$\bf \cfrac{dy}{dx}=2xy\implies \cfrac{d^2y}{dx^2}=2\stackrel{product~rule}{\left( 1\cdot y+x\cfrac{dy}{dx} \right)}\implies \cfrac{d^2y}{dx^2}=2y+2x\cfrac{dy}{dx}$

4 0

3 years ago

A knitter wants to make a rug for a dollhouse. The length of the rug will be 2 inches more than it’s width. The total area of th

steposvetlana [31]

The width of the rug is 3 inches

Step-by-step explanation:

A knitter wants to make a rug for a dollhouse

The length of the rug will be 2 inches more than it’s width
The total area of the rug ( in square inches) based on the width w of the rug (in inches ) is given by A(w) = w (2 + w)
The desired area of the rug is 15 square inches

We need to find the width of the rug

∵ The area of the rug is A(w) = w(2 + w)

- Simplify the right hand side

∴ A(w) = 2w + w²

∵ The desired area of the rug is 15 square inches

- Equate A(w) by 15

∴ 2w + w² = 15

- Subtract 15 from both sides

∴ 2w + w² - 15 = 0

- Its a quadratic equation arrange its terms from the greatest power of x

∴ w² + 2w - 15 = 0

Factorize it into two binomial factors

∵ w² = w × w

∵ 15 = 3 × 5

∵ 5w - 3w = 2w

∴ w² + 2w - 15 = (w -3)(w + 5)

∴ (w - 3)(w + 5) = 0

- Equate each factor by 0

∴ w - 3 = 0 OR w + 5 = 0

∵ w - 3 = 0

- Add 3 to both sides

∴ w = 3

∵ w + 5 = 0

- Subtract 5 from both sides

∴ w = -5 ⇒ rejected because no dimension with -ve value

∴ w = 3 only

The width of the rug is 3 inches

Learn more:

You can learn more about the quadratic equation in brainly.com/question/9328925

#LearnwithBrainly

8 0

4 years ago

pls help! how would I solve this problem ?The figures shown are similar. Find the lengths of x, y, and z.

Fynjy0 [20]

When looking at it, you can see that the location of the 9 and 12 are the same. So, you can solve by first finding the difference in the two. Turns out 12 is 4/3 times bigger than 9. So, divide each of your sides to figure out what each side is.
X = 17.25
Y = 18
Z = 17.25

Hope this helps :)

3 0

2 years ago