Write a recursive formula for the amount of helium in the balloon after n days.

Which of the following is the accurate APA format for writing out the bragger condition main effect result for dependent variabl

Svetllana [295]

Answer:

Answer is given below.

Step-by-step explanation:

3. Option a is correct

we ran a univariate ANOVA for 2 independent variables and 1 dependent variable.

for the bragger condition (truthful or non truthful), we got the F (1,116)=68.646 and p value = 0.000 < 0.01 that necessarily implies that there is no significant main effect of the bragger condition on the likeability of Edward.

4 0

3 years ago

PLS HELP Find the m∠RLU.<br> A. 10º<br> B. 6º<br> C. 25º<br> D. 50º

alexdok [17]

Rlu is 50 as rlu and alu are equal

7 0

3 years ago

H is inversely proportional to p

NeTakaya

Answer:

Direct & Inverse Proportion (H) - Version 2 January 2016 . A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, . 1. 2. Write an expression for y in terms of x. [4]. 2. A pebble is thrown vertically upwards. . (b) Find the initial speed of the pebble if the maximum height reached is 16 m. . T is given by.

4 0

3 years ago

First, drag a value to represent the missing angle in the triangle. Then, complete the trigonometry equality statements.

noname [10]

The missing trigonometric values are listed below:

Angle A = 90 - θ
sin 28° = cos (62°)
Cos 33° = sin 57°
Cos 31° = sin 59°
Cos (90 - θ) = sin(θ)

<h3>Meaning of Trigonometry</h3>

Trigonometry is a branch of mathematics that studies angles of triangles and its side length.

Trigonometry is so important that every student must come across this branch of mathematics.

In conclusion, the missing trigonometric values are listed above

Learn more about trigonometry: brainly.com/question/24349828

#SPJ1

6 0

1 year 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 $\rho sin\phi=1$

7 0

2 years ago