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Alex Ar [27]
3 years ago
13

Points for points?

Mathematics
1 answer:
sattari [20]3 years ago
6 0

All the best!!

thanks for the points!

it was nice to meet you <3

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A rectangular box is 32 cm wide and 36 cm high. If the surface area of the box is 4344 square​ centimeters, find the length of t
AnnZ [28]

To find the surface area, multiply length x width x height.

let "length" = l

l x 32 x 36 = 4344

Simplify

l x (32 x 36) = 4344

l x 1152 = 4344

Isolate the length. Divide 1152 from both sides

(l x 1152)/1152 = (4344)/1152

l = 4344/1152

l = 3.77 (rounded)

3.77 cm is your length.

hope this helps

8 0
3 years ago
Annita, Gary, and Tara all run races. Annita has 7 less than 4 times the number of race medals as Tara. Gary has 13 more than 2
harkovskaia [24]

Answer:

4 t - 7  = 2 t+ 13  is the required equation.

The number of race medals Tara has is t = 20 medals.

Step-by-step explanation:

Let the number of medals Tara has = t medals

So, the number of medal Anita has  = 4( Medals of Tara) - 7

= 4t - 7

And the number of medals Gary has = 2 times (Medals of Tara) + 13

= 2(t)  + 13  = 2t + 13

Now, Annita and Gary has same number of medals.

⇒  4t - 7  = 2t+ 13

or, 4t - 2t  = 7 + 13

⇒ 2t  = 20

⇒ t = 20/2 = 10

or t = 10

Hence, the number of race medals Tara has is t = 20 medals

6 0
3 years ago
In physics, we can find the amount of force needed to push or pull an object by multiplying the object’s mass by the object’s ac
Kisachek [45]

Answer:

1875

Step-by-step explanation:

750 x 2.5 = 1,875

6 0
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

7 0
3 years ago
Use the marked parallel lines to find the value of y in the diagram below (1 point)
Inessa [10]
2x + 5 = 3x - 45                    [alternate interior angles]
3x - 2x = 5 + 45
x = 50

4y - 1 + 2x + 5 = 180                [supplementaly angles]
4y + 2(50) + 4 = 180
4y + 100 = 176
4y = 76
y = 19
7 0
3 years ago
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