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kifflom [539]
3 years ago
6

Simplify the radical 7√7-2√28

Mathematics
2 answers:
Umnica [9.8K]3 years ago
7 0

ANSWER

3 \sqrt{7}

EXPLANATION

The given radical is

7 \sqrt{7}  - 2 \sqrt{28}

Remove the perfect square from the second radical.

= 7 \sqrt{7}  - 2 \sqrt{4 \times 7}

= 7 \sqrt{7}  - 2 \sqrt{4}  \times  \sqrt{7}

= 7 \sqrt{7}  - 2  \times 2 \times  \sqrt{7}

= 7 \sqrt{7}  - 4 \sqrt{7}

Subtract the like radicals

= 3 \sqrt{7}

lions [1.4K]3 years ago
5 0

Answer:

7√7-2√28 = 3√7

Step-by-step explanation:

We have given the expression:

7√7-2√28

We have to simplify the expression.

As we know that:

√28 = √4×7

Then we have,

7√7-2√28 = 7√7-2√4×7

7√7-2√28 = 7√7-2√4×√7

7√7-2√28 = 7√7-2×2×√7

7√7-2√28 = 7√7-4√7

7√7-2√28 = 3√7

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Write the composite function in the form f(g(x)).[Identify the inner function u = g(x)and the outer function
Vadim26 [7]

Answer:

a) (g(x), f(u)) = ( 7*√x , e^u )

b)   y ' = 3.5 * e^(7*√x) / √x

Step-by-step explanation:

Given:

- The given function:

                                       y = e^(7*√x)

Find:

- Express the given function as a composite of f(g(x)). Where, u = g(x) and y = f(u).

- Express the derivative of y, y'?

Solution:

- We will assume the exponent of  the natural log to be the u. So u is:

                                     u = g(x) = 7*√x

- Then y is a function of u as follows:

                                     y = f(u) = e^u

- The composite function is as follows:

                                    (g(x), f(u)) = ( 7*√x , e^u )

- The derivative of y is such that:

                                    y = f(g(x))

                                    y' = f' (g(x) ) * g'(x)

                                    y' = f'(u) * g'(x)

                                    y' = e^u* 3.5 / √x

- Hence,

                                   y ' = 3.5 * e^(7*√x) / √x

                               

7 0
3 years ago
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