To solve the problem, use the concept of differential equations and solve for the rate of water leakage. Then, find the time at which the tank will be half empty and the volume of water after 4 days.
Explanation:To solve this problem, we can use the concept of differential equations. Let's denote the volume of water in the tank at any time t as V(t). We are given that the rate at which water leaks is proportional to the square root of the remaining volume, so we can write the differential equation:
dV/dt = k * sqrt(V)
Where k is the proportionality constant. We also know that during the first day, 20 liters leak out, so we can find k:
dV/dt = k * sqrt(350) = -20
Now, we can solve this differential equation to find the time at which the tank will be half empty, and the volume of water after 4 days.
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The tank will be half empty (175 liters remaining) after approximately 3.6 days, and there will be about 135 liters of water remaining after 4 days. The problem involves solving differential equations relating to the leak rate being proportional to the square root of the remaining volume.
This problem involves solving a differential equation based on the rate at which water leaks out of a cylindrical tank. The leak rate is proportional to the square root of the volume of water remaining in the tank.
Differential Equation and Initial Conditions
Given:
Initial volume: 350 liters (V0)20 liters leak out in the first dayRate of leakage, dV/dt = -k√VWhere k is a constant. To find k, we use the initial conditions:
At t = 1 day,
V = 350 - 20
= 330 liters.
We integrate the differential equation:∫dV/√V = [tex]-k\int_{V_0(350)}^{V(330)} dt \quad \text{from} \quad t=0 \quad \text{to} \quad t=1[/tex]
Solving, we get:[tex]2\sqrt{V}\Bigg|_{350}^{330} = -kt\Bigg|_{0}^{1}[/tex]
2(√330 - √350) = -k(1)
Solving for k, we get:k ≈ 2(√350 - √330)
Finding When the Tank is Half Empty
Half of the initial volume is 350/2 = 175 liters.
We need to find t when V = 175.
Integrating the differential equation again:[tex]2\left(\sqrt{V}\Bigg|_{350}^{175}\right)[/tex] = -kt
2(√350 - √175) = kt
Substituting k, we get t ≈ 3.6 days.
Volume After 4 Days
We use our k value and solve for V when t = 4:[tex]2\left(\sqrt{V}\Bigg|_{350}^{V}\right)[/tex] = -k(4)
2√V = 2√350 - 4k
Solving for V, we find V ≈ 135 liters.PJ11
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is divisible by 9". Find P(A).
Answer:
0.15
Step-by-step explanation:
The only outcome that is divisible by 9 is 9 itself. At this point, the probability is 0.15. Hope this helps!
What is the slope of the graphed line ?
Answer:
you cannot see the graph
Step-by-step explanation:
1/3
The slope is determined by change in y / change in x.
Here we can see that it takes 3 blocks from (1,1) until the line is on an integer, (4,2) and that y increases by one while x increases by 3.
Darren invests $4,500 into an account that earns 5% annual interests. How much will be in the account after 10 years if the interest rate is compounded annually, quarterly, monthly, or daily? Which compounded interest rate should Darren choose?
We have been given that Darren invests $4,500 into an account that earns 5% annual interests. We are asked to find the amount in his account after 10 years, if the interest rate is compounded annually, quarterly, monthly, or daily.
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Final amount,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
[tex]5\%=\frac{5}{100}=0.05[/tex]
When compounded annually, [tex]n=1[/tex]:
[tex]A=4500(1+\frac{0.05}{1})^{1\cdot 10}[/tex]
[tex]A=4500(1.05)^{10}[/tex]
[tex]A=4500(1.6288946267774414)[/tex]
[tex]A=7330.025820498\approx 7330.03[/tex]
When compounded quarterly, [tex]n=4[/tex]:
[tex]A=4500(1+\frac{0.05}{4})^{4\cdot 10}[/tex]
[tex]A=4500(1.0125)^{40}[/tex]
[tex]A=4500(1.6436194634870132)[/tex]
[tex]A=7396.28758569\approx 7396.29[/tex]
When compounded monthly, [tex]n=12[/tex]:
[tex]A=4500(1+\frac{0.05}{12})^{12\cdot 10}[/tex]
[tex]A=4500(1.00416666)^{120}[/tex]
[tex]A=4500(1.64700949769)[/tex]
[tex]A=7411.542739605\approx 7411.54[/tex]
When compounded daily, [tex]n=365[/tex]:
[tex]A=4500(1+\frac{0.05}{365})^{365\cdot 10}[/tex]
[tex]A=4500(1.0001369863013699)^{3650}[/tex]
[tex]A=4500(1.6486648137656943695)[/tex]
[tex]A=7418.9916619456\approx 7419.00[/tex]
Since amount earned will be maximum, when interest is compounded daily, therefore, Darren should use compounded daily interest rate.
Find the area of this parallelogram
How are part to part ratios different from part to whole ratios?
Answer:
Part to part ratios are comparing two different things that sum up to its whole, and part to whole ratios are a part of something compared to the whole thing.
Step-by-step explanation:
It's kinda hard to explain..
Un supermercado lanza una promoción para agradecer la fidelidad de sus clientes así: cada que 33 personas pasen por la caja registradora se le regala al cliente de turno un descuento del 50% en sus compras y, cada que pasen 44 personas, al cliente de turno se le obsequiará un televisor LCD de 32 pulgadas. ¿Cada cuántos clientes se ganan los dos premios es una misma compra? A. 77 clientes. B. 88 clientes. C. 99 clientes. D. 132 clientes.
Answer: La respuesta es cada 132 clientes
Lo que hice fue poner la parte de 33 y 44 sumándose entre si:
33+33=66+33=99+33=132 etc
44+44=88+44=132 etc
Y si te diste cuenta concuerdan los dos en 132
Espero que te sirva
Aplicando el mínimo común múltiplo, se encuentra que a cada 132 clientes se ganan los dos premios es una misma compra, opción D.
Los clientes que ganan el descuento de 50% son los múltiplos de 33.Los clientes que ganan el televisor LCD de 32 pulgadas son los múltiplos de 44.Para ver los que ganam ambos, hay que ver lo mínimum común múltiplo de 33 y 44, o sea:
33 - 44|2
33 - 22|2
33 - 11|3
11 - 11|11
1
mcm(33,44) = 2x2x3x11 = 132
O sea, cada 132 clientes se ganan los dos premios es una misma compra, opción D.
Un problema similar es dado en https://brainly.com/question/10894149
there are 80 student in a class if 6 of them are absent then find the percentage of the present student
Answer:92.5%
Step-by-step explanation:
Divide 100 by 80 to find the percentage each student counts for
Then multiply the product(1.25) by 74 (the present students) to get the answer
Answer: 74/80 = 92.5% of the students are present.
what is the input value other than 7 for which g(x)=4
Given:
It is given that the value of the graph when the input 7 is [tex]g(x)=4[/tex]
We need to determine the value of x when [tex]g(x)=4[/tex]
Value of x when [tex]g(x)=4[/tex]:
The value of x can be determined by using the graph.
From the graph, we need to determine the value of x when [tex]g(x)=4[/tex] other than the value x = 7.
This can be determined by finding the point at which the line meets the point y = 4, we can find the corresponding x - value.
Thus, from the graph, it is obvious that the graph also meets the point y = 4 when x = -8.
Therefore, the input value is x = -8 which makes [tex]g(x)=4[/tex]
Hence, the input value other than 7 for which [tex]g(x)=4[/tex] is x = -8.
The input value other than 7 for which g(x) = 4 is x = -8.
It is given that the value of the graph when the input 7 is g(x)=4
We need to determine the value of x when g(x)=4
Value of x when g(x)=4:
The value of x can be determined by using the graph.
This can be determined by finding the point at which the line meets the point y = 4, we can find the corresponding x - value.
From the graph, we get that the graph of g(x) passes through the point (x = -8, y = 4),
Thus, from the graph, it is obvious that the graph also meets the point y = 4 when x = -8.
Then indeed, the input value (x) other than 7 for which g(x) = 4 is x = -8.
As, the function g(x) takes the value of 4 at x = -8, according to the graph.
Therefore, the input value is x = -8 which makes g(x) = 4.
Hence, the input value other than 7 for which g(x) = 4 is x = -8.
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Jayden school is selling tickets to play on the first day of ticket sales to school sold six adult tickets and 12 child tickets for a total of $252 the school took 243 on the second day by selling 14 adult tickets and five child tickets what is the price of one adult ticket and one child ticket
Answer:
iihiuhihiuiu
Step-by-step explanation:
ioiiuouioiiouuioooooooooooooooooooooiuuguygy
Ed genuity
Triangle A B C is shown. Angle A C B is a right angle, angle C A B is 60 degrees, and angle A B C is 30 degrees. The length of the hypotenuse is 10. What are the lengths of the other two sides of the triangle? AC = 5 and BC = 5 AC = 5 and BC = 5 StartRoot 5 EndRoot AC = 5 StartRoot 3 EndRoot and BC = 5 AC = 5 and BC = 5 StartRoot 3 EndRoot
Hope This Helps! :)
Explanation:
The measure of the two sides of the triangle are 5√3 & 5 units respectively.
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: A triangle ABC with angle as C as a right angle and the hypotenuse is equal to 10
Let the perpendicular and the base of the triangle is p and b respectively.
Thus
Sin 60=p/10
p=10×√3/2
p=5√3
Also, Cos 60=b/10
b=10×1/2
b=5
Hence, The measure of the two sides of the triangle are 5√3 & 5 units respectively.
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Find: 0.15 cents of $2 dollars
Answer:
12
Step-by-step explanation:
what is the unit rate of 49 points in 7 games
Answer:
7
Step-by-step explanation:
49÷7
Brian is buying T-shirts for the marching band. He knows that at parades the band forms 24 rows. Each row has 13 students. If T-shirts come in boxes of 100, how many boxes of T-shirts should Brian buy?
Answer:
4 boxes (Brainliest Please)
Step-by-step explanation:
You have to find the amount of students
24 X 13 = 312
You have to get enough for everybody so you need 400 shirts so that everyone can get one.
400 / 100
4 boxes
cos72cos130+sin72sin130
Answer:
.5299192646
Step-by-step explanation:
Just plug it in a calculator
A line passes through the point (-8, 8) and has a slope of 5/2.
Write an equation in point-slope form for this line.
Answer:
y=5/2x + 8
Step-by-step explanation: Y=mx+b is the equation for slope intercept form. Basically you just have to plug in the numbers.
What is the input value for which
f(x)=−3
Answer:
Every value of x.
Step-by-step explanation:
The function is a zero-order polynomial, whose value remains constant for all value of x.
M varies inversely as the square of P. If M is 9 when P is 2, then find M when P is 3.
please h e l p
Answer:
Step-by-step explanation:
If two quantities are inversely proportional, it means that an increase in the value of one variable would cause a corresponding decrease in the other variable and vice versa.
Given that M varies inversely as the square of P, if we introduce a constant of proportionality, k, the expression becomes
M = k/P²
If M = 9 when P = 2, then
9 = k/2² = k/4
k = 9 × 4 = 36
Therefore, the inverse variation equation is
M = 36/P²
When P = 3,
M = 36/3² = 36/9
M = 4
For every 140 feet that Kelly rides on her bicycle, the wheels turn 20 times. About how many times do the wheels turn in 5 miles? (1 mile = 5,280 feet) Round your answer to the nearest whole number.
Answer: The wheels turn about 3771 times in 5 miles.
Step-by-step explanation:
Given, Kelly rides on her bicycle such that the number of times wheels turn for every 140 feet = 20
Turns for every feet = [tex]\dfrac{20}{140}=\dfrac{1}{7}[/tex] ...(i)
To find : Number of times wheels turn in 5 miles.
Since , 1 mile = 5,280 feet
Then, 5 miles = 5 x (5,280 feet) = 26,400 feet
Now , Number of times the wheels turn in 26,400 feet = 26400 x (Turns for every feet)
[tex]26400\times\dfrac{1}{7}=3771.42857143\approx3771[/tex] [From (i)
Hence, the wheels turn about 3771 times in 5 miles.
The three lines represent the number of hot dogs eaten by three contestants at a hot dog eating competition. Which contestant was eating at the slowest rate?
Answer:
Contestent K
Step-by-step explanation:
The contestant who was eating at the slowest rate will be in line K.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The three lines represent the number of hot dogs eaten by three contestants at a hot dog eating competition.
The diagram is shown below.
From the diagram, we can observe that for the same run, the rise of line K will be the least.
The contestant who was eating at the slowest rate will be in line K.
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Please help! Will give brainliest!
Answer:
The answer to your question is 365040000 lb or 3.65 x 10⁸ lb
Step-by-step explanation:
Data
Rectangular pyramid
base = 100 yd x 78 yd
height = 100 yd
weight of a stone = 468 lb/yd³
Process
1.- Calculate the volume of the pyramid
Volume = area of the base x height
-Substitution
Volume = 100 x 78 x 100
-Simplification
Volume = 780000 yd³
2.- Calculate the weight of the pyramid
468 lb ------------------------ 1 yd³
x ------------------------780000 yd³
x = (780000 x 468) / 1
x = 365040000 lb or 3.65 x 10⁸ lb
Where does photosynthesis take place
Answer:chloroplast
Step-by-step explanation:It’s takes place inside plant cells in small things called “chloroplast”
Garrett's family is going to relax at the beach all day! In preparation, Garrett made s
sandwiches for them to eat when they get hungry. Garrett put 3 slices of turkey and 3 slices
of ham on each sandwich.
Pick all the expressions that represent how many slices of meat Garrett used on the
sandwiches.
6s
3 + 3 + S
9s
3s + 3s
Answer:
6s
3s + 3s
Step-by-step explanation:
simplify 3^5 x 3^4
A: 3^9
B: 6^9
C: 3 x 20
D: 3^20
Answer:
3^9
Step-by-step explanation:
when multiplying and the bases are the same number simply add the exponents ex: a^b x a^c = a^b+c
The angle \theta_1θ 1 theta, start subscript, 1, end subscript is located in Quadrant \text{I}Istart text, I, end text, and \cos(\theta_1)=\dfrac{10}{17}cos(θ 1 )= 17 10 cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 10, divided by, 17, end fraction . What is the value of \sin(\theta_1)sin(θ 1 )sin
Answer:
sin ( θ ) = 3√21 / 17
Step-by-step explanation:
Given:-
- The angle (θ) lies in the first quadrant. Where theta is defined as:
cos ( θ ) = 10 / 17
Find:-
- Find sin ( θ ) :
Solution:-
- We will draw a right angle triangle in the first quadrant. With base, B = 10 and hypotenuse H = 17. Since,
cos ( θ ) = B / H = 10 / 17
- Using pythagorean theorem determine the perpendicular side length:
H^2 - B^2 = P^2
17^2 - 10^2 = P^2
√189 = P
P = 3√21
- Now evaluate sin ( θ ):
sin ( θ ) = P / H
sin ( θ ) = 3√21 / 17
Answer:
√111 / 20
Step-by-step explanation:
In order for you to answer the following question correctly, please use the images down below:
Complete the two-column proof of the Segments of Chords Theorem.
Please correct me for any of the answers I got wrong.
AEC is congruent to DEB should be the answer for 5.
ALSO...
You're proving that EB * EA = EC * ED, so the 7th blank should be "EB * EA = EC * ED"
Otherwise, everything else is good.
The area of a square equals the square of a length of the side of the square. The perimeter of a square equals the sum of the lengths of all four sides. The sum of the areas of two squares is 65, while the difference in their areas is 33. Find the sum of their perimeters.
We can call the areas of the squares x and y. x+y=65 and x-y=33.
x would have an area of 49 and y has an area of 16.
Each side of x would be 7 and each side of y would be 4.
A regular octagon has an apothem of 11.6 inches and a perimeter of 87.2 inches. What is the area of the octagon
Answer:
The area of the octagon is 505.76 [tex]inches^{2}[/tex]
Step-by-step explanation:
In this question, we are tasked with calculating the area of an octagon given the values of the apothem and the perimeter
Mathematically, the area can be calculated using the formula below;
Area = 1/2 × apothem × perimeter
where according to the question, the apothem = 11.6 inches and the perimeter = 87.2 inches
Plugging these value into the equation given above, we have
Area = 1/2 × 11.6 × 87.2 = 505.76 [tex]inches^{2}[/tex]
A triangle has one angle that measures 31 degrees, one angle that measures 46 degrees, and one angle that measures 103 degrees. A.
equilateral triangle
B.
scalene triangle
C.
right triangle
D.
isosceles triangle
what is 3.61 in radical form
An online shoe store is having a sale. The original price of each pair of shoes is p dollars. The store sells 15 pairs of shoes and earns a total of (15p−30) dollars.
The factored expression is 15(p - 2) . The discount per pair of shoe is $2
Using the expression given:
15p - 30Factorize :
The greatest common factor of 15 and 30 is 15
15(p - 2)Hence, the factored expression Using GCF is 15(p - 2)
b.)
The discount on the purchase is the constant value:
Total discount = 30Number of shoes = 15
Discount per pair = Total discount/ Number of shoe pairs
Discount per pair of shoes = 30/15 = $2
Therefore, the discount on each pair of shoes is $2
Complete Question:
An online shoe store is having a sale. The original price of each pair of shoes is p dollars. The store sells 15 pairs of shoes and earns a total of (15p−30) dollars. a. Factor the expression using the GCF.
15p−30=
b. The discount per pair of shoes is $