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Anna007 [38]
3 years ago
11

Can someone explain to me this derivative : y=3x√x

Mathematics
1 answer:
dimaraw [331]3 years ago
6 0

Answer:

(9/2)√x.

Step-by-step explanation:

Convert the radical to an exponent.

x√x = x^1 * x^1/2

= x^(1 + 1/2)

= x^3/2

So the derivative of 3x^3/2 is found as follows:

y' = 3 * 3/2x^(3/2 - 1)

= (9/2)x^1/2

= (9/2)√x.

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An apartment complex has a floor plan with dimensions shown. To effectively air condition a room, 20 BTU’s are required for ever
kifflom [539]

12,900 BTU's are required to cool the room effectively.

Step-by-step explanation:

Step 1:

We must calculate the area of the entire shape to determine the minimum BTU's required to cool the room effectively.

It is made up of a semi-circle a rectangle, and a trapezoid.

Step 2:

The area of a semi-circle =\frac{ \pi r^{2} }{2} .

Here, the diameter is 20 feet so the radius is 10 feet.

The area of the semi-circle =\frac{ \pi r^{2} }{2} =\frac{ (\pi) (10^{2}) }{2} = 157.079 square feet.

The area of a rectangle = (l)(w).

The length of the rectangle is 22 feet and the width is 20 feet.

The area of a rectangle = (l)(w) =(22)(20) = 440 square feet.

The area of a trapezoid =\frac{a+b}{2} (h).

Here a=12, b= 20, h= 3.

The area of a trapezoid =\frac{12+20}{2} (3) = 48 square feet.

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The total area of the floor plan =157.079+440+48 = 645.079 square feet.

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