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3 years ago

Answer the question bro

Mathematics

2 answers:

hodyreva [135]3 years ago

4 0

You don’t ask anything.so what should we answer.

kati45 [8]3 years ago

3 0

I think your answer would be A and C

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Suppose you have the 26 letters of the alphabet on separate cards in a hat. You pick out a card, write down the letter, put the

weeeeeb [17]

(1/26)⁶ = 1/308,915,776

4 0

3 years ago

Find the value of x.

Sergeu [11.5K]

$\blue{\huge{\red{\boxed{\green{\mathfrak{QUESTION}}}}}}$

Find the value of x.

$\orange{\underline{\huge{\bold{\textit{\green{\bf{FORMULA}}}}}}}$

SUM OF ANGLES ON STRAIGHT LINE = 180°

$\huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}$

$ANGLES\: R :-( x - 10)°,(3x + 25)°,(x + 5)°, \\ \\ ( x - 10)° + (3x + 25)° + (x + 5)° = 180 \\ 5x + 20 = 180 \\ 5x = 160 \\ x = \frac{160}{5} \\ x = 32° \\$

$\red{ANGLES R :-} \\ \pink{( x - 10)° = 32 - 10 = 22°} \\ \blue{ (3x + 25)° = 32 \times 3 + 25 = 96 + 25 = 121°}\\ \orange{(x + 5)° = 32 + 5 = 37°}$

3 0

3 years ago

Read 2 more answers

The Freedom Trail is 2 1/2 miles long. Ana walked 5/8 mile from Boston Common to the Paul Revere House. Then, she walked 3/8 mil

Julli [10]

Answer:

1 1/2 miles

Step-by-step explanation:

5/8+3/8 is 8/8, or 1 mile. She now has 1 1/2 miles left to go! (2 1/2-1=1 1/2)

5 0

3 years ago

The non-profit organization you volunteer for is throwing a fundraiser cookout. You are in charge of buying the hamburgers, whic

Tcecarenko [31]

Answer: 7

Step-by-step explanation:

7 0

3 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 $\rho sin\phi=1$

7 0

3 years ago