Can someone help me please my grades close today?
1 answer:
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Answer:
-3.47 inches per minute
Step-by-step explanation:
Let the height be 'h' for any time 't'.
Given:
Length of the prism (L) = 10 in
Width of the prism (w) = 16 in
The rate of change of volume of prism is, (The negative sign implies the volume decreases with time.)
Now, rate of change of height of prism =
Length and width remains constant.
Now, we know that, volume of a rectangular prism is given as:
Volume = Length × width × Height
Now, differentiating both sides with respect to time 't', we get:
Plug in the given values and solve for . This gives,
The negative sign implies the height decreases with time.
Therefore, the the rate of change, in inches per minute, of the height when the height is 3 inches is -3.47 inches per minute.
Answer:
change in capital to Improvement in ROE = 2.518%
Step-by-step explanation:
To calculate the improvement in ROE, calculate ROE for current capital structure by using DuPont analysis.
where
Return on Assets = Net Income / Total Assets
Equity Multiplier = Total Assets / Equity
Equity = Total assets x (1 – debt to capital ratio)
= $250,000 x (1-37%)
= $157,500
Equity Multiplier = Total Assets / Equity
ROE =0.075 x 1.58 = 0.11904761 or 11.905%
ROE after change in capital structure:
Equity = Total assets x (1 – debt to capital ratio)
= $250,000 x (1-48%) = $130,000
ROE = (18,750/250,000) x (250,000/130,000)
= 0.1442307692307692 or 14.423%
change in capital to Improvement in ROE = 14.423% - 11.905% = 2.518%