Answer:
the dimensions that will minimize the cost are; 25.2 ft × 25.2 ft × 12.6 ft
Step-by-step explanation:
If the length, width and height of the building are represented by a, b and c, then we have:
Volume = abc
We are given volume as 8000 ft³. Thus;
abc = 8000
Top area = ab
Front area = ac
Back area = ac
End walls area = bc
We are told that cooling costs will amount to $2/ft² for its top, front, and back, and $4/ft² for the two end walls.
Thus, cooling cost equation is;
X = 2(ab) + 2(ac) + 2(ac) + 4bc + 4bc
X = 2ab + 4ac + 4bc
Now, from the volume equation where abc = 8000.
c = 8000/ab
Thus;
X = 2ab + 4a(8000/ab) + 4b(8000/ab)
X = 2ab + 32000/b + 32000/a
To minimize, we will find the a and b derivative and set the equation to zero in both cases.
Thus;
dX/da = 2b - 32000/a² = 0
2b = 32000/a² - - - eq(1)
Also;
dX/db = 2a - 32000/b² = 0
2a = 32000/b² - - - (eq 2)
Making a the subject in eq 2 gives;
a = 32000/2b²
a = 16000/b²
Putting 16000/b² for a in eq (1) gives;
2b = 32000/(16000/b²)²
2b = 32000b⁴/256000000
2b = b⁴/8000
Multiply both sides by 8000 to get;
2b × 8000 = b⁴
16000b = b⁴
Divide both sides by b to get;
16000 = b³
b ≈ 25.2 ft
Putting 25.2 for b in a = 16000/b², we have;
a = 16000/25.2²
a ≈ 25.2
Putting a and b = 25.2 in the volume equation, we have;
25.2 × 25.2 × c = 8000
c = 8000/(25.2 × 25.2)
c = 12.6 ft
Thus, the dimensions that will minimize the cost are; 25.2 ft × 25.2 ft × 12.6 ft
simplify (q+8)2 please help, thank you
q^2 +16q+64
All you have to do is substitute the exponent two.
Q by itself is q squared: q^2
Q times 8 is 8q, and because of exponent you have to double it, which gives you 16q.
And 8 times itself is 64.
Hope this helps
Find the measures of the labeled angles.
(x+92) =5xº
Answer:
X=23
Step-by-step explanation:
First you write the problem without the parenthesis so it's more easier to work out.
Second you need to do is change what is at the end of the problem all the way to beginning of the problem and also change the sign which should look something like this, x=5x-92.
Then you collect like terms which is ( 5x and x)
and sense x is 1 you subtract it and it would give you this -4x=-92. Divide both sides by 4 which would give you 23.
An artist uses 2 ounces of blue paint for every
7 ounces of yellow paint. The artist has 49
ounces of yellow paint. How many ounces of blue
paint will she need to add.
Answer:
14
Step-by-step explanation:
Talia measured a piece of construction
paper to be 6.1 inches wide by 8.2 inches
long. What is the area of the piece of
construction paper in square inches?
Answer:
50.02
Step-by-step explanation:
9.2x6.1=50.02 square inches
Help me with this question pleaseeee
why the factor 1.5 is broken into two numbers in the model.
Which of the following is true about the equation y =
-5x + 10?
A The equation has a positive y-intercept.
B
The equation has a negative y-intercept.
C The equation has a positive slope.
D The equation is proportional.
Answer:
A The equation has a positive y-intercept.
Step-by-step explanation:
pls mark brainliest :)
Answer:
A
Step-by-step explanation:
The y intercept is represented by the letter b in y=mx+b so in this case, 10 is the y intercept and is positive.
Determine the probability that it will not rain for the next two weeks. Express your answer as a decimal precise to two decimal places.
Answer:
Probability of not raining in next two weeks is 0.696
Step-by-step explanation:
Let us calculate -
Probability diagram is attached below .
Probability of not raining in next week is 0.8
Probability of not raining in second week is 0.87
Therefore, Probability of not raining in next two weeks = [tex]0.8\times 0.87[/tex]
= 0.696
Thus , the probability is 0.696
what is it. hurry please.
Step-by-step explanation:
we know that,
area of rectangle = length × breadth
Then,
area of rectangle EFGH = (e + h) × j
Therefore,
Option C is correct ✔.
Need Help Asap) Graph the piecewise function. ( Look at the picture). Will Mark Brainliest. Please show me points on paper. [ Only Answer If You Truly Know How To Please And Thank You].
Answer:
[tex]the \: points \: are : \\ ( - 1, \: - 9) \\ ( 0, \: 3) \\( 4, \: 2)[/tex]
Step-by-step explanation:
[tex]f(x) = 3x - 5 \: ....if \: x \leqslant - 1 : \iff \: ( - 1, \: - 9) \\ if \: x = - 1 \: then \: y = - 9\\ f(x) = - 2x + 3 \: ....if \: - 1 < x < 4 :\: \iff( 0, \: 3) \\if \: x = 0 \: then \: y = 3 \\ f(x) = 2\: ....if \: x \geqslant 4 : \: \iff( 4, \: 2)[/tex]
♨Rage♨
2 over 3 divided by 6 ?
Answer:
1/9
Step-by-step explanation:
whats 10293 x 384? Its really hard!
Answer:
3,952,512
Step-by-step explanation:
need help on homework
The management of a forestry company estimates that acres of forest available for logging will increase at a rate given by R(t) = 56/root t + 7 for 0 leq t leq 20, where R(t) is the rate of new acreage becoming available in thousands of acres per year, t years after the current year. How many acres of forest, Q(t), will become available for logging over the first five years?
A. 46 thousand acres.
B. 148 thousand acres.
C. 296 thousand acres.
D. 92 thousand acres.
Answer:
Step-by-step explanation:
If the acres of forest available for logging will increase at a rate given by
R(t) = 56/√t + 7
In order to determine the acre of forest that become available after 5 years, we will substitute t = 5 into the formula.
R(5) = 56/√5 + 7
R(5) = 56/2.236 + 7
R(5) = 25.044 + 7
R(5) = 32.044
The amount that will be available over the first five years is 32 thousand acres
Help me before 9 24 am pls
Answer:
128calories/cup
256calories
Step-by-step explanation:
Given parameters:
Amount of calories = 96calories
Number of cups = [tex]\frac{3}{4}[/tex]cups
Unknown:
Unit rate(calories per cup) = ?
Number of calories in 2 cups = ?
Solution:
A. To find the unit rate;
Unit rate = [tex]\frac{amount of calories}{number of cups}[/tex]
Insert the parameters and solve;
Unit rate = [tex]\frac{96}{\frac{3}{4} }[/tex]
Unit rate = 96 x [tex]\frac{4}{3}[/tex] = 128calories/cup
B. Number of calories in 2 cups;
Amount of calories = unit rate x number of cups
Amount of calories = 128calories/cup x 2cups
Amount of calories = 256calories
I will give brainliest! :D
Frank had 90 flyers to hang up around the school. After
giving the same number of flyers to each of three
volunteers, he had 12 left to hang up by himself.
Which tape diagram goes with the story? ^
Charmaine purchased a prepaid phone card for $15. Long distance calls cost 7 cents a minute using this card. Charmaine used her card only once to make a
long distance call. If the remaining credit on her card is $13.88, how many minutes did her call last?
the call lasted 16 minutes
The length of a rectangle is 4 inches more than its width, and its perimeter is 34 inches. Find the length and width of the rectangle. Find the width of the rectangle. Type a numerical answer in the space provided.
Answer:
w mean widh
Step-by-step explanation:
p=2l+2w
given w+4 2+w p= 34
34 =2w+4 + 2 w
w=24
26
_ 6.5
4
L w+4 =6.5 +4 =10.5
sort the following number from greatest to least 12%, 3,75, 9/10, 7, 176%, 4/5
Answer:
the answer is
3, 7, 12%, 75, 4/5, 9/10, 176%
Step-by-step explanation:
What is the slope of a line parallel to the line y = 4x – 11?
What is the sum of 34 and its additive inverse?
Answer: 0
Step-by-step explanation:
The inverse property is basically the opposite of the number
Someone helped please xxx
Answer:
es de ingles matt verdad
A.
<A = <Z (both have 2 lines)
<B = <X (both have one line)
<C = <Y (both have 3 lines)
B.
AB = XZ (both have 3 markings)
AC = ZY (both have 1 marking)
BC = XY (both have 2 markings)
If the fabric, thread, buttons, and zipper cost $13.30, how much is the sales tax if the tax is 8%?
Answer:
$1.06 to thousendth is the tax
Step-by-step explanation:
13.30*2/25=Your answer
There are 360 calories in 9 bags of chips.How many calories are in 5 bags of those chips?
Answer:
200 calories
Step-by-step explanation:
360 ÷ 9 = 40
40 X 5 = 200
Answer:
there are 200 calories in 5 bags of chips
Step-by-step explanation:
divide 360÷9=40 and then multiply 40 times five equ3ald 200
-(5x + 6) - x = -6 - 6x
If your question is a True or False question your answer is: True
Point A is rotated 90 degrees counterclockwise around point C to form the image A'. Select three true statements based on the given information.
Answer:
When we rotate a point A, around point C, the distance between the points is invariant.
This means that if A' es the image of the rotated point, then A' must lie in a circle centered in C with radius AC.
Then the correct statements are:
A' lies on a circle centered at point C with radius AC
This is by definition.
m∠ACA' = 90°
This is because A is rotated 90° around C to form the image A', then the measure must be 90°.
AC = A'C
As we already defined, the distance between the rotated point and the center of rotation is invariant, then the distance between A and C must be the same as the distance between A' and C.
Answer:
AC = A'C
A' lies on a circle centered at point C with radius AC
m∠ACA' = 90°
Step-by-step explanation:
When we rotate a point A, around point C, the distance between the points is invariant.
This means that if A' es the image of the rotated point, then A' must lie in a circle centered in C with radius AC.
As we already defined, the distance between the rotated point and the center of rotation is invariant, then the distance between A and C must be the same as the distance between A' and C.
which equation matches this graph?
If ( y+6=3/4(x+4) ) is your equation then A is your answer
Mathematics what is 567divide by 8
Answer:
70.875
Step-by-step explanation:
Don't you have a calculator..?
A pass at a water park is $58. Halfway through the season, the pass is discounted by 20%. What was the discounted price?
Answer:
Step-by-step explanation:
First, list the fractions in between. 2.41, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, 2.49, then 2.5. When looking at the list, you can see that 2.45 is halfway between 2.4 and 2.5. One other way to find it is thinking what is between 0 to 10? The answer is 5.
Jimmy is buying balloons and party hats for his little sister’s birthday party. The party store charges $1.50 for each bag of balloons and $6.00 for each package of hats. Which of the following equations could be used to determine different combinations of b bags of balloons and h packages of party hats that he could buy for a total of $24 ?
Answer:
4 bags of balloons and 3 bags of party hats
Step-by-step explanation:
1.50 x 4= 6
6 x 3= 18
6+18=24
The equation that could be used to determine different combinations will be 4b + 3h.
Based on the information given, the party store charges $1.50 for each bag of balloons and $6.00 for each package of hats.
Therefore, the equation that fits the explanation will be: 4b + 3h.
= 4b + 3h.
= 4(1.50) + 3(6)
= 6 + 18
= 24.
Therefore, the equation is 4b + 3h.
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