(6x10^-6) (5.2x10^4 scientific notation

Mathematics

1 answer:

Art [367]3 years ago

4 0

Step-by-step explanation:

$(6 \times {10}^{ - 6} )(5.2 \times {10}^{4} ) \\ = 6 \times 5.2 \times {10}^{ - 6} \times {10}^{4} \\ = 31.2 \times {10}^{4 - 6} \\ = 31.2 \times {10}^{ - 2} \\ = 0.312 \\ = 3.12 \times {10}^{ - 1}$

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Scalcet8 4. 2. 26. suppose that 2 ≤ f '(x) ≤ 4 for all values of x. what are the minimum and maximum possible values of f(4) − f

ziro4ka [17]

The minimum value of f(4) - f(1) is <u>6</u>.

The maximum value of f(4) - f(1) is <u>12</u>.

In the question, we are given that, 2 ≤ f'(x) ≤ 4 for all values of x.

Taking the given inequality as (i).

We are asked to find the minimum and maximum possible values of f(4) - f(1).

We multiply (i) by dx throughout, to get:

4dx ≤ f'(x)dx ≤ 5dx.

To find this, we integrate (i) in the definite interval [4, 1] with respect to dx, to get:

$\int_{1}^{4}2dx \leq \int_{1}^{4}f'(x)dx \leq \int_{1}^{4}4dx\\\Rightarrow [2x]_{1}^{4} \leq [f(x)]_{1}^{4} \leq [4x]_{1}^{4}\\\Rightarrow 2*4 - 2*1 \leq f(4)-f(1) \leq 4*4 - 4*1\\\Rightarrow 6 \leq f(4) -f(1) \leq 12$