Answer:
3.92*10^3mm
Step-by-step explanation:
In the diagram it gives you 7900mm. There is a figure which was given underneath written 900mm. use 7900 to subtract 900 you will get 7000. Then you can use the Pythagoras theorem to solve it, with a= height, b=5800mm and c=7000mm where, a^2+b^2=c^2.
Answer:
revolutions per minute for 16 inches is 946 / minute
revolutions per minute for 14 inches is 1081 / minute
Step-by-step explanation:
Given data
radius = 16 inch
speed = 90 mph = 90/60 = 1.5 miles/minute = 1.5 × 5280 feet /12 inches = 95040 inches /minute
radius 2 = 14 inches
to find out
revolutions per minute
solution
first we calculate the circumference of the wheel i.e. 2×
×radius
circumference = 2×
×16
circumference = 32
we know that revolution is speed / circumference
revolution = 95040/32
revolution = 945.38 / minute
we have given radius 14 inches than revolution will be i.e.
revolution = speed / circumference
circumference = 2×
×14
circumference = 28
revolution = 95040/ 28
revolution = 1080.43 / minute
Step-by-step explanation:
L.H.S=(1-cosB)(1+cosB)
=(1-cos^2B). {using (a+b) (a-b)=(a^2-b^2)in second step}
=sin^2B
=1/cosec^2B
Therefore,L.H.S=R.H.S proved
Answer:
a) 504
b) 56
c) 0.111
Step-by-step explanation:
Data provided in the question:
There are nine golf balls numbered from 1 to 9 in a bag
Three balls are randomly selected without replacement
a) 3-digit numbers that can be formed
= 
n = 9
r = 3
= ⁹P₃
= 
= 9 × 8 × 7
= 504
b) 3-digit numbers start with the digit 1
= _ _ _
in the above 3 blanks first digit is fixed i.e 1
we and we have 8 choices left for the last 2 digits
Thus,
n = 8
r = 2
Therefore,
= 1 × ⁸P₂
= 1 × 
= 1 × 8 × 7
= 56
c) Probability that the 3-digit number formed is less than 200
Now,
The number of 3-digit number formed is less than 200 will be the 3-digit numbers start with the digit 1 i.e part b)
and total 3-digit numbers that can be formed is part a)
therefore,
Probability that the 3-digit number formed is less than 200
= 56 ÷ 504
= 0.111
78.5/100 as a decimal is just 0.78.5 and as a percent it is 78.5 %