Step-by-step explanation:
Using similar triangles, the height and width of the water is proportional to the height and width of the trough.
w / h = 5 / 1
w = 5h
The volume of the water is:
V = AL
V = (½ wh) (14)
V = 7wh
Substituting:
V = 7(5h)h
V = 35h²
Take derivative with respect to time:
dV/dt = 70h dh/dt
Given that dV/dt = 15 and h = ⅓:
15 = 70 (⅓) dh/dt
dh/dt = 9/14
dh/dt ≈ 0.643 ft/min
For this case we have that by definition, the equation of a line of the slope-intersection form is given by:
Where:
m: It is the slope of the line
b: It is the cut point with the y axis
By definition, if two lines are perpendicular then the product of their slopes is -1.
If we have:
Thus, the equation is of the form:
We substitute the point:
Finally, the equation is:
Answer:
Answer: cups of pineapple juice .
Step-by-step explanation:
Equation of direct proportion between x and y:
As per given,
Let x = quantity of pineapple juice and y = quantity of orange juice.
,
,
Put these values in an equation we get
Hence, he needs cups of pineapple juice .
Answer: The answer is $2.77.
Step-by-step explanation: Given that we have to pay the loan of $1300 at interest rate of 7.5% in 6 months. According to the table,
Amount for interest in payment 1 = $8.13,
Amount of interest in payment 2 = $6.79
and
Amount of interest in payment 3 = $5.45.
We can see here that the difference in the amounts to be paid in consecutive months will be same, i.e., the payments will form an arithmetic progression (A.P.).
The common difference = 8.13-6.79=6.79-5.45=1.34.
Therefore, amount of interest in payment 4 = $(5.45-1.34) = $4.11
and amount of interest in payment 5 = $(4.11-1.34) = $2.77.
Please see the attached modified table.
Thus, the answer is $2.77.
