Answer:
Volume = 112
Step-by-step explanation:
formula: V = (1/3) × L × W × h,
Answer:
x = 70, y = 90
Step-by-step explanation:
A straight line is equal to 180 degrees, so if 180 is split between 110 and x. Subtract the 110 to get the rest. 180-110 = 70.
All sides in a quadrilateral add up to 360 degrees, add all of the remaining angles (112+88+70) to get 270. 360-270 = 90 degrees. Y is 90 degrees.
Answer:
y = √55
Step-by-step explanation:
All the triangles are similar, so the ratio of short side to hypotenuse is the same for all:
5/y = y/(5+6)
y^2 = 55
y = √55
_____
<em>Comment on the geometry</em>
There are three "geometric mean" relationships that apply to this geometry.
- the altitude BD is the geometric mean of BC and BA (√30)
- the long side of the large triangle is the geometric mean of the longer segment of the hypotenuse and the whole hypotenuse (x = √66)
- the short side of the large triangle is the geometric mean of the shorter segment of the hypotenuse and the whole hypotenuse (y = √55)
If you were aware of the last of these relationships, you could write down the answer without any "work."
y = √(5(5 +6)) = √55
__
The geometric mean is the n-th root of the product of n numbers. When there are 2 numbers, it is the square root of their product.
Answer:
Every group of 6 people has at least two uniform 3-person groups.
Step-by-step explanation:
Denote the 6-people by 6-vertices and draw a blue edge between 2-edges. If the two persons representing the vertices are friends. Otherwise, draw a red edge. This gives rise to a colored graph K6, edges arecolored with either blue or red.
There can exist at most 36 mips. so, multicolor triangles can exist at most 36/2 = 18 multicolor triangles.
If there are 20-triangle in graph. Therefore, every graph of 6-people has at least two uniform 3-person groups.
Just divide 300 by 450, to get 0.66667, which can be expressed as a fraction by 2/3
