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2 years ago

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Two classes have a total of 50 students. One of the classes has 6 more students than the other. How many students are in the lar

ger class.

1 answer:

elena-s [515]2 years ago

8 0

Well if the 1 st two classes have 25 each and 25 and 25 is 50 all together then the larger class is 25 + 6 = 31

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A janitor can clean 1/9 of a stadium in 1/3 of an hour. If he continues at this rate how much of the stadium can he clean pre ho

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To find the the amount of how much the stadium is cleaned you can

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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 $\rho sin\phi=1$

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2 years ago

Jessie estimates the weight of her cat to be 10 pounds. The actual weight of the cat is 13.75 pounds. find the percent error.

romanna [79]

Answer:

$\large \boxed{27 \, \%} }$

Step-by-step explanation:

$\begin{array}{rcl}\text{Percent error}&= &\dfrac{\lvert \text{Measured - Actual}\lvert}{ \text{Actual}} \times100 \,\%\\\\& = & \dfrac{\lvert 10 - 13.75\lvert}{13.75} \times 100 \, \% \\\\& = & \dfrac{\lvert -3.75\lvert}{13.75} \times 100 \, \%\\ \\& = & \dfrac{3.75}{13.75} \times 100 \,\%\\\\& = & 0.27 \times 100 \, \%\\& = & \mathbf{27 \, \%}\\\end{array}\\\text{The percent error is $\large \boxed{\mathbf{27 \, \%} }$}$

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2 years ago

18.<br> [Algebra - Expansion]<br> Expand 3(x + 2)

alexira [117]

Answer:

Step-by-step explanation:

3(x + 2) = 3*x + 3*2

= 3x + 6

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3 years ago

Read 2 more answers

100 yards on 20 carries

Svetlanka [38]

Answer:

if u multiply 20 times 5 u would get 100 and and if u add 20+20+20+20+20 u would get 100 so either way ur answer may be 5

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2 years ago