Answer: The father is 37 years and the son is 7 years
Step-by-step explanation:
Let x represent the present age of the father.
Let y represent the present age of the son.
Three years hence a father will four times as old as his son will be. This means that
x + 3 = 4(y + 3)
x + 3 = 4y + 12
x - 4y = 12 - 3
x - 4y = 9- - - - - - - - - - - - - - - -1
Before two years he was seven times as old as his son was. This means that
(x - 2) = 7(y - 2)
x - 2 = 7y - 14
x - 7y = - 14 + 2
x - 7y = - 12- - - - - - - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
3y = 21
y = 21.3 = 7
Substituting y = 7 into equation 1, it becomes
x - 4 × 7 = 9
x - 28 = 9
x = 9 + 28
x = 37
Answer:
y = 650·0.922^t
Step-by-step explanation:
At the end of each year, 92.2% of the amount at the beginning of the year remains. That is, the beginning amount is multiplied by 0.922. The exponent t in 0.922^t tells how many times (years) that multiplication has taken place. At the end of t years, the amount remaining in milligrams (y) is ...
y = 650·0.922^t
Let's solve this problem step-by-step.
STEP-BY-STEP EXPLANATION:
First, we will establish that the shape of the window is a semi-circle. This means we must use the formula for the perimeter of a semi-circle to obtain the perimeter of the window.
The formula for the perimeter of a semi-circle is as follows:
Let perimeter of window or semi-circle = P
P = [ 2( Pi )r / 2 ] + 2r
Where r = radius of circle or semi-circle
From this, we will simply use the value of the radius given from the diagram in the problem and substitute it into the formula to obtain the perimeter of the window.
P = [ 2( Pi )r / 2 ] + 2r
r = 20
THEREFORE:
P = [ 2( Pi )( 20 ) / 2 ] + 2( 20 )
P = 20( Pi ) + 40
P = 102.83...cm^2
P = 102.8cm^2 ( to the nearest tenth )
FINAL ANSWER:
Therefore, the perimeter of the window is 102.8cm^2 ( to the nearest tenth ).
Hope this helps! :)
Have a lovely day! <3
Answer: 0.9
Step-by-step explanation: