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Reika [66]
3 years ago
12

Find the total surface area in square inches, of the following 3-

Mathematics
1 answer:
Ivenika [448]3 years ago
6 0

Answer:

81 in²

Step-by-step explanation:

The 3-dimensional shape given is a square pyramid having a square base, and 4 right triangular side faces that are the same.

The surface area can be calculated by finding the area of the square base and the area of the 4 triangular side faces. Then sum all the areas together.

Or, we can use the following formula below: Base Area + ½(Perimeter of base) × Slant Length

Where,

Base area = s² = 5² = 25 in²

Perimeter of base = 4(s) = 4(5) = 20 in

Slant height = 5.6 in

Surface area = 25 + ½(20) × 5.6

= 25 + 10 × 5.6

= 25 + 56

Surface area = 81 in²

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1<br> Solve - (8x – 12) = 2x – 3<br> 4<br> 218x -<br> pleaseee help!!
Alex Ar [27]

Answer:

1/4.(-96)=2x-3

-1/4.96=2x-3

-24=2x-3

-2x-24=-3

-2x=-3+24

-2x=21

x=-21/2

Step-by-step explanation:

8 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
Find the vertex and focus of the<br> parabola.<br> y2 – 4y + 12x – 8 = 0
IceJOKER [234]

Answer:

1,2

-2 2

Step-by-step explanation:

6 0
2 years ago
If 62% of customers prefer low cholesterol bacon, what number of degrees on a pie chart would be used to represent this?
Natalija [7]
62% of 360° = 0.62*360° = 223.2°
8 0
2 years ago
Hamza is graphing the parabola represented by this equation. 3x-6y^2+6y=0<br> The answer is below!!!
aivan3 [116]

Hamza should draw the vertex at (-0.5, 0.5), the directrix at -0.625, and the focus at (-0.375, 0.5). The parabola will open to the right

The given equation is 3x-6y²+6y=0.

<h3>What is the parabola?</h3>

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Right

Vertex: (-1/2, 1/2)

Focus: (-3/8, 1/2)

Axis of symmetry: y=1/2

Directrix: x=-5/8

The coordinate points to plot (-1/2, 1/2), (0.5, 1.21), (0.5, -1.21), (1.5, 1.5) and (1.5, -0.5).

Therefore, Hamza should draw the vertex at (-0.5, 0.5), the directrix at -0.625, and the focus at (-0.375, 0.5). The parabola will open to the right.

To learn more about the parabola visit:

brainly.com/question/21685473.

#SPJ1

4 0
1 year ago
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