Determine whether each regular polygon tessellates the plane. Explain.
2 answers:
Answer:
b. no; measure of interior angle = 135°
Step-by-step explanation:
A regular polygon can only tessellate the plane when its interior angle divides 360 degrees.
The polygons that tessellate are - the square, the equilateral triangle, and the regular hexagon.
The octagon cannot tessellate because its internal angle does not divide 360 degrees. Tessellation means an arrangement of polygons in a repeated pattern without overlapping.
The internal angle of an octagon is 135 degrees. When we divide 360 by 135 we get,
Its not a complete number this is why octagons do not tessellate.
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Hey there!
<h3>Question 1</h3>Let's use 3.14 for pi during this. It'll make it a lot easier.
The volume for a cone is .
The diameter of this cone is 17.6 inches. Since the radius is half the diameter, we can find the radius by dividing this amount by 2.
17.6 ÷ 2 = 8.8
The height of this cone is 23.4 inches.
Plug the values into the equation.
Next, square 6.8 and divide 23.4 by 3. Also, replace the pi symbol with 3.14.
Multiply the numbers together.
<u>The volume of this cone is approximately 1896.66 cubic inches.</u>
<h3>Question 2</h3>Finding the volume of a trapezoidal prism can be done by finding the are of the trapezoidal face and multiplying it by the depth.
Formula for finding the area of a trapezoid is
The two bases are 10 and 34, and the height is 24.7 feet. Put these values into the equation.
Add 10 and 34, then multiply it by 24.7 and 1/2.
a = 543.4
Multiply that value by 19, which is the depth of the figure.
<u>The volume of the prism is 10324.6 cubic feet.</u>
<h3>Question 3</h3>The formula for volume of a triangular pyramid is v = 1/3ah, with a the area of the base and h the height.
The formula for the area of an equilateral triangle, which is the base, is
The length of the side is 12, so we can square that to get 144.
Now multiply that by to get the area of the base.
The area of the base is about 62.35 square meters.
The height of the pyramid is 20 meters. Plug that and the area of the base into the equation.
v = 1/3 x 62.35 x 20
Multiply the numbers together to get the volume.
<u>The volume of the pyramid is approximately 415.67 cubic meters.</u>
Hope this helps!
If f(X)= 7x +5/3 - x =6x +5/3
y= 6x +5/3
6x= y-5/3
f^-1(y)=x=(y-5/3)/6
So we can write
f(f^-1(y))= f((y-5/3)/6) = 6 (y-5/3)/6 +5/3= y-5/3+5/3= y
The same result can be obtained for f^-1(f(x))=x
If the function is f(x)= 7x +5/(3-x) then it is not invertible since it is not injective (pictures)
