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3 years ago

Factor 2uv+5u+8v+20 factor polynomials

Mathematics

2 answers:

dimaraw [331]3 years ago

5 0

Answer:

(2v + 5)(u + 4)

Step-by-step explanation:

2uv + 5u + 8v + 20 ( factor first/second and third/fourth terms )

= u(2v + 5) + 4(2v + 5) ← factor out (2v + 5) from each term

= (2v + 5)(u + 4)

UNO [17]3 years ago

3 0

Answer: $\left(2v+5\right)\left(u+4\right)$

Step-by-step explanation:

Favtor the terms:

2uv+5u

$u\left(2v+5\right)$

8v+20

$4\left(2v+5\right)$

Add the factored terms and factor out the common term 2v+5:

$u\left(2v+5\right)+4\left(2v+5\right)$

$\left(2v+5\right)\left(u+4\right)$

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Use the substitution x = et to transform the given Cauchy-Euler equation to a differential equation with constant coefficients.

Anika [276]

Answer:

$\boxed{\sf \ \ \ ax^2+bx^{-10} \ \ \ }$

Step-by-step explanation:

Hello,

let's follow the advise and proceed with the substitution

first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t

$x(t)=e^t\\\dfrac{dx}{dt}=e^t\\y'(t)=\dfrac{dy}{dt}=\dfrac{dy}{dx}\dfrac{dx}{dt}=e^ty'(x)y'(x)=e^{-t}y'(t)\\y''(x)=\dfrac{d^2y}{dx^2}=\dfrac{d}{dx}(e^{-t}\dfrac{dy}{dt})=-e^{-t}\dfrac{dt}{dx}\dfrac{dy}{dt}+e^{-t}\dfrac{d}{dx}(\dfrac{dy}{dt})\\=-e^{-t}e^{-t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}\dfrac{dt}{dx}=-e^{-2t}\dfrac{dy}{dt}+e^{-t}\dfrac{d^2y}{dt^2}e^{-t}\\=e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt})$

Now we can substitute in the equation

$x^2y''(x)+9xy'(x)-20y(x)=0\\ e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\ \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\ \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\$

so the new equation is

$y''(t)+ 8y'(t)-20y(t)=0$

the auxiliary equation is

$x^2+8x-20=0\\ x^2-2x+10x-20=0\\x(x-2)+10(x-2)=0\\(x+10)(x-2)=0\\ x=-10\text{ or }x=2$

so the solutions of the new equation are

$y(t)=ae^{2t}+be^{-10t}$

with a and b real

$x(t)=e^t\\ t(x)=ln(x)$

$y(x)=ae^{2ln(x)}+be^{-10ln(x)}=ax^2+bx^{-10}$

hope this helps

do not hesitate if you have any questions

8 0

4 years ago

The two triangles shown have the same perimeters. What is the perimeter of each triangle

Shkiper50 [21]

Answer:

28 units

Step-by-step explanation:

Since the perimeter of both triangles is same,

the sum of all sides of first triangle = sum of all sides of second triangle

or, 6x + 3 + 2x + 4x = 5x + 5x + 3x + 2

or, 12x + 4 = 13x + 2

or, 4-2 = 13x - 12x

or, 2 = x

Now,

Putting the value of x in the perimeter of first triangle,

12x + 4= 12* 2+ 4

= 28 units

7 0

3 years ago

Grace made $3,300 in interest by placing $10,000 in a savings account with simple interest

antoniya [11.8K]

Answer:

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Step-by-step explanation:

3,300 / 3 = 1,100

$1,100 per year

1,100 / 10000

.11 = 11%

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2 years ago

How do i calculate volume and the round it to the nearest cubric centimeter? where do i start?

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Answer:

base times height

Step-by-step explanation:

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3 years ago

Which is the simplified form of the equation 8p + 4 = -p + 7 + 2p + 3p ?

oksian1 [2.3K]

8p + 4 = -p + 7 + 2p + 3p

8p + 4 = 4p + 7 <== simplified form

6 0

3 years ago