A 1125 ft^3 open-top rectangular tank with a square base x ft on a side and y ft deep is to be built with its top lush with the ground to catch runoff water. The costs associated with the tank involve not only the material from which the tank is made but also an excavation charge proportional to the product xy.a. If the total cost isc = 5(x^2 + 4xy) + 10xy,what values of x and y will minimize it?b. Give a possible scenario for the cost function in part (a).
Answer:
The values of x and y that will minimize the cost is 15 ft and 5 ft respectively and the minimum cost will 3,375
Step-by-step explanation:
With a 1125 ft^3 open-top rectangular tank with a square base x ft on a side and y ft deep is to be built with its top lush with the ground to catch runoff water, x is the length, y is the height;
x^2*y = 1125
y = 1125/x^2 ----(1)
The total cost of c = 5(x^2 + 4xy) + 10xy
Then,
c = 5(x^2 + 4x*(1125/x^2)} + 10x*(1125/x^2)
c = 5x^2 + 22,500/x + 11,250/x
c = 5x^2 + 33,750/x
To minimize the cost of c, find the derivatives of c; c'
c' = 10x - 33,750/x^2
c' = (10x^3 - 33,750)/x^2
c'(x) = 0; 10x^3 = 33,750
x = ³√33,750 = 15
x = 15; y = 1125/x^2
y = 1125/15^2 = 5
(x,y) = (15,5)
c = 5x^2 + 33,750/x
c = 5*15^2 + 33,750/15 = 3,375
The values of x and y that will minimize it is 15 ft and 5 ft respectively and the minimum cost will 3,375
The values of x and y that will minimize the cost is 15ft and 5ft. The minimum cost is 3,375
We have volume of a rectangular tank = 1125 ft^3
Side of a rectangular tank = x ft and
Length of a rectangular tank =y ft
So, [tex]x^2y = 1125[/tex]
[tex]y = \frac{1125}{x^2} ...(1)[/tex]
The total cost of rectangular tank (c) = [tex]5(x^2 + 4xy) + 10xy[/tex]
[tex]c = 5(x^2 + 4x(\frac{1125}{x^2} ) )+ 10x(\frac{1125}{x^2} )\\c = 5x^2 +\frac{22,500}{x} + \frac{11250}{x} \\c = 5x^2 + \frac{33750}{x}[/tex]
Differentiating it w.r.t x, we get
[tex]c' = 10x - 33,750/x^2\\c' =\frac{10x^{3}-33750 }{x^{2} } \\c'(x) = 0\\10x^3 = 33,750\\x = \sqrt[3]{33,750} \\ = 15\\x = 15; y = \frac{1125}{x^2} \\y = \frac{1125}{15^{2} } \\= 5\\(x,y) = (15,5)\\c = 5x^2 + \frac{33750}{x} \\c = 5(15)^2 + 33,750/15 \\= 3,375[/tex]
The values of x and y that will minimize the cost is 15 ft and 5 ft and the the minimum cost is 3,375.
Learn more:https://brainly.com/question/6995312
18 bikes, 9 have gears (G), 11 have suspension (S) and 5 with both,What is the probability that a bike with suspension or gears? Make a two-way table to help you!
Answer:
5/9Step-by-step explanation:
Total number of bikes = 18Bikes with gears S = 9Bikes with suspension S = 11Bikes with both GS = 5From the information above we have:
Bikes with gears only = 9 - 5 = 4Bikes with suspension only = 11 - 5 = 6Sum of the above two gives us the number of bikes with suspension or gears:
4 + 6 = 10Probability of selected bike be G or S is:
P(G or S) = 10/18 = 5/9There are 16 girls and 18 boys in a class. The teacher chooses a student's name at random to answer a question.
What is the probability that the teacher chooses a girl to answer the question?
А: 1/34
B:1/16
C:8/17
D: 8/9
Answer:
I would go with c
Step-by-step explanation:
if it is incorrect sorry
F(x) = 2x+6, g(x) = 3² findf(g (-3))
Step-by-step explanation:
If F(x) = 2x+6, g(x) = 3² findf(g (-3))
Solution
f(g (-3)) = 2x+6(3²(-3)) = 2x+6(3×3(-3))
= 2x+6(-27) = 54x-162 = 54x = 162
54/54x = 162/54
x = 3
Answer:
➩ [tex]f(g(-3)) = 24[/tex]
Step-by-step explanation:
➨ Rearrange/Simplify the equations
[tex]F(x)=2x+6\\g(x)=9[/tex]
➨ Find [tex]f(g(-3))[/tex]
[tex]g(-3)=9[/tex] ➩ All x-values have same y-values ➩ Constant Function
Substitute [tex]g(-3) = 9[/tex] in the f(x)
[tex]f(g(-3)) = f(9)\\f(9)=2(9)+6\\f(9)=18+6\\f(9)=24\\f(g(-3)) = 24[/tex]
Thus, the answer ➩ [tex]f(g(-3)) = 24[/tex]
Nichol runs 3/4 mile in 1/4 hour. How many miles can she run in 1 hour?
Answer:
The answer is 3 miles, I had the same question
Fractions finding the whole
Answer:
top left: 1/3
top right: 16
bottom left: 1/3
bottom right: 15
Step-by-step explanation:
Whoever answers this question correctly will get a 5.0 rating, thanks, and a brainlyist.
The question is on the screenshot.
RULE 1: Do not answer just for points because that's just mean.
Hugo and Viviana work in an office with ten other coworkers. Out of these 12 workers, their boss needs to choose a group of four to work together on a project. Suppose Hugo and Viviana absolutely refuse, under any circumstances, to work together. Under this restriction, how many different working groups of four can be formed
Answer:
450
Step-by-step explanation:
The total number of possible working groups of 4 workers selecting from 12 workers is the number of ways of selecting 4 persons from 12 persons
[tex]=\binom{12}{4}=\frac{12\times 11 \times 10 \times 9}{1\times 2 \times 3\times 4}=495[/tex]
The total number of possible groups of 4 workers in which 2 persons (Hugo and Viviana) always come together
[tex]= \binom {12-2}{4-2}=\binom {10}{2}=\frac{10\times9}{1\times2}=45[/tex]
So, the total number of possible working groups in which Hugo and Viviana are not working together in any of the groups [tex]= 495-45=450[/tex].
5. Find x if √x=79.
Answer:
x=6241
Step-by-step explanation:
^2 on both sides.
x=79^2.
x=6241.
Hope this helps plz hit the crown :D
Answer:
6241
Step-by-step explanation:
hope this is correct
Can you help with all label them by there numbers plz thank you
Answer:
13- 25 fish
14- 9 miles
15- 7.825 ft3
16- 11.3 feet
Step-by-step explanation:
13-
14 x 2 = 28 fish
He dropped three things so:
28 - 3 = 25 fish
14-
7 days x 3weeks = 21 days
3laps x 21 days = 63 laps
63 laps x 1/7 mile = 9 miles
15-
all his savings: 2.6 + 7.34 + 5.71 = 15,65 ft3
melted snow = 15.65 / 2 = 7.825 ft3
16-
3.5 - 1.8 = 1.7 feet
1.7 + 9.6 = 11.3 feet
Answer:
Step-by-step explanation:
# 13.
I assume there will be no bonus, because penguin dropped some things.
14 × 2 - 3 × 1 = 25 fish
# 14.
3 laps, [tex]\frac{1}{7}[/tex] mile, 7 days, 3 weeks
3 × [tex]\frac{1}{7}[/tex] × 7 × 3 = 9 miles
# 15.
[tex]\frac{2.6+7.34+5.71}{2}[/tex] = 7.825 ft³
# 16.
[tex]3\frac{1}{2}[/tex] = 3.5
+ 3.5 - 1.8 + 9.6 = (3.5 + 9.6) - 1.8 = 11.3 ft.
Write the point-slope form of the equation of the line through the given point and slope.
through: (1, -2), slope = -6
y - 2 = -6 (x + 1)
y - 2 = 6 (X + 1)
y + 2 = -6 (x - 1)
y + 2 = 6 (x - 1)
Answer:
[tex]y +2 =-6(x - 1)[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (1,-2)[/tex]
[tex]m=-6[/tex]
Required
Determine the point slope equation
This can be determined using the following formula:
[tex]y - y_1 =m(x - x_1)[/tex]
Where:
[tex](x_1,y_1) = (1,-2)[/tex]
[tex]m=-6[/tex]
So, we have:
[tex]y - (-2) =-6(x - 1)[/tex]
This gives:
[tex]y +2 =-6(x - 1)[/tex]
Hence, the point slope form is [tex]y +2 =-6(x - 1)[/tex]
A Super Happy Fun Ball is dropped from a height of 4 feet and rebounds 4 5 of the distance from which it fell. How many times will it bounce before its rebound is less than 1 foot
Answer:
More than 6.21 times
Step-by-step explanation:
The common ratio [tex]r=\dfrac{4}{5}[/tex]
Distance of first bounce
[tex]a_1=4\times \dfrac{4}{5}=\dfrac{16}{5}[/tex]
Second bounce
[tex]a_2=ar^{n-1}=\dfrac{16}{5}(\dfrac{4}{5})^{2-1}\\\Rightarrow a_2=\dfrac{16}{5}(\dfrac{4}{5})[/tex]
n bounce
[tex]a_n=ar^{n-1}\\\Rightarrow a_n=\dfrac{16}{5}(\dfrac{4}{5})^{n-1}[/tex]
Now the nth bounce will be less than 1 feet
[tex]\dfrac{16}{5}(\dfrac{4}{5})^{n-1}<1\\\Rightarrow (\dfrac{4}{5})^{n-1}<\dfrac{5}{16}[/tex]
Applying logarithms on both sides we get
[tex](n-1)\ln \dfrac{4}{5}<\ln\dfrac{5}{16}\\\Rightarrow n>\dfrac{\ln\dfrac{5}{16}}{\ln \dfrac{4}{5}}+1[/tex]
The inequality changes as both [tex]\ln\dfrac{5}{16}[/tex] and [tex]\ln \dfrac{4}{5}[/tex] are negative numbers.
So,
[tex]n>6.21[/tex]
Hence, the number of bounces is more than 6.21 times.
Ramon earns $1,690 each month and pays $53.60 on electricity. To the nearest tenth of a percent, what percent of Ramon's earnings are spent on electricity each month?
Answer:
3.1%
Step-by-step explanation:
divide his electricty payment by his monthly pay
4 quarts of organic grapes cost $20 what is the cost per quart
Please halp me, thanks so much
-Tornado
Answer:
>
Step-by-step explanation:
Step-by-step explanation:
Since c is on the left of -1 on the number line,
c < -1.
If we add 2 to both sides of the inequality we get c + 2 < 1.
Hence the correct sign is "<".
Jack is keeping a record of the number of steps he takes each day.
Monday 8 565 steps
Tuesday
Wednesday
14 707 steps
15 323 steps
Thursday 9 788 steps
Friday
12 482 steps
Work out the range of the numbers of steps
Answer:
6758
Step-by-step explanation:
Given the data:
Monday _______ 8565 steps
Tuesday ______ 14707 steps
Wednesday ____ 15323 steps
Thursday ______ 9788 steps
Friday _________12482 steps
The range from the data is :
(Highest value - lowest value)
(15323 - 8565)
I need help fast thanks
Answer:
In the explanation
Step-by-step explanation:
a) Multiply the second equation by 2, subtract both lines. You get x = -3. Plug this in to get y, y = -2
b) Multiply the first equation by 2, add both lines. You get x = 8. Plug this in to get y, y = -3
c) Multiply the first equation by 5, subtract both lines. You get y = 1. Plug this in to get x, x = -3
d) Multiply the first equation by 2 and the second one by 3, add both lines. You get x = 1. Plug this in to get y, y = 4
Hope this helps!
An object's temperature cools exponentially after it is removed from a furnace (hot oven). If its initial temperature is
730
730
°C and it cools at a rate of
2.95
2.95
% per minute, find the object's temperature after
18.0
18.0
minutes.
Answer: I think 53.1
Step-by-step explanation:
The object's temperature after 18.0 minutes is 425.83.
Given that,
An object's temperature cools exponentially after it is removed from a furnace (hot oven).
If its initial temperature is 730°C and it cools at a rate of 2.95% per minute.
We have to determine,
The object's temperature after 18.0 minutes.
According to the question,
The initial temperature is 730°C and it cools at a rate of 2.95% per minute,
The temperature after t minutes is modeled by an exponential function, which has the following format is,
[tex]T(t) = T(0) . (1-r)^t[/tex]
Where T(0) is the initial temperature, and r is the cooling rate, as a decimal.
Then,
T(0) = 730°c and r = 2.95% = 0.0295
Substitute all the values in the equation,
[tex]T(t) = T(0) . (1-r)^t\\\\T(18) = 730 \times (1-0.0295)^{18}[/tex]
Therefore,
The object's temperature after 18.0 minutes is,
[tex]T(t) = T(0) . (1-r)^t\\\\T(18) = 730 \times (1-0.0295)^{18}\\\\ T(18) = 730 \times 0.5833\\\\T (18) = 425.83[/tex]
Hence, The required value of the object's temperature after 18.0 minutes is 425.83.
To know more about the Exponential function click the link given below.
https://brainly.com/question/16902197
A bag of skittles contains green, orange, red, and yellow candies. 2/3 of the bag contains green and orange candies and 1/12 of the bag is red candies. What is the probability of picking out a yellow skittle from this bag?
Answer:
4/12
Step-by-step explanation:
Watch help video
What is the surface area of the cylinder with height 2 km and radius 8 km? Round
your answer to the nearest thousandth.
Answer:
I think its 502.65 km 2
Step-by-step explanation:
(This is what I think, I might be wrong)
Answer:
502.655km
Step-by-step explanation:
PLS HELP WILL GIVE BRAINLIST
Answer:
The answer is 1050
Step-by-step explanation:
Which of the following expressions is equivalent to (-7)5?
Answer: A would be the answer hope this helps
–4(5x – 9) + 6(2x + 5)?
help pls due today i am just trying to get good grades
Answer:
c
Step-by-step explanation:
because the question already told that a table has four chairs. So, we need the number of tables in the cafe to calculate number of chairs
In a game of chance there is a box filled with 20 black balls, 13 red balls, and 7 green
balls. If a single ball is drawn from the box, then what is the probability that the ball
is green?
Please help me out.
Answer:
7/40
Step-by-step explanation:
7 balls are green-->numerator
7 balls out of 40( in total) are green.
7/40
This means that out of every 40 balls picked, 7 of them should be green.
Evaluate the expression shown for x = 9.
5
--X+7
6
0
-13.
ܝ
2.
Answer: B or -I/2
Step-by-step explanation: I did this question
help please!!! PLEASE HELP!
9514 1404 393
Answer:
x = 8
Step-by-step explanation:
Corresponding segments are proportional.
2x/12 = (x+4)/9
18x = 12(x +4) . . . . . multiply by 9·12
6x = 48 . . . . . . . . . . subtract 12x
x = 8 . . . . . . . . . . . . divide by 6
Answer correct plz if u steal points ill report
Answer:
I my knowledge
option D y=6x
Step-by-step explanation:
and I am 100% sure you
Answer:
y=6x
Step-by-step explanation:
(2 + 9) (3 ÷ 4) answer this
Answer:
Fraction- 33/4
Decimal- 8.25000
Step-by-step explanation:
Hope this helps!
Brain-List?
p-1÷p=5 then p2-1÷p2=? finda the value of p
Answer:
10
Step-by-step explanation:
since everything is doubled
we just do 5 multiplyed by 2