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2 years ago

Find the area of the square rug if its side is (6x + 1) feet. The area of the square rug is ( )

Mathematics

1 answer:

Assoli18 [71]2 years ago

8 0

Area of a square:

A= side^2

= (6x + 1) ^2

=<u> 36x^2 + 12x + 1 feet^2</u>

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Find the second derivative at the point (1,2), given the function below. y^2-2=2x^3

vagabundo [1.1K]

Solution:

Given:

$y^2-2=2x^3$

Lets First Differentiate the given equation with respect to x

$\frac{d}{dx} ( y^2 - 2 ) = \frac{d}{dx} 2x^3$

$2y \cdot \frac{dy}{dx} - 0 = 6x^2$

$\frac{dy}{dx} = \frac{6x^2}{2y}$

$\frac{dy}{dx} = \frac{3x^2}{y}$ -----------------------(1)

this can be rewritten as

$\frac{dy}{dx} =3x^2y^{-1}$

Now differentiating again with respect to x

$\frac{d^2y}{dx^2} =6x^2y^{-1} + 3x^2 \cdot (-y^{-2}) \cdot \frac{dx}{dy}$

Now substituting (1) we get

$\frac{d^2y}{dx^2} =6x^2y^{-1} + 3x^2 \cdot (-y^{-2}) \cdot \frac{3x^2}{y}$

$\frac{d^2y}{dx^2} = \frac{6x^2}{y} + ( \frac{3x^2}{y^2}) \cdot \frac{3x^2}{y}$

$\frac{d^2y}{dx^2} = \frac{6x^2}{y} + ( \frac{9x^4}{y^3})$

At(1,2) $\frac{d^2y}{dx^2} = \frac{6(1)^2}{2} + ( \frac{9(1)^4}{(2)^3})$

$\frac{d^2y}{dx^2} = \frac{6}{2} + ( \frac{9}{8})$

$\frac{d^2y}{dx^2} = 3 + 1.125$

$\frac{d^2y}{dx^2} = 4.125$

5 0

3 years ago

Help asap please with this question

ExtremeBDS [4]

The answer is B. x<7

3 0

3 years ago

Expresa en metros<br>20km=

ser-zykov [4K]

Answer:

20000 m

Step-by-step explanation

multiplica el valor de longitud por 1000

7 0

3 years ago

Read 2 more answers

creativ13 [48]

If the diameter is 12 inches, the radius is 6 inches, because the radius is half the diameter.

Given the formula

$A=\pi r^2$

we have

$A=36\pi$

When you fold the circle in half, the resulting figure has half the area.

So, you start with a circle with area $36\pi$

You fold it once and you have a semicircle with area $18\pi$

You fold it twice and you have a quarter circle with area $9\pi$

7 0

3 years ago

What is x?

mrs_skeptik [129]

Answer:

x = 1/4

Step-by-step explanation:

−12x=−3 (Given)

x = 0.25 (Divide) (value became positive because negative was divided by negative).

0.25 in fraction = 1/4

4 0

2 years ago

Read 2 more answers