The centre of the circumstancribing circle of a triangle can be found by using the

A force is specified by the vector F= 160i + 80j + 120k N. Calculate the angles made by F with the positive x-, y-, and z-axis.

Rashid [163]

Answer:

1) Angle with x-axis = 42.03 degrees

2) Angle with y-axis =68.2 degrees

3) Angle with z-axis = 56.14 degrees

Explanation:

given any vector $\overrightarrow{r}=x\widehat{i}+y\widehat{j}+z\widehat{k}$

and any x axis the angle between them is given by

$\theta_x =cos^{-1}(\frac{\overrightarrow{r}\cdot\widehat{i}}{\sqrt{x^2+y^2+z^2}} )\\\\\theta_x=cos^{-1}(\frac{x\cdot i}{\sqrt{x^2+y^2+z^2}} )$

Applying values we get

$\theta_x=cos^{-1}(\frac{160}{\sqrt{160^2+80^2+120^2}} )=42.03^{o}$

Angle between the vector and y axis is given by

$\theta_y =cos^{-1}(\frac{\overrightarrow{r}\cdot\widehat{j}}{\sqrt{x^2+y^2+z^2}} )\\\\\theta_y=cos^{-1}(\frac{y\cdot j}{\sqrt{x^2+y^2+z^2}} )$

Applying values we get

$\theta_x=cos^{-1}(\frac{80}{\sqrt{160^2+80^2+120^2}} )=68.2^{o}$

Similarly angle between z axis and the vector is given by

$\theta_z =cos^{-1}(\frac{\overrightarrow{r}\cdot\widehat{k}}{\sqrt{x^2+y^2+z^2}} )\\\\\theta_x=cos^{-1}(\frac{z\cdot k}{\sqrt{x^2+y^2+z^2}} )$

Applying values we get

$\theta_z=cos^{-1}(\frac{120}{\sqrt{160^2+80^2+120^2}} )=56.145^{o}$

5 0

4 years ago

You're about to make a measurement with an oscilloscope when you find that the trace appears to be very weak on the screen. Whic

Kisachek [45]

Answer:

C. The intensity control

Explanation:

The focus adjust the sharpness of the trace. The Intensity knob adjusts the brightness of the trace by adjusting the potential of a grid controlling number of electrons reaching the screen. The level control varies the voltage required to generate a trigger. Slope control determines whether the trigger point is on the rising or the falling edge of a signal.

The correct option is therefore the intensity control.

5 0

4 years ago

Read 2 more answers

If a bearing needs 4. 0 s to solidify enough for impact, how high must the tower be?.

maks197457 [2]

The height of the tower is equal to 78.4 meters.
The bearing's impact velocity is equal to 39.2 m/s.

<h3>How to determine the height of the tower?</h3>

In order to determine the height of the tower, we would apply the second equation of motion and assume that the downward motion is negative.

Mathematically, the second equation of motion is given by this formula:

S = ut + ½gt²

Where:

S represents the distance or height.
u represents the initial velocity.
a represents the acceleration.
t represents the time.

Substituting the given parameters into the formula, we have;

S = S₀ + ut - ½gt²

0 = S₀ + (0)4.0 - ½ × (9.8) × 4.0²

0 = S₀ - 4.9 × 16.0

Height, S₀ = 78.4 meters.

<h3>How to calculate the bearing's impact velocity?</h3>

In order to calculate the bearing's impact velocity, we would apply the first equation of motion:

V = u - at

V = 0 - 9.8(4.0)

Impact velocity, V = 39.2 m/s.

Read more on velocity here: brainly.com/question/19365526

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Complete Question:

Ball bearings can be made by letting spherical drops of molten metal fall inside a tall tower, called a shot tower, and solidify as they fall.

a. If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be?

b. What is the bearing's impact velocity?

6 0

1 year ago

A 20 mm diameter rod made of ductile material with a yield strength of 350 MN/m2 is subjected to a torque of 100 N.m, and a bend

vodka [1.7K]

Answer:

a) 42.422 KN

b) 44.356 KN

Explanation:

Given data :

Diameter = 20 mm

yield strength = 350 MN/m^2

Torque ( T ) = 100 N.m

Bending moment = 150 N.m

<u>Determine the value of the applied axial tensile force when yielding of rod occurs </u>

first we will calculate the shear stress and normal stress

shear stress ( г ) = Tr / J = [( 100 * 10^3) * 10 ] / $\pi /32$ * ( 20)^4

= 63.662 MPa

Normal stress( Гb + Гa ) = MY/ I + P/A

= [( 150 * 10^3) * 10 ] / $\pi /32$ * ( 20)^4 + 4P / $\pi * 20^2$

= 190.9859 + 4P / $\pi * 20^2$ MPa

<u>a) Using MSS theory </u>

value of axial force = 42.422 KN

solution attached below

<u>b) Using MDE theory </u>

value of axial force = 44.356 KN

solution attached below

5 0

3 years ago

Hydrogen enters the turbine of an Ericsson cycle at 1040 K, 5 bar with a mass flow rate of 1 kg/s. At the inlet to the compresso

andrew11 [14]

Answer:

a)

Calculate the net power developed by using

the following relation:

Wste=W-W.

Substitute 8728 kw for w, and 2846 kw for w..

Wyle=8728 - 2846

= 5882 kW

Therefore, the net power developed is 5882 kW).

Comment

Step 6 of 7 A

Calculate the thermal efficiency by using the

following relation:

Here, e, is the heat input.

Substitute w, for ..

w

Substitute s882 kw for ws and 8728 kw for w.

5882

1-8728

67.39%

Therefore, the thermal efficiency is 67.39%).

Comments (3)

Step 7 of 7 A

Calculate the back work ratio.

bwr =

Substitute 8728 kw for w, and 2846 kw for w..

bwr - 2846

bwr=8728

=0.326

Therefore, the back work ratio is 10.326).

Explanation:

7 0

3 years ago