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Andre45 [30]
3 years ago
9

HELP PLZ WILL MARK BRAINLIEST

Mathematics
2 answers:
olga55 [171]3 years ago
6 0

Answer:

1 1/21

Step-by-step explanation:

9 × 2 + 4 = 22

22/9 × 3/7 = 66/63

66/63 = 1 3/63 = 1 1/21

9966 [12]3 years ago
5 0
1 1/21

22/9 x 3/7
= 22 x 3 / 9x 7
=66/63
and simplified will be 1 1/21
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Write a trinomial which is degree 2, where the coefficient of the highest degree term is 7.
Nady [450]

Answer:

7x^2 - 2x - 3.

Step-by-step explanation:

Starts with 7x^2  then a term in x then a constant.

4 0
2 years ago
What is the GCF of 35,14
Natali [406]

Answer:The GCF of 14 and 35 is 7. To identify the GCF of 14 and 35, we first need to list all of their factors: 14: 1, 2, 7, 14. 35: 1, 5, 7, 35.

6 0
3 years ago
Read 2 more answers
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
A: What is the smallest increment on the voltmeter
oee [108]

Answer:

RESOLUTION

Step-by-step explanation:

Resolution is the smallest increment a tool can detect and display. For a nonelectrical example, consider two rulers.

4 0
3 years ago
Your friend borrows $7500 to buy an all-terrain vehicle (ATV). The simple annual interest rate is 6%. She pays off the loan afte
e-lub [12.9K]

Answer:

$162.50

Explanation:

The total amount to be paid is 7500+5(7500)(0.06)=$9750.

There were a total of (5)(12)=60 payments, so each payment is 9750/60 = $162.50.

6 0
2 years ago
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