What is the maximum volume of water a hamster bath could hold with a depth of 1 2/3 inches, a length of 2 1/3 inches, and width
1 answer:
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Answer:
Step-by-step explanation:
The word "LAMEFIREALARM" word consists of
2L , 2M, 2E , 2R , 3A , F and I
no of words with the above letters such that M's are not together
=Total No of words- M's are together
Total no of words
When M's are together . considering 2 M's as one
therefore there are
No of ways
(b)No of ways such that M's are separated by at least 2 letters
at least 2 letter means 2 letter, 3 letter ......11 letters
So we have to subtract no of ways where there are 1 letter in between M's from total no of ways where 2 M's are not next to each other
No of ways in which there is 1 letter between 2 M's
This can be done by considering 11 cases
In first case Place first M in Starting Position and 2 M on third place
Second case place First M in 2 nd Position and second M on 4 th place
Similarly For 11th case
Place first M in 11th place and second M on 13th place
Total ways
So , the total number of arrangements of the letters of the word LAMEFIREALARM where the two M's are separated by atleast two letters is
Step-by-step explanation:
Given : A rectangle 4 x 8 , a semicircle
Diagonal intersecting semicircle
To Find :Area of red part
<h3>Solution:</h3>Angle AC make AB α = ∠BAC
tan α = BC/AB = 4/8 = 1/2
=> α = 26.565°
∠ECA = ∠BAC = α
EC = EF = 4
=> ∠CEF = 180° - 2α
∠AED = 45° as AE is diagonal of Square of side 4
=> ∠AEF + 180° - 2α + 45° = 180°
=> ∠AEF = 2α - 45° = 8.13°
in Left side area between square and circle is split in 2 Equal parts
(1/2) area - area AFG = area of Red part
in Left side area between square and circle = 4² - (1/4)π4²
= 3.4336 sq unit
half = 1.7168 sq unit
Now find area AFG = area ΔAEF - sector EGF
area ΔAEF
AE = 4√2 , EF = 4 angle = 8.13°
area ΔAEF = (1/2) 4√2 * 4 sin 8.13° = 1.6 sq unit
area sector EGF = (8.13/360)π4² = 1.135 sq unit
area AFG = 1.6 - 1.135 = 0.465 sq unit
Area of Red part = 1.7168 - 0.465 sq unit
= 1.2518 sq unit
= 1.252 sq unit
= 1.25 sq unit.
Hope this helps!!
