Situation 1:

A rectangular lamina of uniform density is situated with opposite corners at (0,0) and (15,4). calculate its radii of gyration a

Sphinxa [80]

First, you have to find the moment of inertia along the x and y axes. Constant density is denoted as k.

$I_{x}= \int\limits^15_0\int\limits^4_0 {k y^{2} } \, dx dy= \frac{1}{3}k (15-4)^4=4880.33k$

$I_{y}= \int\limits^15_0\int\limits^4_0 {k x^{2} } \, dx dy= \frac{1}{3}k (15-4)^4=4880.33k$

Then, the radii of gyration for

x = √[I_x/m]
y = [I_y/m]

where m = k(15-4)² = 121k. Then,

x = y = [4880.33k/121k] = 40.33

I hope I was able to help you. Have a good day.

7 0

3 years ago

Vector v is shown in the graph.

Elis [28]

Question 4

<h3>Answer: Choice D</h3>

Explanation:

If the initial point is the origin, the coordinates of the terminal point form the vector itself in component form. We go from (-8,6) to <-8,6>. The notation change is from ordered pair to vector format.

We have a right triangle with legs of 8 and 6 units. The pythagorean theorem will help us determine the hypotenuse is 10. Therefore, the vector length is 10 units and we would say ||v|| = 10. We have a 6-8-10 right triangle.

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Question 5

<h3>Answer: Choice B</h3>

Explanation:

Vector v starts at (2,5) and ends at (-3,-2).

The x component of the vector is x2-x1 = -3-2 = -5 meaning we move 5 units to the left when going from the start point to the endpoint.

At the same time we move 7 units down because y2-y1 = -2-5 = -7 which is the y component of the vector.

The component form of vector v is

v = <-5, -7>

it says "move 5 units left, 7 units down".

Apply the pythagorean theorem to find the length of the vector.

a^2+b^2 = c^2

c = sqrt(a^2 + b^2)

||v|| = sqrt( (-5)^2 + (-7)^2 )

||v|| = 8.602 which is approximate.

Now let's use the arctangent function to find the angle

theta = arctan(b/a)

theta = arctan(-7/(-5))

theta = 54.462 which is also approximate.

There's a problem however. This angle is in Q1 but the vector <-5,-7> is in Q3. An easy fix is to add on 180 to rotate to the proper quadrant.

54.462+180 = 234.462

which is the proper approximate angle for theta.

6 0

2 years ago

Aline segment may have more than one midpoint.<br> A. True<br> B. False

wel

Answer:

False

Step-by-step explanation:

Because it not possible

7 0

3 years ago

Read 2 more answers

(25 points)

Licemer1 [7]

Here, y = -15 with x = -20
LCM of 15 & 20 is 60, so divide 15 & 20 from 60,
60/15 = 4 & 60/20 = 3

Now, multiply the results with intial values,
4y = 3x
y = 3/4 x

When y = 12,
x = 12 * 4/3
x = 48 / 3
x = 16

In short, Your Answer would be 16

Hope this helps!

8 0

3 years ago

According to the rational root theorem, which of the following are possible

White raven [17]

Given:

The polynomial function is

$F(x)=4x^3-6x^2+9x+10$

To find:

The possible roots of the given polynomial using rational root theorem.

Solution:

According to the rational root theorem, all the rational roots and in the form of $\dfrac{p}{q}$ , where, p is a factor of constant and q is the factor of leading coefficient.

We have,

$F(x)=4x^3-6x^2+9x+10$

Here, the constant term is 10 and the leading coefficient is 4.

Factors of constant term 10 are ±1, ±2, ±5, ±10.

Factors of leading term 4 are ±1, ±2, ±4.

Using rational root theorem, the possible rational roots are

$x=\pm 1+,\pm 2, \pm 5, \pm 10,\pm \dfrac{1}{2}, \pm \dfrac{5}{2}, \dfrac{1}{4}, \pm \dfrac{5}{4}$

Therefore, the correct options are A, C, D, F.

7 0

3 years ago