Un tanque cilíndrico vertical tiene en su base un agujero de 3 cm de radio. El radio del tanque es de 30 cm. Si el agua escapa del tanque con una velocidad dada por la formula:
V^(2 )=2gh
Donde h es la profundidad del agua y g la aceleración de la gravedad (g = 981 cm/s). Calcular la rapidez de variación de la velocidad.
Answers
Answer:
La razón de cambio de la velocidad del chorro es de aproximadamente 0.022 metros por segundo cuadrado.
Step-by-step explanation:
Tenemos que la velocidad del chorro de agua que escapa del tanque cilíndrico vertical (\(v\)), medida en metros por segundo, está descrita por la siguiente fórmula:
\(v =\sqrt{2\cdot g\cdot h}\) (1)
Donde:
\(g\) - Aceleración gravitacional, medida en metros por segundo al cuadrado.
\(h\) - Profundidad del agua en el cilindro, medida en metros.
Si la aceleración gravitacional es constante, entonces la razón de cambio de la velocidad del chorro es definida por la siguiente fórmula, la cual se obtenida por derivación implícita:
\(\dot v = \left(\frac{\sqrt{2\cdot g }}{2\sqrt{2\cdot g\cdot h}}\right)\cdot \dot h\)
\(\dot v = \frac{\dot h}{2\sqrt{h}}\) (2)
Donde:
\(\dot h\) - Razón de cambio de la profundidad del tanque del agua, medida en metros por segundo.
\(\dot v\) - Razón del cambio de la velocidad del chorro, medida en metros por segundo al cuadrado.
Ahora, por el Principio de Conservación de la masa y considerando que el agua es un fluido incompresible, tenemos que el flujo volumétrico asociado a la razón de cambio de la profundidad de agua es igual al flujo volumétrico del chorro de agua, es decir:
\(\pi\cdot R^{2} \cdot \dot h = \pi\cdot r^{2} \cdot v\) (3)
Donde:
\(R\) - Radio del tanque cilíndrico vertical, medido en metros.
\(r\) - Radio del agujero, medido en metros.
Despejamos la razón de cambio de la profundidad del tanque del agua:
\(\dot h = \left(\frac{r}{R} \right)^{2}\cdot v\)
Aplicando la ecuación anterior a (2), tenemos que:
\(\dot v = \left(\frac{1}{2\sqrt{h}}\right)\cdot \left(\frac{r}{R} \right)^{2} \cdot v\)
Finalmente tenemos por (1) que:
\(\dot v = \left(\frac{1}{2\sqrt{h}} \right)\cdot \left(\frac{r}{R} \right)^{2}\cdot \sqrt{2\cdot g \cdot h}\)
\(\dot v = \frac{\sqrt{2\cdot g}}{2}\cdot \left(\frac{r}{R} \right)^{2}\)
Lo cual significa que la razón de cambio de la velocidad de chorro es independiente de la profundidad del agua en el tanque. Si tenemos que \(g = 9.807\,\frac{m}{s^{2}}\), \(r = 3\,cm\) y \(R = 30\,cm\), entonces la razón de cambio es:
\(\dot v = \frac{\sqrt{2\cdot \left(9.807\,\frac{m}{s^{2}} \right)}}{2}\cdot \left(\frac{3\,cm}{30\,cm} \right)^{2}\)
\(\dot v \approx 0.022\,\frac{m}{s^{2}}\)
La razón de cambio de la velocidad del chorro es de aproximadamente 0.022 metros por segundo cuadrado.
Related Questions
0.5+(-1.5)-(-5.5) Show how to perform the operations using the number line.
Answers
Jessica has a four-sided die, a six-sided die, and a 12-sided die. She rolls the three dice once. Let Z be the number of fours showing. Find E[Z] using the indicator method.
Answers
Answer:
The value of E [Z] is 0.50.
Step-by-step explanation:
The expected value is computed using the formula:
\(E(X)=\sum x\cdot P(X= x)\)
Denote the three dices as follows:
X₁ = a four-sided die
X₂ = a six-sided die
X₃ = a 12-sided die
Define the indicator variables as follows:
\(I_{1}=\left \{ {{1;\ X_{1}=4} \atop {0;\ X_{1}\neq 4}} \right. \\\\I_{2}=\left \{ {{1;\ X_{2}=4} \atop {0;\ X_{2}\neq 4}} \right. \\\\I_{3}=\left \{ {{1;\ X_{3}=4} \atop {0;\ X_{3}\neq 4}} \right.\)
The probability of rolling a 4 in the three dices are as follows:
\(P(X_{1}=4)=\frac{1}{4}\\\\P(X_{2}=4)=\frac{1}{6}\\\\P(X_{3}=4)=\frac{1}{12}\)
Compute the value of E [Z] as follows:
\(E(Z)=E(I_{1})+E(I_{2})+E(I_{3})\)
\(=(1\times\frac{1}{4})+(1\times\frac{1}{6})+(1\times\frac{1}{12})\\\\=\frac{3+2+1}{12}\\\\=\frac{6}{12}\\\\=\frac{1}{2}\\\\=0.50\)
Thus, the value of E [Z] is 0.50.
Mr. Gupta gave his students a quiz with three questions on it. Let
�
XX represent the number of questions that a randomly chosen student answered correctly. Here is the probability distribution of
�
XX along with summary statistics:
�
=
# correct
X=# correctX, equals, start text, \#, space, c, o, r, r, e, c, t, end text
0
00
1
11
2
22
3
33
�
(
�
)
P(X)P, left parenthesis, X, right parenthesis
0.05
0.050, point, 05
0.20
0.200, point, 20
0.50
0.500, point, 50
0.25
0.250, point, 25
Mean:
�
�
=
1.95
μ
X
=1.95mu, start subscript, X, end subscript, equals, 1, point, 95
Standard deviation:
�
�
≈
0.8
σ
X
≈0.8sigma, start subscript, X, end subscript, approximately equals, 0, point, 8
Mr. Gupta decides to score the tests by giving
10
1010 points for each correct question. He also plans to give every student
5
55 additional bonus points. Let
�
YY represent a random student's score.
What are the mean and standard deviation of
�
YY?
Answers
The mean score of a random student (YY) is 574.5. the standard deviation of the random student's score (YY) is 8.
How to answer the aforementioned questionGiven:
- Each correct question is worth 10 points.
- Every student receives an additional 555 bonus points.
Let's calculate the mean and standard deviation of YY:
Mean of YY:
The mean score, denoted as μY, can be calculated using the mean of XX (μX) and the scoring scheme:
μY = μX * 10 + 555
Substituting the value of μX from the given information:
μY = 1.95 * 10 + 555
μY = 19.5 + 555
μY = 574.5
Therefore, the mean score of a random student (YY) is 574.5.
Standard Deviation of YY:
The standard deviation of YY, denoted as σY, can be calculated using the standard deviation of XX (σX) and the scoring scheme:
σY = σX * 10
Substituting the value of σX from the given information:
σY = 0.8 * 10
σY = 8
Therefore, the standard deviation of the random student's score (YY) is 8.
Complete question: Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions
that a randomly chosen student answered correctly. Here is the probability distribution of X along with
summary statistics:
0
1
2
2.
3
X = # correct
P(X)
0.05
0.20
0.50
0.25
Mean: Hex = 1.95
Standard deviation: Ox 0.8
Mr. Gupta decides to score the tests by giving 10 points for each correct question. He also plans to give
every student 5 additional bonus points. Let Y represent a random student's score.
What are the mean and standard deviation of Y?
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29/24 as a decimal rounded to the nearest hundredth
Answers
Answer: 1.21
Step-by-step explanation:
Some help with this pleaseee!
Answers
Answer:
g(x) = |x| + 7
Step-by-step explanation:
Adding the constant +7 on the end of the equation means a translation 7 units up.
Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 618 randomly selected adults showed that 59% of them would erase all of their personal information online if they could. Find the value of the test statistic.
Answers
The value of the test statistic is given as follows:
z = 4.47.
How to obtain the test statistic?The equation to calculate the test statistic using the z-distribution is given as follows:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
In which:
\(\overline{p}\) is the sample proportion.p is the expected value.n is the sample size.The parameters for this problem are given as follows:
\(\overline{p} = 0.59, p = 0.5, n = 618\)
p = 0.5 as the most term means that we are testing if the proportion is either less than or greater than 0.5.
Then the test statistic is obtained as follows:
\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)
\(z = \frac{0.59 - 0.5}{\sqrt{\frac{0.5(0.5)}{618}}}\)
z = 4.47.
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The July bank statement sent by the bank to ABC company shows a balance of cash on deposit at July 31 of Br.4,964.47 Assume that on July 31, assume the on July 31, ABCs ledger shows a bank balance of Br. 4 173. 83. 1. A deposit of Br 410. 90 made after banking hours and doesnt appear in the bank statement2. A check drawn for Br. 79 had been erroneously charged by the bank Br.973. For checks issued in July have not yet been paid by the bank (outstanding checks). : Theses checks are;- Check No date amount 801 June 15 ---Br.100,00 888 July 24 ----Br. 10.25 890 July 27--- Br. 294.50 891 July 30 ---Br. 205.004. A check written for birr 210 had been incorrectly charged by the bank as birr 120 5. Proceeds from collection of a interest bearing note receivable from David. ABC Company had left this note with the banks collection department. The face amount of the note was birr 500 6. Br. 24.75 interest earned on average account balance during July7. A check for Br. 10 returned with the statement had been recorded in the check register as Br. 100. The check was for the payment of an obligation to Davis Equipment Company for the purchase of office supplies on account 8. Br. 5,00 fee charged by bank for handling collection of note receivable 9. Br. 50.25 check from customer John deposited by ABC company charged bank as Non sufficient fund (NSF) 10. Br. 12.70 service charged by bank for the month of July. 11. Check number 875 was issued July 20 in the amount of Br 85 but was erroneously recorded in the cash payment Journal as Br 58 for payment of telephone expense prepare bank reconcilation and journal entry?
Answers
After making all the necessary adjustments, the reconciled bank balance for ABC Company's ledger at the end of July is Br. 4,164.42.
To reconcile the bank statement balance with the company's ledger balance for ABC Company, we need to go through the provided information step by step and make the necessary adjustments. Let's calculate the adjusted bank balance:
Starting with the bank statement balance: Br. 4,964.47
Add the deposit made after banking hours: + Br. 410.90
New bank balance: Br. 5,375.37
Now let's make adjustments for the outstanding checks and other transactions:
Deduct the erroneously charged check: - Br. 973
New bank balance: Br. 4,402.37
Deduct the outstanding checks:
Check No. 801: Br. 100.00
Check No. 888: Br. 10.25
Check No. 890: Br. 294.50
Check No. 891: Br. 205.00
Total deduction: Br. 609.75
New bank balance: Br. 3,792.62
Correct the incorrectly charged check: + Br. 90
New bank balance: Br. 3,882.62
Add the proceeds from the collection of the interest-bearing note: + Br. 500.00
New bank balance: Br. 4,382.62
Add the interest earned on the average account balance: + Br. 24.75
New bank balance: Br. 4,407.37
Deduct the incorrectly recorded check: - Br. 90
New bank balance: Br. 4,317.37
Deduct the fee charged for handling the collection of the note: - Br. 5.00
New bank balance: Br. 4,312.37
Deduct the check returned due to insufficient funds: - Br. 50.25
New bank balance: Br. 4,262.12
Deduct the service charge for the month of July: - Br. 12.70
New bank balance: Br. 4,249.42
Deduct the erroneously recorded check: - Br. 85.00
New bank balance: Br. 4,164.42
Now, we compare the adjusted bank balance (Br. 4,164.42) with the ledger balance provided (Br. 4,173.83).
Adjusted bank balance: Br. 4,164.42
Ledger balance: Br. 4,173.83
The difference between the adjusted bank balance and the ledger balance is Br. 9.41. This difference is likely due to some unrecorded transactions or errors in recording. To reconcile the balances fully, further investigation is required to identify the specific cause of the discrepancy and make the necessary adjustments in the company's ledger.
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Given AC=DF,BC=DE
Prove AB=EF
Answers
Answer:
Hope this helps
Step-by-step explanation:
AC=DF
AB+BC=DE+EF
*BC=DE*
AB+DE=DE+EF
AB=EF
AB = EF can be proved by using the following from the given figure:
- AB + BC = AC
- DE + EF = DF
- AC = DF
- BC = DE
Given,
AC = DF
BC = DE
We need to prove AB = EF.
What does it mean to have a point between two points in a line?If there is a point in between two points of a line:
M________N______________0
MN + N0 = MO
We have,
A_________B______C
D____E___________F
Now,
Putting the condition of a point between two points.
We get,
AC = AB + BC _____(1)
DF = DE + EF ______(2)
Prove AB = EF.
From (1) and (2)
AC = AB + BC _____(1)
DF = DE + EF ______(2)
And,
AC = DF ______(3)
This means (1) = (2)
AB + BC = DE + EF ______(4)
BC = DE ______(5)
From (5), (4) can be written as:
AB + BC = BC + EF ______(6a)
or
AB + DE = DE + EF _____(6b)
Cancel out the common from both sides.
We get,
AB = EF
Thus using the equation (1), (2), (3), (4), and (5) we can prove AB = EF.
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A square garden has a length of (x+3) ft and a width of (x+2) ft. what is the perimeter and area of the garden?
Answers
Answer:
Perimeter:\(4x+10\) feet
Area:\(x^{2}+5x+6\) feet
Step-by-step explanation:
The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=\(x^{2}+2x+3x+6=x^{2}+5x+6\)
In a box of stones, the ratio of red marbles to total marbles is 2:5. The ratio of green stones to total stones is 3:10. If the stones that are neither red nor green are blue, how many blue stones are in the box if there are 40 marbles in the box?
Answers
Answer:
12 blue stones
Steps:
40/5 = 8
8 x 2 = 16 red stones
40/10 = 4
4 x 3 = 12 green stones
40 - (12 + 16) = 12 blue stones
hope this helps!
Name the solid figure formed by the net.
1
A Cube
B Cuboid
c Cylinder
D
Cone
Answers
how to find x in a algebra problem
Answers
1. do the opposite sign of wtv is being added or subtracted since ur goal is to get x by itself on 1 side.
2. once uve subtracted/added take that number and divide it by the number ur x is with. for example, if ur number is 4x u would divide by 4
3. bring down ur x since the numbers cancel out and wtv number u get from dividing is ur answer
Kelly makes fruit juice each morning. She uses 2 1/3 pints of strawberries and 1 2/5 pins of grapes in her juice how many more pints of strawberries than pints of grapes does she use?
Answers
Consider the curve given by the equation x2 − y2 = 2x + y + xy − 4. Find the equation
of the tangent line to the curve at the point (1, 1).
Answers
The equation of the tangent line at (1,1) is given as follows:
y - 1 = -0.25(x - 1).
How to obtain the equation of the tangent line?The curve for this problem is given as follows:
x² - y² = 2x + y + xy - 4.
Applying implicit differentiation, we obtain the slope of the tangent line, as follows:
2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y
(dy/dx)(1 + x + 2y) = 2x - 2 - y
m = (2x - 2 - y)/(1 + x + 2y).
At x = 1 and y = 1, the slope is given as follows:
m = (2 - 2 - 1)/(1 + 1 + 2)
m = -0.25.
Hence the point-slope equation is given as follows:
y - 1 = -0.25(x - 1).
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Factorise the expressions.
Answers
Answer:
Q.1 lx²+mx
=x(lx+m)
Q.2 x² - ax - bx + ab
= x(x - a) - b(x - a)
=(x - b)(x - a)
Q.3 6ab - b²+ 12ac - 2bc
= b(6a - b) - 2a(6a - b)
=(b - 2a)(6a - b)
Find the value of x and y.
3x=8-(2y)
Answers
Answer:
3x = 6y
Step-by-step explanation:
8 - 2y = 6y and 3x is by itself so it would be 3x is equal to 6y.
First one to answer gets BRAINLIEST no cap look at the picture.
Answers
Answer:460
Step-by-step explanation:
(-2x)^4 Simpify the number
Answers
Answer:
d
Step-by-step explanation:
i like ya cut g
100 POINTS
Find the error(s) and solve the
problem correctly in the picture below
Answers
Change the third line only .
<TFS\(\cong \)<PFQReason--(Opposite angles are same )Amd at 4th line
\(\\ \tt\Rrightarrow ∆TFS\cong∆PFQ(ASA)\)
ProvedQuestion 6 of 10 In order to solve the following system of equations by addition, which of the following could you do before adding the equations so that one variable will be eliminated when you add them? 2x - 4y = 5 6x - 3y=10 A. Multiply the top equation by -2. B. Multiply the top equation by -3 and the bottom equation by 2. C. Multiply the top equation by 3 and the bottom equation by 4. D. Multiply the top equation by -3. SUBMIT
???
Answers
Multiply the top equation by -3 and then adding both the equations one variable will be eliminated. So the correct answer is option D.
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
We are having two equations:-
2x - 4y = 5
6x - 3y=10
When we multiply the first equation by -3 the equation will become as follows:-
-6x + 12y = - 15
6x - 3y = 10
By adding both the equations one variable will be eliminated:-
9y = - 5
Therefore Multiply the top equation by -3 and then add both the equations one variable will be eliminated. So the correct answer is option D.
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Helppppopp!!!! I need this ASAP
Answers
Answer:
your smart enough
Step-by-step explanation:
Distribute and simplify the radicals below.
(√12+6)(-√8-√2)
O-18√2-6√√6
O-6√5-2√3
O-6√5+2√3
O 18√2+6√6
Answers
The simplified expression of (√12+6)(-√8-√2) is -6√6 - 18√2
How to simplify the radical?The expression is given as:
(√12+6)(-√8-√2)
Factor out -1
(√12+6)(-√8-√2) = -(√12+6)(√8+√2)
Expand the expression
(√12+6)(-√8-√2) = -(√96 + 6√8 + √24 + 6√2)
Evaluate the radicals
(√12+6)(-√8-√2) = -(4√6 + 12√2 + 2√6 + 6√2)
Evaluate the like terms
(√12+6)(-√8-√2) = -(6√6 + 18√2)
Open the bracket
(√12+6)(-√8-√2) = -6√6 - 18√2
Hence, the simplified expression of (√12+6)(-√8-√2) is -6√6 - 18√2
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Write an equation to represent the image.
Answers
Answer:
2y = 7
Step-by-step explanation:
The top rectangle has two pieces in it. Each one is a "y", so there are two y's...that's 2y. That top rectangle is the same size as the bottom rectangle. So the two rectangles are equal. The bottom rectangle is 7.
2y = 7
If you need to continue on and solve it:
2y = 7 Divide both sides by two.
y = 7/2 This is a perfectly good answer. Or y = 3.5
The answer to your question:
2y = 7
I need help asap please!!!
Answers
The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and
What is sine of angles?he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle. It is defined as the length of the opposite side divided by the length of the hypotenuse
The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360
2∅ 2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720
sin 2∅ = sin0 = 0; Sin90=1; sin180=0; sin240= -0.8660; sin270 = -1;
Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397
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Which of the following is a step in simplifying the expression
Answers
Answer:
option B
explanation:
\(\rightarrow \sf (\dfrac{xy^2}{x^{-3}y^3} )^{-4}\)
multiply powers: \(\bold{(a^b)^c = a^{bc}}\)
\(\rightarrow \sf \dfrac{x^{-4}y^{2*-4}}{x^{-3*-4}y^{3*-4}}\)
simplify the following
\(\rightarrow \sf \dfrac{x^{-4}y^{-8}}{x^{12}y^{-12}}\)
Complete the table by filling in the elapsed tine.
Help pls
Answers
Answer:
RADIUS
==================================
PROBLEM
Mary’s bicycle wheel has a circumference of 226.08 cm². What is its radius?
SOLUTION
We can solve this problem using the circumference formula in which π stands for ( 3.14 ), C stands for circumference itself and r stands for radius.
\bold{Formula \: || \: C = 2πr}Formula∣∣C=2πr
\tt{226.08 = 2(3.14) r}226.08=2(3.14)r
'Now to find the radius,Substitute 226.08 for c which is circumference in the formula.
\begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{C = 2πr} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{226.08 = 2(3.14)\red{r}} \\ \\ \: \: \: \: \: \: \: \: \large \tt{ \frac{226.08}{6.28} = \cancel\frac{6.28 \red{r}}{6.28} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt\green{C = 36}}\end{gathered}
C=2πr
226.08=2(3.14)r
6.28
226.08
=
6.28
6.28r
C=36
To check:
\begin{gathered} \small\begin{array}{|c|}\hline \bold{circumference }\\ \\ \tt{C = 2πr} \\ \tt{C = 2(3.14) (36\:cm) } \\ \tt{C = 2(113.04\:cm) } \\ \underline{\tt \green{C = 226.08\:cm }} \\ \hline \end{array} \end{gathered}
circumference
C=2πr
C=2(3.14)(36cm)
C=2(113.04cm)
C=226.08cm
FINAL ANSWER
If Mary's Bicycle has a circumference of 226.08 cm then the radius is 36.
\boxed{ \tt \red{r = 36}}
r=36
==================================
#CarryOnLearning
Answer:
1 = 0.56
2 = 0.43
3 = 0.55
4 = 0.49
5 = 0.70
Step-by-step explanation:
I not sure
WILL MAKE BRAINLIEST! ANSWER AND ILY
what are the slopes of each line?
Answers
Answer:
Top left is A
Top right is B
Bottom left is D
Bottom right is A
Step-by-step explanation:
7.) A. Undefined
8.) B. 0
9.) D. -1/2
10.) A. -2/5
I need help with both of these!
What is the part in the equation “45 is 15% of what number”?
Answers
Answer:
Step-by-step explanation:
help with both of these!
What is the part in the equation “45 is 15% of what number”?
Which measurements can create more than one triangle? three angles measuring 75 degrees, 45 degrees, and 60 degrees three sides measuring 7 m, 10 m, and 12 m three angles measuring 40 degrees, 50 degrees, and 60 degrees three sides measuring 3 cm, 4 cm, and 5 cm
Answers
We can see here that the measurements that can create more than one triangle is option A. The one that refers to the three angles measuring 75 degrees...
What is triangle?Triangles are known to be three-sided polygons having three vertices. It is one of the basic geometric forms. The name for a triangle with vertices A, B, and C is triangle ABC.
We must think about the triangle inequality theorem, which states that the total of the lengths of any two sides of a triangle must be greater than the length of the remaining side, to figure out which measurements can produce more than one triangle.
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What is the equivalent to the product below when x>_0?
√5x² •√15x²
Answers
√(5x²) • √(15x²) = √(5x² * 15x²)
Using the property of square roots that √(a * b) = √a * √b, we can simplify further:
√(5x² * 15x²) = √(5 * 15 * x² * x²)
Next, we simplify the numerical part:
√(5 * 15 * x² * x²) = √(75 * x² * x²)
Since x ≥ 0, x² is always non-negative, so we can remove the square root:
√(75 * x² * x²) = x * x * √75
Finally, we simplify the square root of 75:
x * x * √75 = x² * √75
Therefore, the equivalent expression is x² * √75 when x ≥ 0.