q=D+is+partly+constant+and+partly+varies+with+v+when+v+=40,D=150,and+when+v=54,D=192+find the value of v when D =100
To solve for v when D = 100, we can use the given information that D is partly constant and partly varies with v.
Let's first find the constant part of D. When v = 40, D = 150. So, the constant part of D is 150.
Now, let's find the variable part of D. When v = 40, D = 150, and when v = 54, D = 192. To find the variable part, we subtract the constant part from the total value of D.
Variable part of D = D - constant part of D = 192 - 150 = 42.
Now, we can set up a proportion to find the value of v when D = 100:
(variable part of D) / (variable part of v) = (constant part of D) / (constant part of v)
42 / (54 - 40) = 150 / (v - 40)
42 / 14 = 150 / (v - 40)
Cross-multiplying:
42(v - 40) = 14 * 150
42v - 1680 = 2100
42v = 2100 + 1680
42v = 3780
v = 3780 / 42
v = 90
Therefore, when D = 100, the value of v is 90.