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3 years ago

12

The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs

3800 pounds on Planet A, find the elephants weight on Planet B

2 answers:

Crank3 years ago

7 0

This problem can be solved using ratios:

$100:3 = 3800:x$

Now we solve for x by doing the following algebra:

$3800*3 = 100x$

$11400 = 100x$

$114 = x$

The answer is 114 pounds

olganol [36]3 years ago

3 0

Answer:

the elephants weight on Planet B is 114.first you divide 3800 by 100 it gives you 38 then multiply 38 times 3 it gives you 114.the answer of the question is 114. you have to use unit rate or the whole enchilada method.

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

Mrs. Johnson has 159 chickens that she puts in shelters at night to keep safe. She places 12 chickens in a shelter and continues

Lesechka [4]

Answer:

3

Step-by-step explanation:

159-12=147-12=... keep going until you get to

15-12=3

8 0

3 years ago

What is equilibrium if autonomous expenditures are $2,000 and the mpe is 0. 5?

STALIN [3.7K]

The equilibrium level if autonomous expenditures are $2,000 and the mpe is 0. 5 is $4000.

<h3>How to calculate the equilibrium?</h3>

From the information given, the autonomous expenditures are $2,000 and the mpe is 0. 5.

Here, the equilibrium level will be:

= 2000/(1 - 0.5)

= 2000/0.5

= 4000

In conclusion, the correct option is $4000.

Learn more about expenditure on:

brainly.com/question/935872

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3 0

2 years ago

Can 2 liters fit into 1/2 of a gallon?

svetlana [45]

Yes. bc once the first two liter goes in it will prolly fill up half of the the 1/2 gallon it will foam down and the other one will fit also

4 0

4 years ago

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You are going to mix a gallon bucket of window cleaner. The instructions direct you to mix 1 part cleaner to 3 parts water. How

Pie

One gallon equals to 4 quarts.

The instructions tell you to add 1 part of cleaner and 3 parts of water, in total 4 parts. It makes it easy as you can take that one part = one quart.

You will use 3 quarts of water and 1 quart of cleaner. The answer is D.

4 0

3 years ago

Read 2 more answers