Answer:
Where is the table
Step-by-step explanation:
I cant answer without it
Answer:
Step-by-step explanation:
Width of the room in the drawing = x
1 : 3 :: x : 18
Product of means = Product of extremes
3 * x = 18 *1
x = 18 ÷ 3
x = 6
Width of the room in the drawing = 6 inches
Answer:
50π ≈ 157.08 cubic units
Step-by-step explanation:
The volume of revolution of a plane figure is the product of the area of the figure and the length of the path of revolution of the centroid of that area. The centroid of a triangle is 1/3 the distance from each side to the opposite vertex. (It is the intersection of medians.)
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<h3>length of centroid path</h3>
One side of this triangle is the axis of revolution. Then the radius to the centroid is 1/3 the x-dimension of the triangle, so is 5/3. Then the circumference of the circle along which the centroid is revolved is ...
C = 2πr
C = 2π(5/3) = 10π/3 . . . units
<h3>triangle area</h3>
The area of the triangle is found using the formula ...
A = 1/2bh
A = 1/2(5)(6) = 15 . . . square units
<h3>volume</h3>
The volume is the product of the area and the path length:
V = AC
V = (15)(10π/3) = 50π . . . cubic units
The volume of the solid is 50π ≈ 157.08 cubic units.
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<em>Additional comment</em>
In the attached figure, the point labeled D is the centroid of the triangle. The label has no significance other than being the next after A, B, C were used to label the vertices.
The volume of revolution can also be found using integration and "shell" or "disc" differential volumes. The result is the same.
Answer:
120 feet by 100 feet
Step-by-step explanation:
6 divided by .5 equals 12. Multiply 12 times 10 to get the length of 120 feet.
5 divided by .5 equals 10. Multiply 10 times 10 to get the width of 100 feet.
I hope this helps! If you need further explanation let me know.
The equation of a circle is (x-h)^2 + (y-k)^2 = r^2. Where "x" and "y" are variables, "h" and "k" are the coordinates of the center of the circle, and "r" is the length of the radius. It is given that the center of the circle is (-27, 120). So, h= -27 and k= 120. If the circle passes through the origin, we can assume that the origin is on the circle. Since a circle's radius is constant no matter where it is drawn/is, we can find the radius of the circle by finding the distance between the circle's center (-27, 120) and the origin, (0, 0). The distance formula is: d= √((x[2]-x[1])^2-(y[2]-y[1])^2). If the coordinates of the center of the circle are (x[2}, y[2]), then x[2]= -27 and y[2]= 120. Then, the origin is the (x[1], y[1]). So, x[1] = 0 and y[1] = 0. Plugging the numbers in we get: √((-27-0)^2-(120-0)^2). This gives us √(729+14400) = 123. So since the distance between the center of the circle and a point on the circle is 123 (units), then the radius has a value of 123.
Plugging all the numbers into the equation of a circle, we get: (x-(-27))^2+(y-120)^2=123^2.