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3 years ago

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There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter .to the nearest meter ,how many meters are in 241 inc

hes ?

1 answer:

matrenka [14]3 years ago

5 0

Answer:

6.12 meters

Step-by-step explanation:

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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

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

What is 788.48 plus 7% rounded to the nearest cent

AveGali [126]

Answer:

$843.67

Step-by-step explanation:

1% = 7.8848

7.8848 x 7 = 55.1936

788.48 + 55.1936 = 843.6736

Rounded to nearest cent = $843.67

7 0

3 years ago

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Solve for x.<br><br> logx+log3=log18

ad-work [718]

<u>Answer:</u>

<em>The value of x in log x + log 3 = log 18 is </em><em>6</em><em>.</em>

<u>Solution:</u>

From question, given that log x + log 3 = log 18 ---- eqn 1

Let us first simplify left hand side in above equation,

We know that log m + log n = log (mn) ----- eqn 2

Adding log m and log n results in the logarithm of the product of m and n (log mn)

By using eqn 2, log x + log 3 becomes log 3x.

log x + log 3 = log 3x ---- eqn 3

By substituting eqn 3 in eqn 1, we get

log 3x = log 18

Since we have log on both sides, we can cancel log and the above equation becomes,

3x = 18

$x = \frac{18}{3} = 6$

Thus the value of x in log x + log3 = log18 is 6

6 0

3 years ago

Read 2 more answers

If you can help me it will mean a lot.

Assoli18 [71]

Answer:

y - -x + 2.

Step-by-step explanation:

The line passes through (0, 2) and 5, 1) so it slope = (1-2) / (5-0)

= -1 and the y-intercept is at y = 2 so the equation is

y - -x + 2.

3 0

3 years ago

Someone please help me with this

TEA [102]

Answer:

Quotient is 75 Remainder is 49

Step-by-step explanation:

5 0

3 years ago

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