A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 100 cm wide at the top, and has height 60 cm. If the trough is being filled with water at the rate of 0.1 m3/min, how fast (in m/min) is the water level rising when the water is 10 cm deep

Answers

Answer 1

Answer:

0.238 m/min

Explanation:

The volume of water in the trough V =Ah' where A = area of cross-section = area of isosceles trapezoid = 1/2(a + b)h where a = length of bottom of isosceles trapezoid = 40 cm = 0.4 m, b =  length of top of isosceles trapezoid = 100 cm = 1 m and h = height of isosceles trapezoid = 60 cm = 0.6 m. So,

A = 1/2(a + b)h = 1/2(0.4 m + 1 m)0.6 m = (1.4 m)0.3 m = 0.42 m² and h' = height of water level in trough = H - h" where H = length of trough = 10 m and h" = depth of water level in trough = 10 cm = 0.1 m

So, V = Ah'

V = A(H - h") = A(10 - h")

Now, the rate of change of volume of the trough with respect to time dV/dt = d[A(10 - h")]/dt

dV/dt = -Adh"/dt

dh"/dt = -dV/dt/A

Since dV/dt = 0.1 m³/min, substituting the other variables into the equation, we have

dh"/dt = -dV/dt/A

dh"/dt = -0.1 m³/min/0.42 m²

dh"/dt = -0.238 m/min

This is the rate at which the depth is decreasing

Since the height h' = 10 - h"

dh'/dt = d(10 - h")/dt

= -dh"/dt

= -(-0.238 m/min)

= 0.238 m/min

So the water level is increasing at a rate of 0.238 m/min


Related Questions

• What value is used to identify each element in the periodic table?​

Answers

Answer:

protons

Explanation:


Give the relationship between the number of valence electrons in an atom's
valence electron shell and the position of the element on the Periodic Table​

Answers

Answer:

they're reactions

Explanation:

The relationship between the valence electrons and position is: the number of valence electrons determines the position

What is valence electron?

This is the number of electrons in the outermost shell of an atom.

NOTE: The outermost shell is called valence shell

Position in Periodic table

This is where an element is located in the periodic table

Relationship between valence electrons and position

The position of an element in the periodic table is determined by the number of valence electrons.

For example

Sodium, Na (atomic number of 11) has the following electronic configuration

1st shell = 2 electrons2nd shell = 8 electrons 3rd (valence) shell = 1 electron

Since the valence electron is 1, thus, sodium is located in group 1 of the periodic table.

Thus, we can see that the position of an element in the periodic table is related to the valence electron(s) in the atomic shell of the element.

Learn more about valence electron:

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1.A body of mass 10kg falling freely was found to be falling at a rat of 20m/s what force will stop the body in 2second?​

Answers

Answer:

50N

Explanation:

force it is falling with can be found by mass into acceleration and then devide by half to find force that could stop it in 2 sec

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Answers

I’m sorry I can’t understand

Please Help!!!

For A&B

Answers

Answer:

A. 40N

B. 5m/s

Explanation:

A.

Impulse is equal to the area under the curve of a force vs. time graph. In this case, the area is in the shape of a triangle with base 8 (12-4=8) and perpendicular height 10:

Area of a triangle = (1/2)bh

A=(1/2)*8*10

=40

ANSWER: 40N

B.

Impulse = mass * velocity

40 = 8v

v = 5

ANSWER: 5m/s

A 1.50x103-kilogram car is traveling east at 30 meters per second.
The brakes are applied and the car is brought to rest in 9.00 seconds.
A. Calculate the magnitude of the total impulse applied to the car to
bring it to rest. [Show all work, including the equation and
substitution with units.]
B. State the direction of the impulse applied to the car. [East or
West?]


PLEASE HELP!!!!

Answers

Answer:

[tex]39000\ \text{kg m/s}[/tex]

West

Explanation:

m = Mass of car = [tex]1.3\times 10^{3}\ \text{kg}[/tex]

t = Time = 9 seconds

u = Initial velocity = 30 m/s

v = Final velocity = 0

Impulse is given by

[tex]J=m(v-u)\\\Rightarrow J=1.3\times 10^3(0-30)\\\Rightarrow J=-39000\ \text{kg m/s}[/tex]

The magnitude of the total impulse applied to the car to bring it to rest is [tex]39000\ \text{kg m/s}[/tex].

The direction is towards west as the sign is negative.

Select the correct answer.
Which of the following best describes an intermediate runner?

A. Able to alternate running 2 minutes, walking 1 minute

B. Able to run a mile without stopping

C. Able to run at least 30 minutes, 3-5 times a week

D. Able to run 1 mile in 10 minutes or less

Answers

I would say answer D

A is very easy, so that's off the table, while be is a little too advanced for intermediate, and C is way to advanced for intermediate.

So yeah, D

It would probably be D

1. You are given a bottle that contains 4.59 cm of a metallic solid. The total mass of the bottle
is 35.66 g. The empty bottle weighs 14.23 g. What is the density of the solid?​

Answers

26.3g hcvovvyvubbihihhijiubvuvuvyvyv

An object is placed 250 cm in front of a concave circular mirror, and the image of the object also appears at 250 cm in front of the mirror. What is the radius of curvature of the mirror?
500 cm
125 cm
25.0 cm
250 cm

Answers

Answer:

Radius of curvature of the mirror = 250 cm

Explanation:

Given:

Object distance from mirror = 250 cm (u=-250)

Object distance appears in mirror = 250 cm (v=-250)

Find:

Radius of curvature of the mirror

Computation:

Using mirror formula

1/f = 1/v + 1/u

1/f = 1/(-250) + 1/(-250)

f = (-250/2)

f = -125 cm or 125 cm

Radius of curvature of the mirror = 2(f)

Radius of curvature of the mirror = 2(125)

Radius of curvature of the mirror = 250 cm

Philosophy: The Big Picture Unit 8

Would an existentialist argue that the study of philosophy was a good use of a life?

A. Yes, if society valued the results of the study.
B. Yes, but only if the individual found it meaningful.
C. No, a life should be spent minimizing the role of anxiety.
D. No, there is no way that philosophy could create a meaningful life.

Answers

the answer to this would be C

HELP PLZZZZZ
Vitiligo is an example of a condition that comes from
A. your habits
B. your predisposed genetics
C. your social network
D. your physical environment

Answers

B. your predisposed genetics

Answer:

the answer is b vitiligo is a genetic skin condition

1. An atom that loses electrons has a ________________________ charge and an atom that gains
electrons has a ___________________________ charge.
Charged atoms are called ___________________.
2. What is an insulator? Give 4 examples.
3. What is a conductor? Give an example.
4. How can we move electrons from one place to another? What actually causes the electrons to
move?
5. Static electricity is ______________________________________________________________________
_______________________________________________________________________________________
6. Explain the attraction and repulsion of charges.
7. Why does a balloon stick to the wall?
8. Why does your hair stand up when you take off your hat?
9. Why do you get a shock when you walk across a carpet?
10. When is static electricity most noticeable and why?
11. State the Principle of Conservation of Charge.

12. The invisible electric force field around charged objects depends on __________________________,
__________________________, and _____________________________.
13. What is the relationship between the charges and the field strength?
What is the relationship between the field strength and the distance between the charges?
1. What is DC?
What is AC?
2. Name 3 ways to get DC.
3. What is an electrical circuit?
4. What is voltage?
What is current?
What is resistance?
What causes heat and light in a wire?
COPY THE TABLE comparing water in a hose-DC-units
5. Which electricity do we use in our homes?
CLICK ON ALTERNATING CURRENT
1. Explain AC.
2. Who invented the light bulb?
3. Who really invented AC?
4. Who discovered the advantages of AC over DC?
5. How is AC made?
6. What is the main advantage of AC over DC?

Answers

1-positive charge
negative charge
ions
2- insulator through which current cant flow easily (rubber wood)
3-conductor through which current can easily flow

: A small block with mass 0.130 kg is attached to a string passing through a hole in a frictionless, horizontal surface. The block is originally revolving in a circle with a radius of 0.800 m about the hole with a tangential speed of 4.00 m/s. The string is then pulled slowly from below, shortening the radius of the circle in which the block revolves. The breaking strength of the string is 30.0 N. What is the radius of the circle when the string breaks

Answers

Answer:

r = 0.0173 m = 1.73 cm

Explanation:

Here, the centripetal force of the block will be providing the required breaking tension in the string:

[tex]Tension = Centripetal Force\\T = F_c\\\\T = \frac{mv^2}{r} \\\\r = \frac{mv^2}{T}\\[/tex]

where,

r = radius = ?

m = mass of block = 0.13 kg

v = tangential spee of block = 4 m/s

T = Breaking Strength = 30 N

Therefore,

[tex]r = \frac{(0.13\ kg)(4\ m/s)^2}{30\ N}[/tex]

r = 0.0173 m = 1.73 cm

When finding the radius of the string at the point it breaks, the tangential

velocity is assumed to be constant.

The radius when the string breaks is [tex]\underline{6.9 . \overline 3 \times 10^{-3}} \ m[/tex]

Reasons:

The mass of the small block, m = 0.130 kg

Initial radius of the circle of rotation = 0.800 m

Tangential velocity, v = 4.00 m/s

The radius of the path of rotation is reduced as the string is pulled

Breaking strength of the string = 30.0 N

Required:

The radius of the circle when the string brakes

Solution:

[tex]Centripetal \ force = \dfrac{m \cdot v^2}{r}[/tex]

Where;

r = The radius of the circle of rotation

When the string brakes, w have;

Centripetal force = Breaking strength of the string = 30.0 N

Which gives;

[tex]\displaystyle r = \mathbf{\dfrac{m \cdot v^2}{Centrifugal \ force}} = \frac{0.130 \times 4^2}{30} =6.9\overline 3 \times 10^{-2}[/tex]

The radius of the circle when, the string breaks r = [tex]\underline{6.9\overline 3 \times 10^{-2}} \ m[/tex]

Learn more here:

https://brainly.com/question/20905151

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Answers

Answer:

so you have a question

Explanation:

either way,you have a nice day

A house is lifted from its foundations onto a truck for relocation. The house is pulled upward by a net force of 2850 N. This force causes the house to move from rest to an upward speed of 15 cm/s in 5.0 s. What is the mass of the house?​

Answers

Answer:

m = 95000 kg

Explanation:

Given that,

Net force acting on the house, F = 2850 N

Initial speed, u = 0

Final speed, v = 15 cm/s = 0.15 m/s

We need to find the mass of the house. Let the mass be m. We know that the net force is given by :

F = ma

Where

a is the acceleration of the house.

So,

[tex]F=m\dfrac{v-u}{t}\\\\m=\dfrac{Ft}{(v-u)}\\\\m=\dfrac{2850\times 5}{(0.15-0)}\\\\m=95000\ kg[/tex]

So, the mass of the house is equal to 95000 kg.

A wave has a frequency of 30Hz and wave length of 40cm. What is the velocity of the wave?

Answers

Answer:

12m/s

Explanation:

v=fλ

30×(40÷100)=

12m/s

A woman has one damaged fallopian tube. The damage completely blocks the opening of the tube at the ovary. How will this most likely affect her fertility?
Her likelihood of conceiving will be reduced by at least 50%.
Her eggs, if fertilized, will not implant properly.
Her eggs will not mature inside the ovary.
Her chances of conceiving twins will be doubled.

Answers

Answer:Her likelihood of conceiving will be reduced by at least 50%.

Explanation:

EDGE 2020

Answer:

Her likelihood of conceiving will be reduced by at least 50%

Explanation:

took the test on edge, got it right

Which list of elements is placed in order from most reactive to least reactive?
A. K, Ca, Kr, Ge
B. K, Ca, Ge, Kr
C. Ca, K, Kr, Ge
D. Ge, Kr, Ca, K

Answers

All four elements given in the answer choices are on the same period. The least reactive element should be Kr, since it is a noble gas. By that fact alone, B would be the correct answer.

B is also correct as non-d-block metals increase in reactivity from left to right on along a period. The order of the metals (Ge is often considered a metalloid) conforms with that trend.

What are the issues that hinders efforts to achieve sustainability?

Answers

Answer:

who will solve environmental problems, who is responsible for environmental problems, and who pays the cost of implementing solutions

Explanation:

Before we make measurements, let's make sure we understand the circuit. 1. Select all of the following that correctly describe what a volt meter and ammeter measure. Select all that apply: A volt meter measures the potential difference (or voltage) across a circuit element. A volt meter measures the potential difference (or voltage) passing through a circuit element. A ammeter measures the electric current passing through a circuit element. A ammeter measures the electric current across a circuit element.

Answers

Answer:

the correct answers are a and c

Explanation:

In an electrical circuit there are two important quantities to measure, such as voltage and current.

Voltage is the potential difference between two points in a circuit

current is the number of electrons you pass through a given point per unit of time.

Now let's analyze each answer

a) true. The potential difference across an element

b) False. The potential difference is u field there is no physical entity that moves

c) True. The current is electrons in motion and these pass through the given element

d) False. There is a physical quantity that passes through the point

the correct answers are a and c

What could we call the
grocery store?
A. Linear motion
B. Reference point
C. Rotary

Answers

Reference point

Explanation:

I am not sure

In which region is there most likely to be a volcano?
A, African plate
B, north american plate
C, south America plate,
D, Pacific plate ​

Answers

Answer:

D. Pacific plate

Explanation:

took the quiz

What keeps the Earth's atmosphere from floating away? Earth's gravity keeps the air molecules of the atmosphere from escaping the area surround Earth The attraction between the different molecules of atmospheric gases The temperature of the gas is not high enough to allow it to spread out and escape the area surrounding Earth The differentiation between temperatures of the Earth and outer space traps the gases in the atmosphere

Answers

Answer: it is the earth gravity :’)

Explanation:

Earth's gravity keeps the air molecules of the atmosphere from escaping the area surround Earth

Question 1 of 10 Which characteristic of nuclear fission makes it hazardous?
O A. The process destroys every atomic nucleus that goes through it.
O B. The process changes existing atoms into atoms of different elements
C. The process requires very high pressures.
O D. The radioactive wastes it produces can spread to any part of the environment

Answers

Answer:

D.

The radioactive wastes it produces can spread to any part of the environment.

Explanation:

Fission is the name given to the splitting of a heavy nucleus into two medium-mass nuclei. Fission is said to be induced if it results from the absorption of a neutron to form an unstable nucleus that decays by fission. The induced fission usually produces further neutrons accompanying the fission fragments.

Answer:  D. The radioactive wastes it produces can spread to any part of the environment

Explanation:

Why do astronomers use frequencies other than the visible ones when they are
investigating the universe?

Answers

Because not all of the universe can be seen with a visible spectrum

One of the scientists suggests that he can build a
cooling system for the theoretical photovoltaic cells
Experiment 2, which will keep the cells 1°C cooler
dan normal but decrease their efficiency by 1%. The
teoretical photovoltaic cells capturing which frequency
ranges
, if any, would benefit from this cooling system?

Answers

Answer: SORRY

SORRY AM DOING IT FOR POINTS

Explanation:

1 kg block slides down a frictionless inclined plane that makes an angle of 300 with respect to the ground. The total length of the plane is 2 m, but midway down it collides with a second block, weighing 0.5 kg. The two blocks stick together and travel as one unit the rest of the way down the ramp. What is the kinetic energy of the combined 1.5 kg block when it reaches the bottom of the plane

Answers

Answer:

the kinetic energy of the combined 1.5 kg block when it reaches the bottom of the plane is 10.62 J

Explanation:

Given that the data in the question;

angle of inclination with respect to the ground [tex]\theta[/tex] = 30°

length of plane d = 2m

m₁ = 1 kg

m₂ = 0.5 kg

now, velocity of the first block at midpoint;

[tex]\frac{1}{2}[/tex]mv² = mgsin[tex]\theta[/tex][tex]\frac{d}{2}[/tex]

[tex]\frac{1}{2}[/tex]v² = gsin[tex]\theta[/tex][tex]\frac{d}{2}[/tex]

v² = gsin[tex]\theta[/tex]d

v = √( gsin[tex]\theta[/tex]d)

g is 9.8 m/s

so we substitute

v = √( 9.8 × sin30° × 2)

v = √( 19.6 )

v =  3.13 m/s

Now, velocity just after collision of the blocks will be;

(m₁ + m₂)v₂ = m₁v

v₂ = m₁v / (m₁ + m₂)

we substitute

v₂ = (1 × 3.13) / (1 + 0.5)

v₂ = 3.13 / 1.5

v₂ = 2.0866 m/s

now, final kinetic energy will be;

[tex]KE_f[/tex] = (m₁ + m₂)gsin[tex]\theta[/tex][tex]\frac{d}{2}[/tex] + Initial Kinetic energy

[tex]KE_f[/tex] = (m₁ + m₂)gsin[tex]\theta[/tex][tex]\frac{d}{2}[/tex] + [tex]\frac{1}{2}[/tex]mv₂²

we substitute

[tex]KE_f[/tex] = [(1 + 0.5)9.8 × sin30 × [tex]\frac{2}{2}[/tex]] + [[tex]\frac{1}{2}[/tex] × 1.5 × 2.0866 ]

[tex]KE_f[/tex] = 7.35 + 3.2654

[tex]KE_f[/tex] = 10.62 J

Therefore, the kinetic energy of the combined 1.5 kg block when it reaches the bottom of the plane is 10.62 J

The magnetic field due to a utility wire is 0.10 mT when you are at a distance of 10 meters from it. What current (in Amperes) flows through the wire?

Answers

Answer:

I = 5000 A

Explanation:

We will use Ampere's Law to calculate the current:

[tex]B = \frac{\mu I}{2\pi r}\\\\[/tex]

where,

B = Magnetic Field Strength = 0.1 mT = 1 x 10⁻⁴ T

μ = Permeability of Free Space = 4π x 10⁻⁷ N/A²

I = Current = ?

r = radius = 10 m

Therefore,

[tex]1\ x\ 10^{-4}\ T = \frac{(4\pi\ x\ 10^{-7}\ N/A^2)(I)}{2\pi(10\ m)}\\\\I = \frac{(1\ x\ 10^{-4}\ T)(2\pi (10\ m))}{4\pi\ x\ 10^{-7}\ N/A^2}[/tex]

I = 5000 A

A 5kg block rests on a 30° incline. The coefficient of static friction between the block and the incline is 0.20. How large a horizontal force must push on the block if the block is to be on the verge of sliding. a) up the incline, b) down the incline ? ​

Answers

Answer:

Hope It Help

Explanation:

That's all I know

PLEASE HELP

name 4 fundamentally different options for cooking a chicken​

Answers

Answer:

roasting,

broiling,

pan-broiling,

pan-frying,

grilling.

Explanation:

good luck

Answer:

Explanation:

1. Stir frying

2. Pan frying

3. Grilling /BBQ

4. Baking/roasting

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