What is the value of arctan 0.866?

A 30-N stone is dropped from a height of 10 m and strikes the ground with a speed of 13 m/s.

Anon25 [30]

Answer:

4.1 N

Step-by-step explanation:

We can solve this problem by using considerations about energy.

At the moment the stone is dropped, it has only gravitational potential energy:

$PE=mgh$

where

$mg=30 N$ is the weight of the stone

h = 10 m is the initial height of the stone

As the stone falls, part of this energy is converted into kinetic energy, while part into thermal energy due to the presence of the air friction, acting opposite to the motion of the stone:

$KE+E_t = \frac{1}{2}mv^2 + E_t$

where:

$m=\frac{mg}{g}=\frac{30}{9.8}=3.06 kg$ is the mass

v = 13 m/s is the final speed of the stone

$E_t$ is the thermal energy

The thermal energy is actually equal to the work done by the air friction on the stone:

$E_t=W=Fh$

where

F is the average force of friction

h = 10 m

Since the total energy must be conserved, we can combine the three equations, so we find:

$mgh=\frac{1}{2}mv^2+Fh$

And solving for F, we find the average force of air friction:

$F=\frac{mgh-0.5mv^2}{h}=\frac{(30)(10)-0.5(3.06)(13)^2}{10}=4.1 N$

3 0

2 years ago

Evaluate the line integral, where c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)

Arada [10]

The value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)

<h3>What is integration?</h3>

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

The parametric equations for the line segment from (0, 0, 0) to (2, 3, 4)

x(t) = (1-t)0 + t×2 = 2t

y(t) = (1-t)0 + t×3 = 3t

z(t) = (1-t)0 + t×4 = 4t

Finding its derivative;

x'(t) = 2

y'(t) = 3

z'(t) = 4

The line integral is given by:

$\rm \int\limits_C {xe^{yz}} \, ds = \int\limits^1_0 {2te^{12t^2}} \, \sqrt{2^2+3^2+4^2} dt$

$\rm ds = \sqrt{2^2+3^2+4^2} dt$

After solving the integration over the limit 0 to 1, we will get;

$\rm \int\limits_C {xe^{yz}} \, ds = \dfrac{\sqrt{29}}{12} (e^{12}-1)$ or

= 73037.99 ≈ 73038

Thus, the value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)

Learn more about integration here:

brainly.com/question/18125359

#SPJ4

7 0

1 year ago

Help on this one please

kvv77 [185]

Answer:

d ≈ 1732 ft

Step-by-step explanation:

Angle of elevation = Angle of depression

Following this truth,

m∠PAQ (Angle of depression) = m∠APB (Angle of elevation) = 30°

By applying tangent rule in the given triangle ABP,

tan(30°) = $\frac{AB}{PB}$

$\frac{1}{\sqrt{3}}=\frac{1000}{d}$

d = 1000√3

d = 1732.05

d ≈ 1732 ft

6 0

2 years ago

Graph the solution set. please help

Ratling [72]

Answer:

In the attachment.

Step-by-step explanation:

Rewrite $x\geq-3y-6$ as a $y\geq -\frac{1}{3}x-2$ . Then mark each set with different color and take the intersection of these.

7 0

2 years ago

Consider the function f(x)= 2/5x-4

Gre4nikov [31]

Answer: a) $\frac{5}{2}x+10=f^{-1}(x)=g(x)$

Step-by-step explanation:

Since we have given that

$f(x)=\frac{2}{5}x-4$

a.) Find the inverse of f(x) and name it g(x).

Let f(x) = y

So, it becomes

$y=\frac{2}{5}x-4$

Switching x to y , we get

$x=\frac{2}{5}y-4$

$5x=2y-20\\\\5x+20=2y\\\\\frac{5x+20}{2}=y\\\\\frac{5}{2}x+10=y\\\\\frac{5}{2}x+10=f^{-1}(x)=g(x)$

b) . Use composition to show that f(x) and g(x) are inverses of each other.

$\mathrm{For}\:f=\frac{2}{5}x-4\:\\\\\mathrm{substitute}\:x\:\mathrm{with}\:g\left(x\right)=\frac{5}{2}x+10\\\\=\frac{2}{5}\left(\frac{5}{2}x+10\right)-4\\\\=x$

Similarly,

$\mathrm{g\left(x\right)=\frac{5}{2}x+10,\:f\left(x\right)=\frac{2}{5}x-4,\:g\left(x\right)\circ \:f\left(x\right)}\\\\\mathrm{For}\:g=\frac{5}{2}x+10\:\mathrm{substitute}\:x\:\mathrm{with}\:f\left(x\right)=\frac{2}{5}x-4\\\\=\frac{5}{2}\left(\frac{2}{5}x-4\right)+10\\\\=x$

so, both are inverses of each other.

c) Draw the graphs of f(x) and g(x) on the same coordinate plane.

As shown below in the graph , Since for inverse function we need an axis of symmetry i.e. y=x

And both f(x) and g(x) are symmetry to y=x.

∴ f(x) and g(x) are inverses of each other.

5 0

3 years ago

What is the value of arctan 0.866?​

What is the value of arctan 0.866?