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Trava [24]
4 years ago
15

Find the derivative of f(x)= sqrt(12-x^6)

Mathematics
1 answer:
In-s [12.5K]4 years ago
5 0

Answer:

-3x^5 /√(12 - x^6).

Step-by-step explanation:

f(x)= sqrt(12-x^6)

f(x) = ( 12 - x^6)^1/2

Using the Chain Rule:

f'(x) = 1/2(12 - x^6)^-1/2 * -6x^5

=  -6x^5 /  2(12 - x^6) ^ 1/2

= -6x^5 /2√(12 - x^6)

= -3x^5 /√(12 - x^6).

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fenix001 [56]

9514 1404 393

Answer:

   5/9 m/min

Step-by-step explanation:

The depth of the water is 2/5 of the depth of the trough, so the width of the surface will be 2/5 of the width of the trough:

  2/5 × 2 m = 4/5 m

Then the surface area of the water is ...

  A = LW = (18 m)(4/5 m) = 14.4 m²

The rate of change of height multiplied by the area gives the rate of change of volume:

  8 m³/min = (14.4 m²)(h')

  h' = (8 m³/min)/(14.4 m²) = 5/9 m/min

8 0
3 years ago
What is the median of this set of measurements? 10cm, 15cm, 15cm, 18cm, 20cm.
Alinara [238K]

Answer:

15 cm

Step-by-step explanation:

Median means middle number

10,15,15,18,20

4 0
3 years ago
Read 2 more answers
State the restrictions, if any.<br> F(x)= x/x2-81
Crazy boy [7]

Answer:

f=1/x^2-81

Step-by-step explanation:

Step 1: Multiply both sides by x^2-81.

fx3−81fx=x

Step 2: Factor out variable f.

f(x3−81x)=x

Step 3: Divide both sides by x^3-81x.

f(x3−81x)

x3−81x =x x3−81x f= 1 x2−81

3 0
3 years ago
Solve for the area of the combined shape
ludmilkaskok [199]

Answer:

47 cm²

Step-by-step explanation:

3(9 - 4) + 8 × 4 = 15 + 32 = 47

7 0
3 years ago
Determine if the following relation represents a function or not.
artcher [175]

Answer:

It is a function.

Step-by-step explanation:

Functions are relations in which one domain value is assigned to exactly one range value. The x-value must not repeat in the relation set for it to be a function.

{(2,3), (4,3), (6,3), (5,9), (3,9)}

There are no repeating x-values given.

The relation should be a function.

Hope this helps.

6 0
3 years ago
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