If a varies inversely as the cube root of b and a=1 when b=64, find b

  b = 64/a³

Step-by-step explanation:

Using the given information, we can only find a relation between a and b. We cannot find any specific value for b.

Since a varies inversely as the cube root of b, we have ...

  a = k/∛b

Multiplying by ∛b lets us find the value of k:

  k = a·∛b = 1·∛64 = 4

Taking the cube of this equation gives ...

  64 = a³b

  b = 64/a³ . . . . . divide by a³

The value of b is ...

  b = 64/a³

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step-by-step explanation:

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: