The length of the sign in centimeters is 50 while in millimeters it is 500 because....
1 cm = 10 mm
so then it would be
Answer:
B. No the ordered pair does not satisfy the equation
Step-by-step explanation:
y = -9x - 2
Substitute the point in and see if it is true
-37 = -9(4) -2
-37 = -36 -2
-37 = -38
This is not true so the point is not a solution
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.
84 sq. ft of the wall has to be covered with paint or wallpaper.
Step-by-step explanation:
- Step 1: Find the area of wallpaper to be covered by calculating the area of the wall and subtracting the areas of the window, mirror and fireplace from it. All are rectangular in shape with are given by A = length × width
Area of the wall = 8 × 16 = 128 ft²
Area of the window = 18/12 × 14 = 1.5 × 14 = 21 ft² (since 1 ft = 12 in)
Area of the fireplace = 5 × 3 = 15 ft²
Area of the mirror = 4 × 2 = 8 ft²
- Step 2: Calculate the area to be painted or covered with wallpaper
Area of the wall to be covered with paint or wallpaper = 128 - (21 + 15 + 8)
= 128 - 44
= 84 ft²
First, you can eliminate 1 and 2 because irrational cant be non-repeating or terminating.
Since 18^2 is a whole number, it terminates.
Hope this helps!