval are 0, 1, 2 and 3
Average Value = (0+1+2+3)/4=1.5
The average value of the numbers in the interval {0,3} is 1.5.
What is an average?Average is defined as the ratio of the sum of the number of the data sets to the total number of the data. The average actually determines the middle value of the data.
Mean is defined as the ratio of the sum of the number of data sets to the total number of data.
Given that the value c is in the interval [0,3]. The interval is written {0,1,2,3}.
The average of the numbers is calculated as,
Average Value = (0+1+2+3)/4
Average Value =1.5
Therefore, the average value of the numbers in the interval {0,3} is 1.5
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Solve the system of equations by substitution.
3x + y = 9z
-5x + 2y = -4z
What is the value for y from the first equation, that could be substituted into the second equation?
-9z + 3x
3z + 9x
9z - 3x
-3x - 9z
Answer:
x = 1.27
y = 5.18
Step-by-step explanation:
to solve this system of equation by simultaneous equation we say that let
3x+y=9.............................. equation 1
-5x+2y=4 .......................... equation 2
from equation 1
3x+y=9.............................. equation 1
y = 9 -3x.............................. equation 3
substitute the value of y = 9 -3x into equation 2
-5x+2y=4 .......................... equation 2
-5x + 2( 9 -3x) = 4
-5x + 18 - 6x = 4
collect the like terms
18 - 4 = 6x + 5x
14 = 11x
divide both side by 11
14/11 = 11x/11
x = 14/11
x = 1.27
put the value of x = 1.27 into equation 3
y = 9 -3x.............................. equation 3
y = 9 - 3( 1.27)
y = 9 - 3.82
y = 5.18
to check if you are correct put the value of x and y into either equation 1 or equation 2.
3x+y=9.............................. equation 1
3( 1.27) + 5.18 = 9
3.81 + 5.18 = 9
9 = 9
5-3x=Px+7
what value must P have for the equation to have no solutions?
Answer:
P = - 3
Step-by-step explanation:
For the equation to have no solutions the the coefficient of x on both sides must be the same.
5 - 3x = Px + 7 ← P = - 3 , then
5 - 3x = - 3x + 7 ( subtract 5 from both sides )
- 3x = - 3x + 2 ( add 3x to both sides )
0 = 2 ← not possible
Meaning the equation has no solutions
Please help I've never been more confused
Step-by-step explanation:
2.
Two pairs of corresponding angles
i. angle C angle D
ii. angle G angle F
Two pairs of alternate angles
i. angle B angle D
ii. angle H angle F
Two pairs of interior angles
i. angle C angle H
ii. angle D angle E
To get a free bonus gift, you must spend at least $100 in a
certain department store on Tuesday. On Tuesday, Mary made
purchases of $15, $26.50, and $40. What is the least amount she
needs to spend in order to be eligible for the bonus gift?
Spent amount= $81.50
Pending= $18.50
Write 567.4892 correct to (I)the nearest ten (II)2 decimal places
Answer:
i think the answer to your question
1) 570
2)567.49
solve pls brainliest
Answer:5868<9845<91387<969156
Step-by-step explanation:
help with this please! :)
Answer:
w x 7 + 6 x 7
Step-by-step explanation:
Advice: Please make sure you cut out your tabs and your personal information while asking questions. I can easily see on the screenshot that your name is Isabella Fletcher.
ben baked 6 times as many cookies as francis. francis baked 42 cookies. how many cookies did ben bake
Answer:
252
Step-by-step explanation:
If Francis baked 42 cookies, that means ben backed 252, because you can add 42 plus 42 plus 42 blah blah blah 6 times, and it gets you 252. Or you can just do 42 times 6.
find the equation of the line passing through (3,-6) with the gradient of -1/2
Answer:
2y+x+9=0
Step-by-step explanation:
eqn is given by
[tex]m = \frac{y - y1}{x - x1} [/tex]
given
[tex] - \frac{1}{2} \: as \: m[/tex]
and
[tex]{3 \: and \: - 6} \: as \: x \: and \: y \: respectively[/tex]
subtitute values into the formula
[tex] - \frac{1}{2} = \frac{y - - 6}{x - 3} [/tex]
cross multiply giving
[tex] - 1{x - 3}= 2{y + 6[/tex]
[tex] - x + 3 = 2y + 12 \\ 2y + 12 + x - 3 = 0 \\ 2y + x + 9 = 0[/tex]
Jess had 212 deer stickers. Jess gave 47 stickers to Sandy and 24 stickers to Mike. How many stickers does Jess still have?
Answer:
141 stickers
Step-by-step explanation:
212-47=165
165-24= 141 stickers
Please help thankssssss
[tex]0,2a^{2}b^3 . (-5a^3b)^2 = 0,2a^{2}b^3 . 25a^6b^2 = 5a^8 b^5[/tex]
ok done. Thank to me :>
helppp yalll my mind is closed
Answer:
16
Step-by-step explanation:
(Trust me)
What is 0.4184 in standard form
Answer:4.184*10^-1
Step-by-step explanation: in standard form or scientific notation
832.078107648 to the nearest whole number.
can someone help with this question
Answer:
<1= 60
<2=120
<3=60
<4=60
<5=120
<6=120
<7=60
Step-by-step explanation:
Answer Asap!
<3 <3 <3
Thx
Answer:
the answer is 15/17
because cosine=b/h=UV/UW=15/17
If the red marker is red why isn’t the blue marker blue when it rains...?
An electrician charges a
service fee of $89 plus an
hourly rate of $35.
Identify the y-intercept
in this linear equation.
HELPP.
Answer:
89
Step-by-step explanation:
The y intercept is the value when x = 0
Even when you have 0 hours you still have to pay the service fee
The equation is
y = 35x+89
The y intercept is 89
Please help with this question.
Answer:
x=52º
Step-by-step explanation:
A triangle's angles are equal to 180º.
Given the opposite angle to H is 66º, we can find the opposite angle of angle I. The opposite angle of angle K is 62º, assuming that it is equivalent to the opposite angle of angle I we can solve for x.
66+62+x=180
Add 66 and 62.
128+x=180
Subtract 128 from both sides of the equation.
x=52
Angle x is equal to 52º.
Hope this helps :)
help me urgent thankyouu
Answer:
The answer is B.
Step-by-step explanation:
0.0605
help me please on my math I need All of this FACTORS and the LCM
Answer:
the LCM is :
1. 144
2.40
3.870
4. 63
5.216
6.150
7. 112
8.162
9. 96
10. 40
What is the value of the first term in an=n+6?