Ask question

Ask question

All categories

3 years ago

15

he perimeter of a rectangle is 48 m. If the width were doubled and the length were increased by 24 m, the perimeter would be 112

m. What are the length and width of the rectangle?

1 answer:

ratelena [41]3 years ago

8 0

I believe its 36 but im not sure

You might be interested in

Compute the second partial derivatives ∂2f ∂x2 , ∂2f ∂x ∂y , ∂2f ∂y ∂x , ∂2f ∂y2 for the following function. f(x, y) = 2xy (x2 +

blsea [12.9K]

Answer with step-by-step explanation:

We are given that a function

$f(x,y)=2xy(x^2+y^2)^2$

Differentiate partially w.r.t x

Then, we get

$\frac{\delta f}{\delta x}=2y(x^2+y^2)^2+8x^2y(x^2+y^2)=(x^2+y^2)(2x^2y+2y^3+8x^2y)=2(5x^2y+y^3)(x^2+y^2)$

Differentiate again w.r.t x

$\frac{\delta^2f}{\delta x^2}=2(10xy)(x^2+y^2)+4x(5x^2y+y^3)=20x^3y+20xy^3+20x^3y+4xy^3=40x^3y+24xy^3$

Differentiate function w.r.t y

$\frac{\delta f}{\delta y}=2x(x^2+y^2)^2+2xy\times 2(x^2+y^2)\times 2y$

$\frac{\delta f}{\delta y}=(x^2+y^2)(2x^3+2xy^2+8xy^2)=2(x^2+y^2)(x^3+5xy^2)$

Again differentiate w.r.t y

$\frac{\delta^2f}{\delta x^2}=2(2y)(x^3+5xy^2)+20xy(x^2+y^2)=4x^3y+20xy^3+20x^3y+20xy^3=24x^3y+40xy^3$

Differentiate partially w.r.t y

$\frac{\delta^2f}{\delta y\delta x}=2(2y(5x^2y+y^3)+(x^2+y^2)(5x^2+3y^2))=10x^4+36x^2y^2+10y^4$

$\frac{\delta^2f}{\delta y\delta x}=10x^4+36x^2y^2+10y^4$ $\frac{\delta^2f}{\delta x\delat y}=2(2x(x^3+5xy^2)+(3x^2+5y^2)(x^2+y^2))=10x^4+36x^2y^2+10y^4$

$\frac{\delta^2f}{\delta x\delat y}=10x^4+36x^2y^2+10y^4$

Hence, if f(x,y) is of class $C^2$ (is twice continuously differentiable), then the mixed partial derivatives are equal.

i.e $\frac{\delta^2f}{\delta y\delta x}=\frac{\delta^2f}{\delta x\delta y}$

8 0

4 years ago

Divide 1 1/5 divided into 5 1/4

alina1380 [7]

Answer:

8 over 35 or Decimal Form: 0.228571

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A circle has a circumference of 16π. What is the area of the circle? Show your work.

DIA [1.3K]

Answer:

i cant show my work im sorry i cant help

Step-by-step explanation:

1

6 0

3 years ago

Which statement describes the system of equations

Contact [7]

Answer:

2y-2x-2y= - 22x = 0x + 2y = 1

Step-by-step explanation:

7 0

3 years ago

WILL GIVE BRAINLIEST, RATING, AND THANKS.

attashe74 [19]

Juan went slower because it took him more minutes to go the same distance at Rita. She went 8 miles in 8 minutes. Juan went 8 miles in like 17 minutes

6 0

3 years ago