We split [2, 4] into subintervals of length ,
so that the right endpoints are given by the sequence
for . Then the Riemann sum approximating
is
The integral is given exactly as , for which we get
To check: we have
For this, we need to know the length of the base at the time of interest. It will be
... A = (1/2)bh
... b = (2A)/h = 2(81 cm²)/(10.5 cm) = 108/7 cm
Differentiate the formula for area and plug in the given numbers.
... A = (1/2)bh
... A' = (1/2)(b'h +bh')
... 3.5 cm²/min = (1/2)(b'·(10.5 cm) + (108/7 cm)·(2.5 cm/min))
... 7 cm²/min = 10.5b' cm + 38 4/7 cm²/min . . . . simplify a bit
... -31 3/7 cm²/min = 10.5b' cm . . . . . . . . . . . . . . . subtract 38 4/7 cm²/min
... (-220/7 cm²/min)/(10.5 cm) = b' ≈ -3.0068 cm/min
The base is changing at about -3 cm/min.
Because JKLM is a parallelogram, MT = TK.
MT: 8y + 18
TK : 12y - 10
MT = TK
8y + 18 = 12y - 10
8y - 12y = -10 -18
-4y = -28
y = -28/-4
y = 7
MT: 8y + 18 → 8(7) + 18 = 56 + 18 = 74
<span>TK : 12y - 10 </span>→ 12(7) -10 = 84 - 10 = 74
The value of y is 7.
Answer:
9x-10y
Step-by-step explanation:
9x+y-2y-9y(Multiply by 1)
Combine like terms
9x-10y