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3 years ago

I will give brainiest to whoever answers correctly !!

Mathematics

1 answer:

Dmitriy789 [7]3 years ago

7 0

Answer:

27.4

BUT I AM NOT SURE IF ITS CORRECT!!!!

Step-by-step explanation:

REFER TO PIC ATTACHED

HOPE IT HELPS

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Use the method of "undetermined coefficients" to find a particular solution of the differential equation. (The solution found ma

Naddika [18.5K]

Answer:

The particular solution of the differential equation

= $\frac{-1,36,656cos5x+1,89,800 sin5x}{-1204}$ + $\frac{1}{37}185e^{6x})$

Step-by-step explanation:

Given differential equation y''(x) − 10y'(x) + 61y(x) = −3796 cos(5x) + 185e6x

The differential operator form $(D^{2} -10D+61)y(x) = −3796 cos(5x) + 185e^{6x}$

Rules for finding particular integral in some special cases:-

let f(D)y = $e^{ax}$ then

the particular integral $\frac{1}{f(D)} (e^{ax} ) = \frac{1}{f(a)} (e^{ax} ) if f(a)$ ≠ 0

let f(D)y = cos (ax ) then

the particular integral $\frac{1}{f(D)} (cosax ) = \frac{1}{f(D^2)} (cosax ) =\frac{cosax}{f(-a^2)}$ f(-a^2) ≠ 0

Given problem

$(D^{2} -10D+61)y(x) = −3796 cos(5x) + 185e^{6x}$

Particular integral:-

$P.I = \frac{1}{f(D)}( −3796 cos(5x) + 185e^{6x})$

$P.I = \frac{1}{D^2-10D+61}( −3796 cos(5x) + 185e^{6x})$

$P.I = \frac{1}{D^2-10D+61}( −3796 cos(5x) + \frac{1}{D^2-10D+61}185e^{6x})$

P.I = $I_{1} +I_{2}$

we will apply above two conditions, we get

$I_{1}$ =

$\frac{1}{D^2-10D+61}( −3796 cos(5x) = \frac{1}{(-25)-10D+61}( −3796 cos(5x) ( since D^2 = - 5^2)$ $= \frac{1}{(36-10D}( −3796 cos(5x) \\= \frac{1}{(36-10D}X\frac{36+10D}{36+10D} ( −3796 cos(5x)$

on simplification we get

= $\frac{1}{(36^2-(10D)^2}36+10D( −3796 cos(5x)$

= $\frac{-1,36,656cos5x+1,89,800 sin5x}{1296-100(-25)}$

= $\frac{-1,36,656cos5x+1,89,800 sin5x}{-1204}$

$I_{2}$ =

$\frac{1}{D^2-10D+61}185e^{6x}) = \frac{1}{6^2-10(6)+61}185e^{6x})$

$\frac{1}{37}185e^{6x})$

Now particular solution

P.I = $I_{1} +I_{2}$

P.I = $\frac{-1,36,656cos5x+1,89,800 sin5x}{-1204}$ + $\frac{1}{37}185e^{6x})$

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3 years ago

Hemework -13 . Express the ratio 20cm to 15m in the form 1:n

ankoles [38]

Answer:

1: 75

Step-by-step explanation:

20cm : 15m

Convert meters to cm

1 meter = 100 cm

15m = 15 x 100 = 1500 cm

20cm:1500cm

Divide both sides of the ratio by 20

=> 1 : 1500/20 = 1: 75

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2 years ago

How to write an algebraic expression for 0.75 + 0.25

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Hello meroo girolar syin seyirciler justein bieberin in allah belasini versin olsun o oruspu
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3 years ago

An artist creates a right prism whose base are regular pentagons. He wants to paints the lateral surfaces of the prism. One can

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He needs 13 cans of paint.

The lateral area is given by the area of 5 rectangles, whose dimensions are 15 by 5:
5(15)(5) = 375

Divide this by 30:
375/30 = 12.5 ≈ 13

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Sam bought 2 3/4 pounds of shrimp and 2 1/2 pounds of crabmeat. How much seafood did he buy?

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