MATHEMATICS COLLEGE

A cube-shaped water tank having 6 ft side lengths is being filled with water. The bottom is solid metal but the sides of the tank are thin glass which can only withstand a maximum force of 200 lb. How high (in ft) can the water reach before the sides shatter?(Assume a density of water rho = 62.4 lb/ft3.
Round your answer to two decimal places.)

Answers

Answer 1

Answer:

The distance the in which the water will reach before it shatters will be 1.03ft

Data;

Let the integral run from surface (y = 0) to maximum depth (y = d)ft
Let the differential depth = dydt
The area of each depth = 6dy ft^2

The Force Acting at any Depth

Using integration, the force at any depth y is 62.4y lb/ft^3

$200 = \int\limits^d_0 {62.4y} \, 6dy\n 200 = \int\limits^d_0 {374.4y} \, dy\n 200 = \int\limits^6_0 {374.4y} \, dy\n 200 = [374.4/2 y^2]_0^d\n200 = 187.2(d^2 - 0)\n200 = 187.2d^2\nd^2 = 200/187.2\nd = 1.03ft$

From the calculations above, the distance in which the water will reach before it shatters is 1.03ft

Learn more on force acting at any depth;

brainly.com/question/2936875

Related Questions

Find the distance between two points A (-2,-3) B (6,8)
Sleeping in college. A recent article in a college newspaper stated that college students get an average of 5.5 hrs of sleep each night. A student who was skeptical about this value decided to conduct a survey by randomly sampling 25 students. On average, the sampled students slept 6.25 hours per night. Identify which value represents the sample mean and which value represents the claimed population mean.
Use the technique developed in this section to solve the minimization problem. Minimize C = −3x − 2y − z subject to −x + 2y − z ≤ 20 x − 2y + 2z ≤ 25 2x + 4y − 3z ≤ 30 x ≥ 0, y ≥ 0, z ≥ 0 The minimum is C = at (x, y, z) = .
Let n = 5.What is the value of the expression 9n2−2−n? Enter your answer in the box.
Suppose Jesse won five bags of eight goldfish use math you know to represent the problem and find the number of goldfish Jesse won

The function f(x,y,z)equals2 x plus z squared has an absolute maximum value and absolute minimum value subject to the constraint x squared plus 2 y squared plus 3 z squaredequals16. Use Lagrange multipliers to find these values.

Answers

Answer:

Absolute maxima an minma both occured at $(25)/(3)$ .

Step-by-step explanation:

Given function is,

$f(x,y,z)=2x+z^2\hfill (1)$

subject to,

$x^2+2y^2+3z^2=16\hfill (2)$

Let $g(x,y,z)=x^2+2y^2=3z^2-16$

To find absolute maxima and absolute minima using Lagranges multipliers method consider $\lambda$ as the multipliers such that,

$\nabla f=\lambda \nabla g$

$\leftrightarrow (2, 0 ,2z )=\lambda (2x, 4y, 6z)$

on compairing both side we get,

$2z=6\lambda z\implies \lambda=(1)/(3)$

$4\labda y=0\implies y=0$

$2=2\lambda x\implies x=(1)/(\lambda)=3$

From (2),

$x^2+2y^2+3z^2=16$

$\implies 9+0+3z^2=16$

$\implies z=\pm\sqrt{(7)/(3)}$

Absolute maxima, at x=3, y=0, $z= \sqrt{(7)/(3)}$ is,

$|f(x,y,z)|_(max)=(2x+z^2)_(3,0,\sqrt{(7)/(3)})=(2*3)+(7)/(3)=(25)/(3)$

Absolute minima, at x=3, y=0, $z= -\sqrt{(7)/(3)}$ is,

$|f(x,y,z)|_(max)=(2x+z^2)_(3,0,-\sqrt{(7)/(3)})=(2*3)+(7)/(3)=(25)/(3)$

Hence the result.

Consider the optimization problem where A m × n , m ≥ n , and b m . a. Show that the objective function for this problem is a quadratic function, and write down the gradient and Hessian of this quadratic.

b. Write down the fixed-step-size gradient algorithm for solving this optimization problem.

c. Suppose that Find the largest range of values for α such that the algorithm in part b converges to the solution of the problem.

Answers

Answer:

Answer for the question :

Consider the optimization problem where A m × n , m ≥ n , and b m .

a. Show that the objective function for this problem is a quadratic function, and write down the gradient and Hessian of this quadratic.

b. Write down the fixed-step-size gradient algorithm for solving this optimization problem.

c. Suppose that Find the largest range of values for α such that the algorithm in part b converges to the solution of the problem.

is explained din the attachment.

Step-by-step explanation:

Li enters a competition to guess how many jelly beans are in a jar.Li’s guess is 345 jelly beans.
The actual number of jelly beans is 300.

What is the percent error of Li’s guess?

Answers

Answer:

Step-by-step explanation:

345-300 X 100 = 15%

300

Answer:

Percent error =

15%

Li’s guess was off by

15%.

Step-by-step explanation:

TTM </3

Which inequalities are equivalent to r + 45 < 16? Check all that apply.r + 45 < 16 - 45
r + 45 – 16 < 16 – 16
r + 45 + 3 < 16 + 3
r + 45 - 16 < 16
r + 45 - 45 < 16 - 45

Answers

Answer

Which inequalities are equivalent to r + 45 < 16? Check all that apply.

✅r + 45 – 16 < 16 – 16

✅ r + 45 + 3 < 16 + 3

✅r + 45 - 45 < 16 - 45

the last option I'm thinking, hope this helps

Length 21cm area 315cm2 find the breath

Answers

___________________________________

Symbols of:

$\quad\quad\quad\quad\tt{A = A rea}$

$\quad\quad\quad\quad\tt{ l = length}$

$\quad\quad\quad\quad\tt{ b \: = breadth}$

Given that:

$\quad\quad\quad\quad\tt{A = 315 {cm}^(2) }$

$\quad\quad\quad\quad\tt{l = 21cm}$

$\quad\quad\quad\quad\tt{b = \: ? }$

Formula for breadth (b):

$\quad\quad\quad\quad\tt{breadth = (Area)/(length) }$

Solution:

$\quad\quad\quad\quad\tt{b = \frac{315 {cm}^(2) }{21cm} }$

$\quad\quad\quad\tt{\:\:b = {15cm}}$

So, the breadth (b) is:

$\quad\quad\quad\quad\tt \boxed{ \boxed{ \color{magenta}{b = 15cm }}}$

___________________________________

#CarryOnLearning

✍︎ C.Rose❀

Answer:

Breadth = 15 cm

Step-by-step explanation:

Area = length x breadth

315 = 21 x breadth

$(315)/(21) = (21)/(21) * breadth$ [ dividing both sides by 21 ]

$15 = 1 * breadth\n\nbreadth = 15 \ cm$

a softball league has 13 teams, if every team must play every other team in the first round of league play, how many games must be scheduled

Answers

Answer:

78 games

Step-by-step explanation:

Think of it this way. Let's name the teams Team 1 through Team 13. Team 1 needs to have 12 games to play each other team. Once those are scheduled, Team 2 needs to have 11 games scheduled to play all the other teams (remember their game against Team 1 was already scheduled). Team 3 needs to have 10 games scheduled to play all the other teams (remember their games against Team 1 and Team 2 have already been scheduled). This patten continues until you schedule a single game between Team 12 and Team 13. So the total number of games that need to be scheduled are:

12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 78

I don't know if the concept of triangular numbers has been touched on in your class, but if so, there is a much simpler way to calculate this using the triangular number formula with n = 12. The formula is:

T = (n * (n + 1)) / 2

So in this case:

(12 * (12 + 1)) / 2 = (12 * 13) / 2 = 6 * 13 = 78

Other Questions

A stone which is dropped into a dry well hits the bottom in 2.2s how deep is the well. take g=10m/s

A goliath grouper at the local aquarium ate 112 fish over the course of 8 hours. At this rate how many fish can he eat in 3.5 hours

P (-5, -6), Q (-1, 2), R (4, 4)Scale factor = 2P' =Q' =R' =

An angelfish was 1 1/2 inches long when it was bought. Now it is 2 1/3 inches long.a. How much has the angelfish grown? b. An inch is 1/12 of a foot. How much has the angelfish grown in feet? 40 points!