Which of these is the triangle proportionality theorem? First person to answer CORRECTLY gets brainliest

Answers

Answer 1

Answer:

Answer: A.

Step-by-step explanation: Brainliest plz

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Name/ Uid:1. In this problem, try to write the equations of the given surface in the specified coordinates.(a) Write an equation for the sphere of radius 5 centered at the origin incylindricalcoordinates.(b) Write an equation for a cylinder of radius 1 centered at the origin and running parallel to thez-axis inspherical coordinates.

Answers

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,

$x=rcos\theta,y=rsin\theta,z=z$

$r^(2)=x^(2)+y^(2),tan\theta=(y)/(x),z=z$

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 $\rho sin\phi=1$

Find the value of x. Round to the nearest tenth.

Answers

36
i think. hope it helped sorrh if it’s wrong i’m not good at math

A missile uses an internal computer clock to measure time in tenths of a second. The missile guidance system needs the time from launch, in seconds, in order to calculate its distance from the launch site. It obtains this by multiplying the computer clock time by 0.1. So, for example, a reading of 50 tenths of a second is 5 seconds. For one particular missile system, the conversion factor of 0.1 is stored in 8 bits as the binary number 0.000110012.The missile’s internal computer clock shows 200 tenths of a second. Convert this to seconds using your result from Part (i) of this question. Do not round your answer. The missile guidance system now records that it has travelled for this number of seconds.

Answers

Using proportions, it is found that the missile's internal computer clock is of 20 seconds.

According to the information given, this question can be solved by proportions, using a rule of three.

50 tenths of a second is equivalent to 5 seconds, and we want to find the equivalent to 200 tenths of a second, thus, the rule of three is:

50 tenths - 5 seconds

200 tenths - x seconds

Applying cross multiplication:

$50x = 5(200)$

$50x = 1000$

$x = (1000)/(50)$

$x = 20$

The missile's internal computer clock is of 20 seconds.

A similar problem is given at brainly.com/question/24372153

This year, a small business had a total revenue of $81,900 . If this is 26% more than their total revenue the previous year, what was their total revenue the previous year?

Answers

Answer:

total revenue was $65,000

Step-by-step explanation:

A small business had a total revenue this year = $81,900

This is 26% more than their total revenue the previous year.

Let the revenue of previous year be 'r'.

r + ( 26% of r ) = $81,900

r + ( 0.26r ) = 81,900

1.26r = 81,900

r = $(81,900)/(1.26)$

r = 65,000

Their total revenue was $65,000 the previous year.

$65000 was the total revenue for the previous year.
65000 x .26 = 16900
65000 + 16900 = 81,900

WILL GIVE BRAINLIEST!!

Answers

Answer:

6.9

Step-by-step explanation:

12 x 4 = x^2

48 = x^2

x = 6.9

Answer:

6.9

explanation:

I did the test.

hope this helps you!

5. You are a packer for Acme Bottling Company. You fill cartons with bottles,seal the cartons, and stack them on pallets. Monday through Friday you are
paid $0.41 for each carton you fill. On Saturday you are paid an additional
$0.21 for each carton you fill. What is your total pay for a week in which you
filled the following number of cartons?
Copyright by The McGraw-Hill Companies, Inc. All rights
Mon.
Tues.
Wed.
Thurs.
Fri.
Sat.
210
175
224
160
216
90

Answers

Answer:

$459.65

Step-by-step explanation:

The total number of cartons you filled was ...

210 +175 +224 +160 +216 +90 = 1075

so your pay for filling those is ...

$0.41 × 1075 = $440.75

You get an additional amount of pay for the cartons filled on Saturday:

$0.21 × 90 = $18.90

So your pay for the week is ...

$440.75 +18.90 = $459.65

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