Help Please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The table below shows all of the possible outcomes for rolling two six-sided number cubes.

Mice21 [21]

C. 1/4

There is a table with 36 possible outcomes. 9 of them are desired outcomes because they have an even number rolled first and then an odd number rolled second (a few random examples from the table would be 2,1, 2,3, 4,1, 4,5, 6,3 etc.)

All we have to do is make a fraction of the desired outcomes over the total number of possible outcomes. 9/36. That can be simplified into 1/4 and <em>voilà</em>, there is your answer.

Hope this helped ッ

3 0

3 years ago

Read 2 more answers

In a given right triangle, If 0 º < x < 90 º and cos x = √ 3 / 2, then sin x = ?

nordsb [41]

Answer:

1/2

Step-by-step explanation:

The "Pythagorean relation" between trig functions can be used to find the sine.

<h3>Pythagorean relation</h3>

The relation between sine and cosine is the identity ...

sin(x)² +cos(x)² = 1

This can be solved for sin(x) in terms of cos(x):

sin(x) = √(1 -cos(x)²)

<h3>Application</h3>

For the present case, using the given cosine value, we find ...

sin(x) = √(1 -(√3/2)²) = √(1 -3/4) = √(1/4)

sin(x) = 1/2

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<em>Additional comment</em>

The sine and cosine of an angle are the y and x coordinates (respectively) of the corresponding point on the unit circle. The right triangle with these legs will satisfy the Pythagorean theorem with ...

sin(x)² + cos(x)² = 1 . . . . . . where 1 is the hypotenuse (radius of unit circle)

A calculator can always be used to verify the result.

6 0

1 year ago

How exactly do you do this because my teacher didn't teach me how

mylen [45]

The area is found by base x height

To find the missing height in the first one you divide 147 by 15 3/4 and get 9 1/3.
To find the missing base in the second one you divide 140 5/8 by 11 1/4 and get 12 1/2.
To find the missing height in the third one you divide 151 3/16 by 10 1/4 and get 14 3/4.

Make me brainliest ! :)

6 0

3 years ago

Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation

Gemiola [76]

To find:

(a) Equation for the sphere of radius 5 centered at the origin in cylindrical coordinates

(b) Equation for a cylinder of radius 1 centered at the origin and running parallel to the z-axis in spherical coordinates

Solution:

(a) The equation of a sphere with center at (a, b, c) & having a radius 'p' is given in cartesian coordinates as:

$(x-a)^{2}+(y-b)^{2}+(z-c)^{2}=p^{2}$

Here, it is given that the center of the sphere is at origin, i.e., at (0,0,0) & radius of the sphere is 5. That is, here we have,

$a=b=c=0,p=5$

That is, the equation of the sphere in cartesian coordinates is,

$(x-0)^{2}+(y-0)^{2}+(z-0)^{2}=5^{2}$

$\Rightarrow x^{2}+y^{2}+z^{2}=25$

Now, the cylindrical coordinate system is represented by $(r, \theta,z)$

The relation between cartesian and cylindrical coordinates is given by,

$x=rcos\theta,y=rsin\theta,z=z$

$r^{2}=x^{2}+y^{2},tan\theta=\frac{y}{x},z=z$

Thus, the obtained equation of the sphere in cartesian coordinates can be rewritten in cylindrical coordinates as,

$r^{2}+z^{2}=25$

This is the required equation of the given sphere in cylindrical coordinates.

(b) A cylinder is defined by the circle that gives the top and bottom faces or alternatively, the cross section, & it's axis. A cylinder running parallel to the z-axis has an axis that is parallel to the z-axis. The equation of such a cylinder is given by the equation of the circle of cross-section with the assumption that a point in 3 dimension lying on the cylinder has 'x' & 'y' values satisfying the equation of the circle & that 'z' can be any value.

That is, in cartesian coordinates, the equation of a cylinder running parallel to the z-axis having radius 'p' with center at (a, b) is given by,

$(x-a)^{2}+(y-b)^{2}=p^{2}$

Here, it is given that the center is at origin & radius is 1. That is, here, we have, $a=b=0,p=1$ . Then the equation of the cylinder in cartesian coordinates is,

$x^{2}+y^{2}=1$

Now, the spherical coordinate system is represented by $(\rho,\theta,\phi)$

The relation between cartesian and spherical coordinates is given by,

$x=\rho sin\phi cos\theta,y=\rho sin\phi sin\theta, z= \rho cos\phi$

Thus, the equation of the cylinder can be rewritten in spherical coordinates as,

$(\rho sin\phi cos\theta)^{2}+(\rho sin\phi sin\theta)^{2}=1$

$\Rightarrow \rho^{2} sin^{2}\phi cos^{2}\theta+\rho^{2} sin^{2}\phi sin^{2}\theta=1$

$\Rightarrow \rho^{2} sin^{2}\phi (cos^{2}\theta+sin^{2}\theta)=1$

$\Rightarrow \rho^{2} sin^{2}\phi=1$ (As $sin^{2}\theta+cos^{2}\theta=1$ )

Note that $\rho$ represents the distance of a point from the origin, which is always positive. $\phi$ represents the angle made by the line segment joining the point with z-axis. The range of $\phi$ is given as $0\leq \phi\leq \pi$ . We know that in this range the sine function is positive. Thus, we can say that $sin\phi$ is always positive.