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BaLLatris [955]
3 years ago
12

1. x = y + 10 x=2y + 3 How do we solve this

Mathematics
1 answer:
Dmitrij [34]3 years ago
7 0

Answer:

y=7 x=17

Step-by-step explanation:

2y+3=y+10

x=7+10

You might be interested in
What is the sum of 52 and its additive inverse?
Lisa [10]
Hello there!

The additive inverse of any number just means to flip it's value.

For example;

The number "3" would have an additive inverse of "-3".
The number "-15" would have an additive inverse of "15".

Since we have "52", we can flip the value sign of it.
We now have -52 and 52.

Since the question asked us to sum our numbers, we need to add them.

-52 + 52 = 0

The sum of 52 and its additive inverse is 0. 

 I hope this helps!
5 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
Find the radius or diameter of each circle with the given dimensions.<br><br> d=30 m
Alex_Xolod [135]

Answer:

r=94.2

Step-by-step explanation:

C=pi`d

C=3.14 multiplied by 30

C equals about 94.2

6 0
2 years ago
Pauline gets a 2% commission on her sales at her job. She sells $23,500 worth of products in May.
Illusion [34]
470 dollars . 2% Of 23,500
7 0
2 years ago
Using the temperature conversion tables below, what is 50°F in degree Celsius?
vfiekz [6]

Answer:

The answer to your question is:

Step-by-step explanation:

Convert 50°F to Celsius

Formula

                  °C = (°F - 32) x 0.56

Process

                   °C = (50 - 32) x 0.56

                  °C = 18 x 0.56

                  °C = 10.08

6 0
2 years ago
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