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
Kryger [21]
3 years ago
13

Find the distance between the points (4,5) and (10, – 3). Round decimals to the nearest tenth

Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
3 0

Answer:

10 is the distance.

You might be interested in
Combine like terms<br><br> 4y^2+4(7y^2-8)=<br><br> please show your work
kirza4 [7]

Answer:

32y^2-32

Step-by-step explanation:

4y^2+4(7y^2-8)

4y^2+28y^2-32

32y^2-32

if you need extra steeps explaining then plz let me know and I will help :)

8 0
3 years ago
Solve for q. Write your answer as “q=___”
wolverine [178]

Answer:

7q-46= 3q +6

7q-3q = 6+ 46

4q= 52

4q/4= 52/4

q= 13

3 0
3 years ago
Read 2 more answers
Help fast if it’s correct I’ll make you the Brainly thing
Leto [7]
The correct expressions are
-8.8
11(-2)
-6.7
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.

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
Ana and chuyen are exploring underground caves anas location is -30 feet below the cave entrance and chuyen's patience is -12 fe
ki77a [65]
Ana' location is further away from the entrance
3 0
3 years ago
Other questions:
  • 6glass of water each contained 300ml Andrew drank 2 liters of water how many drank together
    6·1 answer
  • If y varies directly as x and y=4 when x=-2 find y when x=30
    14·1 answer
  • There is a ​$40 fee to rent a chain​ saw, plus ​$9 per day. Let x represent the number of days the saw is rented and y represent
    14·1 answer
  • How can a veto be overridden?
    9·2 answers
  • What is the y-intercept of the function, y = 3x -5?
    9·2 answers
  • PLS HELP ASAP!
    14·1 answer
  • Which is the least valid way to stimulate how many boys and girls are in a random sample of 20 students from a school that is ha
    5·2 answers
  • A soccer team is selling doughnuts to raise money for new uniforms. They are selling the doughnuts for $8 per dozen. They must p
    9·1 answer
  • Which expression is equivalent to 6x+7-12*2-(3 to the power 2 +3)-x
    10·2 answers
  • 3p- 2c^3- 3c^3p +2 Write as a product
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!