M = 3rt^2 - 2rv
2rv = 3rt^2 - M
v = (3rt^2 - M)/2r
Answer:
0.9 for the top box and 1.68 for the bottom box
Step-by-step explanation:
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Answer:
The change in volume is estimated to be 17.20 
Step-by-step explanation:
The linearization or linear approximation of a function
is given by:
where
is the total differential of the function evaluated in the given point.
For the given function, the linearization is:

Taking
inches and
inches and evaluating the partial derivatives we obtain:

substituting the values and taking
and
inches we have:

Therefore the change in volume is estimated to be 17.20 
Answer:
1) 25
2) 2
3) f(g(1)) = 42
Step-by-step explanation:
1) Given that f(x) = 4x^2 + 9
If x = -2
f(-2) = 4(-2)^2 + 9
f(-2) = 4(4) + 9
f(-2) = 16 + 9
f(-2) = 25
2) Given that f(x) = 4x - 6
y = 4x - 6
Replace y with x
x = 4y - 6
MAke y the subject of the forfmula
4y = x+ 6
y = (x+6)/4
SInce x = 2
f^(-1)(2) = (2+6)/4
f^(-1)(2) = 8/4 = 2
3) If f(x) = 6x and g(x) = x+6
f(g(x)) = f(x+6)
f(x+6) = 6(x+6)
Since x = 1
f(g(1)) = 6(1+6)
f(g(1)) = 6(7)
f(g(1)) = 42
C. 4
14 + 13 - (23)
27 - 23
4