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3 years ago

12

Janice has a summer job giving tours at the zoo. she earns 62.50 for 5 hours a day. she is trying to earn 500 by the end of the

summer. how many tours will she need to give the zoo? (I need unit rate per tour and how many she needs)

1 answer:

lana66690 [7]3 years ago

5 0

$62.50 / 2 = $12.50 per tour
500 / 12.59 = 40 tours.
Janice needs to do 40 tours to make $500.

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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

A tennis ball has a radius of about 1.4 inches What is the volume of the tennis ball to the nearest half inch.? Use 3.14 as an a

Ilya [14]

Answer:

Volume of tennis ball = 11.49 inch³

Step-by-step explanation:

Given:

Radius of tennis ball = 1.4 inches

Value of π = 3.14

Find:

Volume of tennis ball

Computation:

Volume of sphere = [4/3][π][r]³

Volume of tennis ball = [4/3][π][Radius of tennis ball]³

Volume of tennis ball = [4/3][3.14][1.4]³

Volume of tennis ball = [1.333][3.14][1.4]³

Volume of tennis ball = [1.333][3.14][2.744]

Volume of tennis ball = [4.1856][2.744]

Volume of tennis ball = 11.4852

Volume of tennis ball = 11.49 inch³

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3 years ago

What value of X makes the equation true -7x - (-5-x) = -9(2x-1) -1

Bond [772]

Answer:

x = 1/4

Step-by-step explanation:

-7x - (-5-x) = -9(2x-1) -1

-7x + 5 + x = -18x + 9 - 1

combine like terms:

-6x + 5 = -18x + 8

add 18x to each side of the equation:

12x + 5 = 8

subtract 5 from each side:

12x = 3

divide both sides by 12:

x = 3/12 = 1/4

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3 years ago

If P + Q=16 and<br> P+10=20<br> What Is The Possible Value Of Q?

aleksklad [387]

P + 10 = 20 Subtract 10 from both sides
P = 10

Substitute P = 10 into P + Q = 16

P + Q = 16 Plug in 10 for P
10 + Q = 16 Subtract 10 from both sides
Q = 6

3 0

3 years ago

Read 2 more answers

What is the complement of an 18 degree angle

svlad2 [7]

Answer:

The complementary angle is 72

Step-by-step explanation:

Complementary angles add to 90 degrees

Let x be the complementary angle

x+18 = 90

Subtract 18 from each side

x = 90-18

x = 72

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3 years ago