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3 years ago

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

Mathematics

1 answer:

Mrrafil [7]3 years ago

7 0

Answer:

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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6 0

3 years ago

(a) Use a linear approximation to estimate f(0.9) and f(1.1). f(0.9) ≈ f(1.1) ≈ (b) Are your estimates in part (a) too large or

olasank [31]

Answer:

(Missing part of the question is attached)

$L(x)=2x+3$

Estimates are too large.

Step-by-step explanation:

Suppose the only information we know about the function is:

$f(1)=5$

where the graph of its derivative is shown in the attachment

If the function $f\\$ is differentiable at point $x=1$ , the tangent line to the graph of $f$ at 1 is given by the equation:

$y=f(1) +f'(1)(x-1)$

So we call the linear function:

$L(x)=f(1) +f'(1)(x-1)$

We know the $f(1)=5$ as it is given in the question, and $f'(1)=2$ from the graph attached. Substitute in the equation of $L(x)$ .

$L(x)=5+2(x-1)\\L(x)=5+2x-2\\L(x)=2x+3\\$

At x=1, $f'(x)$ is positive but it is decreasing. However. if we draw the tangent lines, we see that the tangent lines are becoming less steeper, so the tangent lines lie above the curve $f$ . Thus, The estimates are too large.