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Nata [24]
3 years ago
14

Help pls. i’m taking a geometry quiz and don’t really understand

Mathematics
1 answer:
kramer3 years ago
5 0
Mw is 118 because a whole circle equals 360. you would do 360= 156+86+mw
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Kathy swam 3 laps in the pool this week. She must swim more than 12 laps.
Marysya12 [62]

Answer:10

Step-by-step explanation:

7 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.

Thus, we can square root both sides and only consider the positive root as,

\Rightarrow \rho sin\phi=1

This is the required equation of the cylinder in spherical coordinates.

Final answer:

(a) The equation of the given sphere in cylindrical coordinates is r^{2}+z^{2}=25

(b) The equation of the given cylinder in spherical coordinates is \rho sin\phi=1

7 0
3 years ago
What is the solution to the inequality
Dvinal [7]

Answer:

p > 5 and p <-8

Step-by-step explanation:

To solve this, you first need to isolate p.

First add 6 on both sides of the equation:

-6 + |2p+3| >7\\\\(+6) -6 + |2p+3| >7 +6\\\\2p + 3 > 13

Then subtract 3 from both sides of the equation.

2p+3-3>13-3\\\\2p > 10\\

The divide both sides by 2.

\dfrac{2p}{2}>\dfrac{10}{2}\\\\p>5

Another solution is possible because of the absolute value.

If |2p+3|>13

Then |2p+3|

<em>Thus we can solve the second solution:</em>

|2p+3|

2p+3

Isolate P again by subtracting both sides by 3

2p+3-3

2p

Then divide both sides by 2:

\dfrac{2p}{2}

p

3 0
3 years ago
Read 2 more answers
Please please please please please please thank please please please help me please ASAP
atroni [7]

Answer:

4

Step-by-step explanation:

3x^2 + 2(y-1)/x+y^2

3(4)^2 + 2(3-1)/4+3^2

3x16+2x2/4+9

48+4/13

52/13

4

4 0
3 years ago
What property allows you to conclude that 5x+7x=12x
Andrei [34K]
Since both of the numbers have a variable which is x ready to be multiplied, there is no expression leading to the variable therefore you will add normally but you will need to put the missing variable which needs to be multiplied. So overall you can just add and once you get your variable you can be abe to multiply and get your final answer.

Hope this helps
6 0
3 years ago
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