Answer:
13000
Step-by-step explanation:
A pool with a square bottom is to have a volume of 2000 cubic feet. The owners plan to use a fancy tile to complete the pool. The sides of the pool will cost $80 per square foot and the bottom of the pool will cost $40 per square foot. Find the pool dimensions that will minimize the cost of construction.
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
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haircut josiah went to the local barber to get his hair cut.it cost $18 foto the haircut josiah tipped the barber 15%
15% of $18 is $2.70...........
Y=6 z=7 h=0 what is y+h
Evaluate
[tex] \sf \longmapsto \: y + h[/tex]
When
[tex]y = 6[/tex][tex]z = y[/tex][tex]h = 0[/tex]Let's start.
[tex] \sf \longmapsto \: y + h[/tex]
Put the values[tex] \sf \longmapsto6 +0[/tex]
Answer[tex] \sf \longmapsto6[/tex]
But there is no use of z = 7 . Z is excluded from y+h.о
3. Aspect Ratios (Tires)
If you have changed the tires on your car, the original diameter is 21 inches. to a new diameter of 25.2 inches,
how fast are you actually going if your speedometer is reading 53 mph?
a
44.2 mph
b. 63.6 mph
c. 60.8 mph
d. 53 mph
The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.50 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
What is 7536 to 1 significant figure
Answer:
8000
Step-by-step explanation:
Two friends, Gabriel and Hudson, had just bought their first cars. Gabriel uses 10 gallons of gas to drive 339 miles in his car. The table below represents the number of miles, yy, that Hudson can drive his car for every xx gallons of gas.
How much farther can Gabriel's car travel on one gallon of gas than Hudson's car?
Answer- 15.8 Miles
Explanation photo was given above.
Help with elimination
Many Thanks
[tex]\left \{ {{-6y = -12} \atop {3x + 2y = -2}} \right. <=> \left \{ {{y = 2} \atop {3x + 2y = -2}} \right. <=> \left \{ {{y=2} \atop {3x + 2*2 = -2}} \right. <=> \left \{ {{y=2} \atop {3x = -6}} \right. <=> \left \{ {{y=2} \atop {x=-2}} \right.\\ => \left \{ {{y=2} \atop {x=-2}} \right.[/tex]
What is the total surface area of a cylinder with a diameter of 10.8 and a height of 2.6?
Answer:
271.433606 (in, cm, or whichever unit)
Step-by-step explanation:
To find the areas of the ends of the cylinder, the circles, you would use the formula:
2(π * r²)
The diameter is twice the length of the radius so to find the radius, you would divide the length of the diameter in half. So with a diameter of 10.8 units, it would become 5.4 units.
2(π * 5.4²) = 183.217684
To find the surface area of the rectangle of the cylinder, you would multiply the circumference of the base of the cylinder by the height. The formula to find the circumference is 2πr. The circumference would be 33.9292007 units. 33.9292007 * 2.6 = 88.2159218.
Then add the areas to find the total.
183.217684 + 88.2159218 = 271.433606
HELP PLEASEE!!!
In Asha's science experiment, her bacteria are dying at a constant rate of $600$ an hour. If she drew a graph of the number of bacteria in her culture where $x$ represented the time in minutes since the start of the experiment and $y$ represented the number of bacteria remaining in the colony, her graph would be a line. What would be the slope of this line?
Answer:
-10
Step-by-step explanation:
The rate of change is also known as the slope of the function thus the slope will be -600.
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
The slope is also calculated by differentiation for example slope of y = sinx will be y' = cosx.
As per the given,
Bacteria are dying at a constant rate of $600$ an hour.
The rate of change = -600/hour
Slope = y/x = number of bacteria change/time taken
If the graph is a straight line then it will remain constant.
Slope = -600
Hence "The rate of change is also known as the slope of the function thus the slope will be -600".
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4x^2 - 3 when x= -10
Answer:
397
Step-by-step explanation:
1. To evaluate this expression, we plug in the value of x and simplify.
[tex]4x^2 - 3[/tex] [tex]4(-10)^2 - 3[/tex] [tex]4(100)-3[/tex] [tex]400-3[/tex] [tex]397[/tex]Therefore, the answer is 397.
Write an equation in Slope intercept form for the line that passes through the given point and has the given slope (-2,-3) , (4,5)
Answer:
[tex]y=\frac{4}{3}x-.333[/tex]
Step-by-step explanation:
Using the Slope Formula:[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex][tex]\frac{5-(-3)}{4-(-2)}=\frac{5+3}{4+2}=\frac{8}{6}=simplify=\frac{4}{3}[/tex]The rectangle below has been enlarged by a scale of 3.5.
A rectangle with a length of 8 and width of 6.
Multiply the original dimensions by the scale:
8 x 3.5 = 28
6 x 3.5 = 21
New dimensions: length = 28, width = 21
help meee plzzz
help me
Answer:
I only know the second one sooorrry
if you say its classification so that type of traingle is obtuse triangle
Step-by-step explanation:
A person has a bag containing quarters and dimes. There are a total of 72 coins in the bag, and the total value of the coins is $13.20. Determine how many quarters and dimes are in the bag.
Answer:
40 quarters and 32 dimesStep-by-step explanation:
Given:
Quarter = 25 ¢, number of quarters = qDime = 10 ¢, number of dimes = dTotal amount = $13.20 = 1320 ¢Required equations:
q + d = 7225q + 10d = 1320Solve by elimination, multiply the first equation by 10 and subtract from the second equation:
25q + 10d - 10q - 10d = 1320 - 10*7215q = 600q = 600/15q = 40Find p:
40 + p = 72p = 72 - 40p = 32Let's take the given as,
→ q = quarters (25)
→ d = dimes (10)
→ 1320 will be the amount
→ q + d = 72
→ 25q + 10d = 1320
Now we can solve for q,
→ (25q - 10q) + (10d - 10d) = 1320 - (10 × 72)
→ 15q = 1320 - 720
→ 15q = 600
→ q = 600/15
→ [ q = 40 ]
From this equation,
→ q + d = 72
We can solve for the d,
→ 40 + d = 72
→ d = 72 - 40
→ [ d = 32 ]
There are 40 quarters & 32 dimes.
Please help me with this MATH question.
Answer:
y=4
Step-by-step explanation:
84=30y-9y, first you collect like terms.
84=21y, swap the sides
21y=84, devide both sides and you get y =4
Decide which of the following numbers does not belong in the group.
108
502
603
360
And why does it not belong?
Answer:
502
Step-by-step explanation
108 has the numbers 0, 1, and 8 which added together totals 9
603 has the numbers 0, 3, and 6 which added together totals 9
360 has the numbers 0, 3, and 6 which added together totals 9
502 has the numbers 0, 2, and 5 which equal 7
502 is the odd one out
write the ratio in simplest form 30 in. to 1ft
Jacob was out at a restaurant for dinner when the bill came. His dinner came to $18. After adding in a tip, before tax, he paid $20.70. Find the percent tip.
Answer:
The answer is 2.70
Step-by-step explanation:
18+2.70= 20.70
20.70-2.70=18
Simplify the expression. -8n - 2n
Answer:
-10n
Step-by-step explanation:
To simplify, you add like terms so by looking at the problem you can see the 8 and the 2 both have an n after, so you can combine them.
so negative 8 minus 2 = -10 and since there are like terms you add the n making the answer -10n
If it was -8n -2 you could not simplify it since the 2 is single and without the same letter
Same with -8n - 2p because it is not the same letter
HELPPPP PLS!! TY
Look at triangle ABC.
Coordinate grid shows negative 5 to positive 5 on the x axis and y axis at intervals of 1. A triangle ABC is shown with A at ordered pair 4, 5, B at ordered pair 1, 2, and C at ordered pair 4, 2.
What is the length of side AB of the triangle? (1 point)
Square root of 6
3
Square root of 18
6
Step-by-step explanation:
as you can see, the distance between 2 points can always be seen as the Hypotenuse or baseline of a right-angled triangle created by the differences of the x and y coordinates of both points.
the drawn triangle is nothing else than that.
to calculate the length of a side in such a triangle we need to use Pythagoras :
c² = a² + b²
c is the Hypotenuse of baseline of the triangle and is opposite of the 90 degree angle.
a and b are the legs of the triangle "enclosing" the 90 degree angle.
so, we have
AB² = AC² + BC²
AC and BC we know : the coordinate differences in x and y directions.
AC = (4, 5) to (4, 2). as the x coordinates are the same, the difference is just the difference in the y coordinates : 5-2 = 3.
BC = (1, 2) to (4, 2). as the y coordinates are the same, the difference is just the difference in the x coordinates : 5-1 = 3.
AB² = 3² + 3² = 9 + 9 = 18
AB = sqrt(18)
FYI : sqrt(18) = sqrt(9×2) = 3×sqrt(2)
a
Blue and green dye are mixed in a 7:4 ratio to make 44 litres
of a teal-coloured dye. A further 8 litres of green dye are added
to the mixture. What is the new ratio of blue to green dye in its
simplest form?
Answer:
7:4 is the new ratio.
Step-by-step explanation:
set a proportion; (8+4 = 12)
7 x
-- = --
4 12
12/4 = 3
3 x 7 = 21
x = 21
new ratio: 21:12
simplifies: 7:4 (division of 3)
The new ratio of blue to green dye in its simplest form is 7/6.
Blue and green dye are mixed in a 7:4 ratio to make 44 litres of a teal-coloured dye. A further 8 litres of green dye are added to the mixture. What is the new ratio of blue to green dye in its simplest form to be determined.
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
Calculating the fraction of blue and green in the teal dye,
Blue dye = 7/(4+7) * 44
Blue dye = 7/11 * 44
Blue dye = 28 liters
Similarly,
Green dye = 7/12*44
Green dye = 16
Now
Blue dye = green dye = 28+16 = 44
Now gree dye is increase by 8 liters
new volume fraction of green dye = 16+8
= 24
a fraction of blue dye remains the same,
the ratio of blue dye to new green dye in teal colored.
= 28/24
=7/6
Thus, the new ratio of blue to green dye in its simplest form is 7/6.
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Two of the angles in a triangle measure 154° and 20°. What is the measure of the third angle?
Answer:
6°
Step-by-step explanation:
The angles in a triangle always add up to 180°. Let’s call the third angle x. That means that:
154 + 20 + x = 180 ->
174 + x = 180 ->
x = 180 - 174 ->
x = 6°
Hope that help! :)
Crossword math please help
Answer:
The code is 8415
Step-by-step explanation:
the value if /14-15/ is
Answer:
1
Step-by-step explanation:
/14-15/
/-1/
1(because absolute value of any real number is always positive and for zero itself zero)
4x+y=8
x+2y=5
substutuion method
Answer:
i dont know sry....i ned points..
Evaluate the formula z=
x−μ
σ
n when μ=119, n=29, x=116, and σ=9.
Work Shown:
[tex]z = \frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\\\\z = \frac{116-119}{\frac{9}{\sqrt{29}}}\\\\z \approx \frac{-3}{\frac{9}{5.3851648}}\\\\z \approx \frac{-3}{1.671258}\\\\z \approx -1.795055\\\\z \approx -1.795\\\\[/tex]
need help please i’m struggling to solve
I can't give a very good answer as I don't know what resources are available to you, but this is what I managed to find with a ti-84 calculator.
[tex]y=-31.24+1.34x[/tex]
If you want a better step-by-step, tell me what's in that 'open statistics calculator' option and I'll see what I can figure out.
edit: missed that second part of the question
Using this equation to calculate a test grade with a homework grade of 90:
[tex]y=-31.24+1.34(90)=89[/tex]
Please HeLp 100 PoInTs + bRaNlEyIsT
Answer:
It is congruent doe to the angle side angle congruence thereom AKA ASA
Step-by-step explanation:
That means there are two angles and one side in between. A pair of triangles that follow this rule has an angle that is congruent to one angle. Then a side that has a tick mark after the angle must match another. Then the last angle has to match another angle ( and it can't be the same angle as before). Usually the first pair angles have 1 semicircle and the second pair has 2 semicircles.
The coordinates of the end points of TU are T(2,4) and U(11,13)
Answer:
[tex]T(2,4) and U(11,13)[/tex]
Step-by-step explanation: