1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
MrRissso [65]
3 years ago
15

Halfway point between 4 and 16

Mathematics
2 answers:
Luba_88 [7]3 years ago
8 0

Take the arithmetic mean, or the average of the two values to get the halfway point.

\dfrac{4+16}{2}

Simplify

=\dfrac{20}{2}

And simplify again.

=10

The halfway point of 4 and 16 is 10. Let me know if you need any clarifications, thanks!

~ Padoru

muminat3 years ago
5 0

Answer:

10

Step-by-step explanation:

You might be interested in
What is the value of x? O 13 O 14 O 26 O 28​
BartSMP [9]

It’s A. 13


hope this helps

7 0
1 year ago
My brain is destroying itself so i need a little help I give brain award
klasskru [66]
The third one is the right one on e2020
7 0
2 years ago
Can someone help me find X
bearhunter [10]

Answer:

x = 122 degrees

Step-by-step explanation:

6 0
2 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
2 years ago
X+8 is atleast 18 solving one step inequalities by adding and. Subtracting
Mamont248 [21]
X + 8 >= 18

(>= means greater than or equal to)

x + 8 - 8 >= 18 - 8
x >= 10
7 0
3 years ago
Other questions:
  • What is the substitution for 4x+6y=332 & x+y=10
    6·1 answer
  • ∣14−3x∣ for x=6x=6 show work
    14·1 answer
  • Given p ≠ q ≠ 0, what is the equation of the line that passes through the points (–p, –q) and (p, q)?
    14·2 answers
  • What is the GCF of 33,55,132
    8·1 answer
  • PLEASE HELP TIMED
    6·2 answers
  • How to solve 9 and 10?
    13·1 answer
  • 1. If a (x) = 3x + 1 and b (x)=√x-4, what is the domain of (b*a) (x)?
    5·1 answer
  • YALLLL SOMEONE HELP A GIRL OUTTTT (ALSO NO LINKS I KNOW UR TRYING TO SCAM LOL)
    15·1 answer
  • Help me solve this question pls
    9·2 answers
  • Find the coordinates of the point of intersection of the line with equation 3x + 4y = 10 and the line with equation 5x − 6y = 23
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!