Answer:
A width: 3 unit cubes
height 3 unit cubes
Step-by-step explanation:
Volume of rectangular prism = 81 unit cubes
= Length of rectangular prism = 9 unit cubes
= Width of rectangular prism
= Height of rectangular prism
Volume of a rectangular prism is given by
The product of width and height must be 9 so from the options this is only possible when width and height both are 3 units.
So, the width is 3 unit cubes and the height is 3 unit cubes.
Answer: the height in inches, of the pile after 3 weeks is 34 11/12 inches
Step-by-step explanation:
Each consecutive week for the next 5 weeks the height of pile increase by 8 7/12 inches. Converting 8 7/12 inches to improper fraction, it becomes 103/12 inches. The height is increasing in an arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
a = 17 3/4= 71/4 inches
d = 103/12 inches
n = 3 weeks
the height in inches, of the pile after 3 weeks, T3. Therefore,
T3 = 71/4 + (3 - 1)103/12
T3 = 71/4 + 2 × 103/12 = 71/4 + 103/6
T3 = 419/12 inches = 34 11/12 inches
847 over 100 that is the answer
LETS prove the 2nd part of the Question
Here concept of right angles is used
We can see BA is perp to BD
and BC is perp to BE
We have to prove angle 1 = angle 3
i will denote angle by a
therefore we need to prove a1 = a3
as BA is perp to BD hence angle between them will be 90 degree
a1 + a2 = 90 degree
Similarly BC is perp to BE
a2 + a3 = 90 degree
as both equations add up gives 90 degree so will equate them
a1 + a2 = a2 + a3
which means a1 = a3
Hence Proved
To learn more about Right Angles:
brainly.com/question/7116550
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