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olya-2409 [2.1K]
2 years ago
14

An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquariu

m. (Use 9.8 m/s2 for g and the fact that the density of water is1000 kg/m3.)Show how to approximate the required work by a Riemann sum. (Let x be the height in meters below the top of the tank. Enter xi* as xi.)lim n ? ?
Mathematics
1 answer:
loris [4]2 years ago
6 0

Answer:

Workdone = 2450Joules

Step-by-step explanation:

Let the top of the aquarium be at height 0.

Let the bottom of the aquarium be at height 1

F = mg = 2p◇x × g

F= 2000◇x × 9.8

F = 19600◇x

Workdone = 19600xdx

Total workdone = Integral (limits 0.5 -0)19600×dx

Total work = [9800x^2]^0.5

Total work= 9800× 0.5^2 = 2450 Joules

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Rebekah put the bottom of a 12 foot ladder 5 feet from the side of a house what is the distance form the bottom of the house to
monitta

Answer:

13

Step-by-step explanation:

12^2 + 5^2 = c^2

144 + 25 = c^2

169 = c^2

13 = c

7 0
2 years ago
Write the recurring decimal 0.4 as a fraction in its simplest form.
Ugo [173]

Answer:

2/5

Step-by-step explanation:

0.4 = 4/10 which in simplest form is 2/5

8 0
2 years ago
Read 2 more answers
I'm horrible at this so can I please get help, the rest says "solve for a. a=
Inessa05 [86]

Answer:

a = \sqrt{63}

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

a² + 9² = 12²

a² + 81 = 144 ( subtract 81 from both sides )

a² = 63 ( take square root of both sides )

a = \sqrt{63}

8 0
2 years ago
The area of a rectangular piece of cardboard is represented by
Liula [17]

This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.

Area of a rectangle:

The area of rectangle of length l and width w is given by:

A = wl

w(2w + 3) = 9

From this, we get that:

l = 2w + 3, A = 9

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}

x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}

\Delta = b^{2} - 4ac

In this question:

w(2w+3) = 9

2w^2 + 3w - 9 = 0

Thus a quadratic equation with a = 2, b = 3, c = -9

Then

\Delta = 3^2 - 4(2)(-9) = 81

w_{1} = \frac{-3 + \sqrt{81}}{2*2} = 1.5

w_{2} = \frac{-3 - \sqrt{81}}{2*2} = -3

Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.

Another similar problem can be found at brainly.com/question/16995958

5 0
2 years ago
How many 12th are in 3 and describe situation
Mashutka [201]

Answer:

1) 36

2) My mom was trying to quiz me and she told me to pick a fraction and a number. I picked 1/12 and 3, she then told me to figure out how many 12ths there are in 3 which I found was 36.

Step-by-step explanation:

3 * 12 = 36

6 0
2 years ago
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