If y=ws^3/d^4
find the % increase in 'y' when 'w' increases by 2% and 's' decreases by 3% and 'd' increasee by 1%......
There a little error in the first question i post here it is plz i need the working and explanation
dy/dw = s^3/d^4
dy/ds = 3 w s^2/d^4
dy/dd = [d^4(0) - 4 w s^3 d^3 ] / d^8
= - 4 w s^3 / d^5
total change:
dy = dy/dw * dw + dy/ds * ds + dy/dd * dd
if all variables are 1
y = 1
then the changes
dw = .02
ds = -.03
dd = .01
so
dy = 1 * .02 - 3 *.03 - 4 * .01
= .02 -.09 - .04
= -.11
or Down 11%
No calculus needed here, but Damon's exposition is clear. Let's see another easy way. The new value is
(1.02w)(0.97s)^3/(1.01d)^4
= (1.02)(0.97^3)/(1.01^4) ws^3/d^4
= 0.8946 ws^3/d^4
= 0.8946y
so, the y value has decreased by 10.54%
To find the percentage increase in 'y' when 'w' increases by 2%, 's' decreases by 3%, and 'd' increases by 1%, we need to calculate the new value of 'y' and then calculate the percentage increase.
Let's break down the steps:
1. Calculate the new value of 'w' after a 2% increase:
New 'w' = (1 + 2/100) * 'w'
2. Calculate the new value of 's' after a 3% decrease:
New 's' = (1 - 3/100) * 's'
3. Calculate the new value of 'd' after a 1% increase:
New 'd' = (1 + 1/100) * 'd'
4. Substitute the new values of 'w', 's', and 'd' into the expression for 'y':
New 'y' = 'w' * ('s')^3 / ('d')^4
5. Calculate the percentage increase in 'y':
Percentage increase = (New 'y' - Initial 'y') / Initial 'y' * 100%
Here are the step-by-step calculations:
1. New 'w' = (1 + 2/100) * 'w'
2. New 's' = (1 - 3/100) * 's'
3. New 'd' = (1 + 1/100) * 'd'
4. New 'y' = 'w' * ('s')^3 / ('d')^4
5. Percentage increase = (New 'y' - Initial 'y') / Initial 'y' * 100%
Plug in the values and perform the calculations to find the final result.
To find the percent increase in 'y' when 'w' increases by 2%, 's' decreases by 3%, and 'd' increases by 1%, we need to first calculate the original value of 'y' and then calculate the new value of 'y' after the changes to 'w', 's', and 'd' have been made.
Let's start with the original equation:
y = ws^3/d^4
Now, let's calculate the original value of 'y' using the given values of 'w', 's', and 'd'.
Next, we will calculate the new values of 'w', 's', and 'd' after their respective changes:
1. Increase 'w' by 2%:
new_w = w + (w * 2/100)
2. Decrease 's' by 3%:
new_s = s - (s * 3/100)
3. Increase 'd' by 1%:
new_d = d + (d * 1/100)
Now, substitute the new values of 'w', 's', and 'd' into the original equation to find the new value of 'y':
new_y = new_w * (new_s)^3 / (new_d)^4
Finally, to calculate the percent increase in 'y', we can use the formula:
percent increase = ((new_y - original_y) / original_y) * 100
Let's plug in the values and do the calculations.