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2 years ago

PLEASE ANSWER THIS IT'S 30 POINTS

Mathematics

1 answer:

sergey [27]2 years ago

5 0

Answer:

Step-by-step explanation:

since we know that the 50 degrees is one side of the line then the angle that is strait opposite from this angle is 50 degrees, so 50+60=110degrees and 180-110=70, so x=70 degrees

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3y''-6y'+6y=e*x sexcx

Simora [160]

From the homogeneous part of the ODE, we can get two fundamental solutions. The characteristic equation is

$3r^2-6r+6=0\iff r^2-2r+2=0$

which has roots at $r=1\pm i$ . This admits the two fundamental solutions

$y_1=e^x\cos x$
$y_2=e^x\sin x$

The particular solution is easiest to obtain via variation of parameters. We're looking for a solution of the form

$y_p=u_1y_1+u_2y_2$

where

$u_1=-\displaystyle\frac13\int\frac{y_2e^x\sec x}{W(y_1,y_2)}\,\mathrm dx$
$u_2=\displaystyle\frac13\int\frac{y_1e^x\sec x}{W(y_1,y_2)}\,\mathrm dx$

and $W(y_1,y_2)$ is the Wronskian of the fundamental solutions. We have

$W(e^x\cos x,e^x\sin x)=\begin{vmatrix}e^x\cos x&e^x\sin x\\e^x(\cos x-\sin x)&e^x(\cos x+\sin x)\end{vmatrix}=e^{2x}$

and so

$u_1=-\displaystyle\frac13\int\frac{e^{2x}\sin x\sec x}{e^{2x}}\,\mathrm dx=-\int\tan x\,\mathrm dx$
$u_1=\dfrac13\ln|\cos x|$

$u_2=\displaystyle\frac13\int\frac{e^{2x}\cos x\sec x}{e^{2x}}\,\mathrm dx=\int\mathrm dx$
$u_2=\dfrac13x$

Therefore the particular solution is

$y_p=\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x$

so that the general solution to the ODE is

$y=C_1e^x\cos x+C_2e^x\sin x+\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x$

7 0

3 years ago

Hailey is making 36 mini- pumpkin pies. Each pie takes 6 ounces of pumpkin. The cans of pumpkin are 2 pounds each. How many can

serious [3.7K]

1 pound = 16 ounces

6 ounces each pie

36 mini pies to make

36 × 6 = 216 ounces needed to make 36 mini pies

216 ÷ 16 = 13.5 pounds
if each can of pumpkin is 2 pounds,
13.5 ÷ 2 = 6.75 so that would be 7 cans of pumpkin

3 0

3 years ago

Which is the graph of the linear equation X=-2

tankabanditka [31]

Answer:

photomath thats what u should use or put it in a calculator

3 0

4 years ago

The ratio of blue crayons to red crayons in a classroom is 32:28. The classroom has 16 blue crayons.

AnnyKZ [126]

32/28=16/x
32x= 448
x=14
There are 14 red crayons in classroom

5 0

2 years ago

Read 2 more answers

Pls can you help me here PLSSSS. it would mean a lot for me.

VLD [36.1K]

Answer:

27.183m. squared

Step-by-step explanation:

Find the base, then find the volume

Base:

(2.6*4.1*0.5)=

(10.66*0.5)=

5.33

Volume:

(5.33*5.1)=

27.183

Hope that this helped!

8 0

3 years ago