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4 years ago

Draw and label a hexagonal prism then identify each of the following a. Parallel planes,b.skew lines,c. Intersecting planes

Mathematics

1 answer:

Natasha_Volkova [10]4 years ago

5 0

Explanation:

a) Opposite faces of a regular hexagonal prism are parallel. For each of the four "visible" numbered faces in the attachment, the opposite (parallel) face is not numbered.

b) Skew lines are ones that cannot reside in the same plane. They are not parallel and do not intersect. The blue arrows in the attached show an example of a pair of skew lines. Any of the base edges will be skew with any lateral face edge that it does not intersect. Any base edge will be skew with any non-parallel edge of the opposite base.

c) Any edge of the figure is where planes intersect. In general, any pair of planes that are not parallel will be intersecting planes. So, for each plane of the figure, there are 6 other intersecting planes. (The line where the planes intersect is not always shown.) For example, planes 1 and 2 in the figure are intersecting planes.

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The edges of the bases of the frustum of a regular square pyramid have length 5 and 9, and the slant height of the frustum is 6.

Karo-lina-s [1.5K]

Answer:

Volume of the frustum = 225.0952

Surface area = 274

Step-by-step explanation:

The volume can be calculated as the difference of the complete pyramid and the tip of the pyramid.

To find the height of the frustum, we can use pythagoras theorem in the following triangle:

first side: 9 - 5 = 4

second side h (height)

hypotenusa: slang = 6

6^2 = h^2 + 4^2

h^2 = 36 - 16 = 20

h = 4.4721

To find the height of the complete pyramid (H), we can use the following rule of three:

H / 9 = (H - 4.4721) / 5

5H = 9H - 40.2489

4H = 40.2489

H = 10.0622

Volume of complete pyramid:

V_complete = (1/3)*9^2*10.0622 = 271.6794

Volume of the tip:

V_tip = (1/3)*5^2*(10.0622 - 4.4721) = 46.5842

Volume of the frustum:

V_frustum = V_complete - V_tip = 225.0952

The surface area is the bigger base area + smaller base area + four side areas.

Bigger base area = 9^2 = 81

Smaller base area = 5^2 = 25

Side area = (9+5)*6/2 = 42

Total surface area: 81 + 25 + 4*42 = 274

4 0

3 years ago

If x+y=16 and x-y=-2, what is the value of xy?

Fantom [35]

Answer:

Y=7 and

X=9

Step-by-step explanation:

X+Y=16

X=2+Y

2+Y+Y=16

2+2Y=16

2Y=16-2

2Y=14

2Y/2=14/2

Y=7

X =2+Y

So X=9

8 0

1 year ago

Find the inverse of function of a function g=((a,1),(b,2),(2,3),(d,4))

Shalnov [3]

Answer:

g inverse = (1,a),(2,b),(c,3),(4,d)

Step-by-step explanation:

I think the third part of the question should be (c,3) not (2,3)

if it's (2,3) then the inverse becomes (3,2)

8 0

2 years ago

Read 2 more answers

Consider the circle of radius 5 centered at (0,0), how do you find an equation of the line tangent to the circle at the point (3

Flauer [41]

$\text{We know that the tangent at any point on a circle is perpendicular}\\
\text{to the radius at that point.}\\
\\
\text{so first we find the equation of the line joining (0,0) and (3,4)}\\
\text{and then using the slope, we find the line perperndicular to it at (3,4)}\\
\\
\text{the equation of the line passing through (0,0) and (3,4) is}\\
\\
y-0=\frac{4-0}{3-0}(x-0)$

$\Rightarrow y=\frac{4}{3}x\\
\\
\text{so the slope of radius is }m=\frac{4}{3}.\\
\\
\text{we know that the product of the perpendicular lines is }-1. \\
\\
\text{so the slope of the perpendicular line would be}=-\frac{1}{4/3}=-\frac{3}{4}\\
\\
\text{So the equation of the tangent line has slope }-\frac{3}{4} \text{ and}\\
\text{passing through (3,4). so equation of tangent line is}$

$y-4=-\frac{3}{4}(x-3)\\
\\
\Rightarrow y-4=-\frac{3}{4}x+\frac{9}{4}\\
\\
\Rightarrow y=-\frac{3}{4}x+\frac{9}{4}+4\\
\\
\Rightarrow y=-\frac{3}{4}x+\frac{9+16}{4}\\
\\
\text{so the equation of tangent line is:} y=-\frac{3}{4}x+\frac{25}{4}$

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4 years ago

Find the possible values of r in the inequality 5 > r - 3.

ioda

The answer to this question is A

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4 years ago

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