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3 years ago

7

Convert the Cartesian equation 2 xy = 1 in polar equation form.

1 answer:

blondinia [14]3 years ago

7 0

2 cry = 1 polar equations form is

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Can anyone help me on number 9

ipn [44]

Answer:

3 1/2

Step-by-step explanation:

[(8/10+7/10)+2]= [(15/10)+2] = (2 15/10) = (3 5/10) = (3 1/2)

8 0

3 years ago

Rory is playing a video game where each game lasts 1 3/4 hours he wants to play for 9 hours today and evening how many games can

sesenic [268]

Answer: He will play 5 games in 9 hours .

Explanation:

In $1\frac{3}{4}\text hours$ , he is playing 1 game

So, in 1 hour , he will play = $\frac{4}{7} games$

In 9 hours, he will play

$=\frac{4}{7}\times 9\\=\frac{4\times9}{7}\\=5.14$

Number of games can't be in decimals it must be in integers so we will take 5 only .

so he will play only 5 games in 9 hours .

6 0

3 years ago

Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

djverab [1.8K]

I'll assume the ODE is

$y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}$

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

has roots at $r=1$ and $r=2$ . Then the characteristic solution is

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

$y'' - 3y' + 2y = e^x$

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

$y'' - 3y' + 2y = e^{2x}$

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

6 0

1 year ago

The baseball diamond is really a square. The distance between each of the bases is 90 feet. How far does the catcher have to thr

Zina [86]

A^2 + b^2 = c^2

base lines: home to first is a, first to second is b, home to second is c.

90^2 + 90^2 = c^2
or
$\sqrt{ {90}^{2} + {90}^{2} } = c$
$c = 127.28$
...approximately

5 0

3 years ago

Read 2 more answers

What are the coordinates of the vertex of the graph:

Aleks04 [339]

Answer is C. (-7, -16)

8 0

3 years ago

Read 2 more answers