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8_murik_8 [283]

2 years ago

15

A 2 feet piece of wire is cut into two pieces and once a piece is bent into a square and the other is bent into an equilateral t

riangle. Where should the wire cut so that the total enclosed area by both shapes is at the maximum?

1 answer:

SpyIntel [72]2 years ago

3 0

Answer:

Explanation:

Let x ft be used to make square and 2-x ft be used to make equilateral triangle.

each side of square = x/4

area of square = ( x /4 )²

Each side of triangle

= (2-x) /3

Area of triangle = 1/2 (2-x)²/9 sin 60

= √3 / 36 x (2-x)²

Total area

A = ( x /4 )² +√3 / 36 (2-x)²

For maximum area

dA/dx = 0

1/16( 2x ) -√3 / 36 x2(2-x) = 0

x / 8 - √3(2-x)/ 18 = 0

x / 8 - √3/9 + √3/18 x = 0

x ( 1/8 + √3/18 ) = √3/9

x(.125 +.096 ) = .192

x = .868 ft

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A water pipe tapers down from an initial radius of R1 = 0.21 m to a final radius of R2 = 0.11 m. The water flows at a velocity v

Aleks [24]

Answer:

$0.116 m^3/s$

Explanation:

The volume flow rate of a fluid in a pipe is given by:

$Q=Av$

where

A is the cross-sectional area of the pipe

v is the speed of the fluid

In this problem, at the initial point we have

v = 0.84 m/s is the speed of the water

r = 0.21 m is the radius of the pipe, so the cross-sectional area is

$A=\pi r^2 = \pi (0.21 m)^2 =0.138 m^2$

So, the volume flow rate is

$Q=(0.138 m^2)(0.84 m/s)=0.116 m^3/s$

8 0

3 years ago

Calculate the mass of -1.5C of electrons

algol13

The electron is a type of low-mass, very negatively charged with a particle. As such, it can easily be deflected by passing close to other electrons or the positive nucleus of an atom. m = mass of an electron in kg = 9.10938356 × 10-31 kilograms. e = magnitude of the charge of an electron in coulombs = 1.602 x 10-19 coulombs. Hope this helps!

8 0

2 years ago

An air balloon is moving upward at a constant speed of 3 m/s. Suddenly a passenger realizes that she left her camera on the grou

frosja888 [35]

Answer:t=0.3253 s

Explanation:

Given

speed of balloon is $u=3\ m/s$

speed of camera $u_1=20\ m/s$

Initial separation between camera and balloon is $d_o=5\ m$

Suppose after t sec of throw camera reach balloon then,

distance travel by balloon is

$s=ut$

$s=3\times t$

and distance travel by camera to reach balloon is

$s_1=ut+\frac{1}{2}at^2$

$s_1=20\times t-\frac{1}{2}gt^2$

Now

$\Rightarrow s_1=5+s$

$\Rightarrow 20\times t-\frac{1}{2}gt^2 =5+3t$

$\Rightarrow 5t^2-17t+5=0$

$\Rightarrow t=\dfrac{17\pm \sqrt{17^2-4(5)(5)}}{2\times 5}$

$\Rightarrow t=\dfrac{17\pm 13.747}{10}$

$\Rightarrow t=0.3253\ s\ \text{and}\ t=3.07\ s$

There are two times when camera reaches the same level as balloon and the smaller time is associated with with the first one .

(b)When passenger catches the camera time is $t=0.3253\ s$

velocity is given by

$v=u+at$

$v=20-10\times 0.3253$

$v=16.747\ m/s$

and position of camera is same as of balloon so

Position is $=5+3\times 0.3253$

$=5.975\approx 6\ m$

8 0

3 years ago

The conservation of energy principle applies to a. all systems. b. open systems. c. closed systems. d. Ideal gas systems.

Ainat [17]

Answer:closed systems

Explanation:

A closed system is one in which matter does not enter or leave the system but there is exchange of energy between the system and its environment. In a closed system, the principle of energy conservation applies. The principle of energy conservation states that energy can neither be created nor destroyed but is converted from one form to another. An example of a closed system is a reaction vessel whose lid is closed.

5 0

3 years ago

Read 2 more answers

SI UNIT OF GRAVITY is the

pickupchik [31]

Answer:

G

Explanation:

4 0

2 years ago