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3 years ago

The capacity of a small children's swimming pool is 105 gallons of water. There

Mathematics

1 answer:

gizmo_the_mogwai [7]3 years ago

6 0

Answer:

11.25 minutes

Step-by-step explanation:

The capacity of the swimming pool is 105 gallons of water.

There are currently 15 gallons of water

∴I need to fill (105-15) = 90 gallons of water

Now,

8 gallons of water are filled within 1 minute

∴1 gallon of water will be filled within = 1/8 minute

∴90 gallons of water will be filled within = 90/8 minutes

=11.25 minutes

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If f(x) = 9x10 tan−1x, find f '(x).

djverab [1.8K]

Answer:

$\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = 9x^{10} \tan^{-1}(x)$

Step 2: Differentiate

[Function] Derivative Rule [Product Rule]: $\displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle f'(x) = 9 \frac{d}{dx}[x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Basic Power Rule: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]$
Arctrig Derivative: $\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + \frac{9x^{10}}{x^2 + 1}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

7 0

2 years ago

In Jaden’s yard, there is a triangular garden patch. He wants to plant a geranium in the patch at a point equidistant from all i

Lelu [443]

Answer:

Jaden has to plant the geranium in the circumcentre of the triangular yard in order such that it is equidistant from all its vertices.

Step-by-step explanation:

In Jaden’s yard, there is a triangular garden patch. He wants to plant a geranium in the patch at a point equidistant from all its vertices.

" The CIRCUMCENTER (C) of a triangle is the point in the plane equidistant from the three vertices of the triangle "

Hence Jaden has to plant the geranium in the circumcentre of the triangular yard in order such that it is equidistant from all its vertices.

5 0

2 years ago

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What is the factored form of the polynomial? X^2 -12+27?

Natali5045456 [20]

Answer:

(x-9)(x-3)

Step-by-step explanation:

Look to the number on the right, 27, and list out the factors. (1 and 27, 3 and 9, -1 and -27, -3 and -9)

Next, find the factors that would equal the middle number, -12, when added. -3 and -9 add to -12. Therefore, choose these numbers and put them in the form (x-9)(x-3).

5 0

2 years ago

Using a calculator, find the square root (to the nearest tenth). Square root of 69,081 =

Lelu [443]

Square root of 69,081 is 262.832646, so the answer to the nearest tenth will be 262.8. Good luck!

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2 years ago

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Man i wish i could see this answer

strojnjashka [21]

Man, I wish I could see this answer.
Just copy you that the best answer.

7 0

3 years ago