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3 years ago

I need help with this

Mathematics

1 answer:

Semmy [17]3 years ago

5 0

9514 1404 393

Answer:

x = 32
y = 51

Step-by-step explanation:

Angle U = angle N = 180° -142° -24° = 14°

The expression for angle U tells us the value of x.

2x -50 = 14

x -25 = 7 . . . . . divide by 2

x = 32 . . . . . . . .add 25

The measure of side SU is the same as that for side PN.

13 = (2x -y)

y = 2x -13 = 2(32) -13 . . . . solve for y, substitute for x

y = 51

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Write the given differential equation in the form L(y) = g(x), where L is a linear differential operator with constant coefficie

melamori03 [73]

Answer:

The complete solution is

$\therefore y= Ae^{3x}+Be^{-\frac13 x}-\frac43$

Step-by-step explanation:

Given differential equation is

3y"- 8y' - 3y =4

The trial solution is

$y = e^{mx}$

Differentiating with respect to x

$y'= me^{mx}$

Again differentiating with respect to x

$y''= m ^2 e^{mx}$

Putting the value of y, y' and y'' in left side of the differential equation

$3m^2e^{mx}-8m e^{mx}- 3e^{mx}=0$

$\Rightarrow 3m^2-8m-3=0$

The auxiliary equation is

$3m^2-8m-3=0$

$\Rightarrow 3m^2 -9m+m-3m=0$

$\Rightarrow 3m(m-3)+1(m-3)=0$

$\Rightarrow (3m+1)(m-3)=0$

$\Rightarrow m = 3, -\frac13$

The complementary function is

$y= Ae^{3x}+Be^{-\frac13 x}$

y''= D², y' = D

The given differential equation is

(3D²-8D-3D)y =4

⇒(3D+1)(D-3)y =4

Since the linear operation is

L(D) ≡ (3D+1)(D-3)

For particular integral

$y_p=\frac 1{(3D+1)(D-3)} .4$

$=4.\frac 1{(3D+1)(D-3)} .e^{0.x}$ [since $e^{0.x}=1$ ]

$=4\frac{1}{(3.0+1)(0-3)}$ [ replace D by 0 , since L(0)≠0]

$=-\frac43$

The complete solution is

y= C.F+P.I

$\therefore y= Ae^{3x}+Be^{-\frac13 x}-\frac43$

4 0

3 years ago

The equation x2 − 6x − 27 = 0 when solved is:

Amiraneli [1.4K]

Answer:

-3 , 9

Step-by-step explanation:

Sum = - 6

Product = -27

Factors = 3, -9

x² - 6x-27 = 0

x² + 3x - 9x - 9*3 = 0

x(x + 3) - 9(x + 3) = 0

(x + 3) (x - 9) = 0

x +3 = 0 ; x - 9 = 0

x = - 3 ; x = 9

Solution: x = -3 , 9

8 0

3 years ago

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svlad2 [7]

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3 years ago

If r and s represent two numbers, write the following:

Tanzania [10]

Answer:

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4 0

2 years ago

A company manufactures both mountain bikes and trail bikes. The cost of materials for a mountain bike is $40, and the cost of ma

Keith_Richards [23]

An equation is formed when two equal expressions. The company is planning to produce 25 mountain bikes and 15 trail bikes.

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of mountain bikes produced by the company be x, while the number of trail bikes produced by the company is y.

The cost of materials for a mountain bike is $40, and the cost of materials for a trail bike is $40. Also, the budget of the company is $1,600. Therefore,

1600 = 40x + 40y

x + y = 40

y = 40-x

The cost of labour to manufacture a mountain bike is $90, and the cost of labour to manufacture a trail bike is $30. Also, the budget for labour is $2,700.

2700 = 90x + 30y

2700 = 90x + 30(40-x)

2700 = 90x + 1200 - 30x

1500 = 60x

x = 25

Substitute the value of x,

y = 40 - x

y = 15

Hence, the company is planning to produce 25 mountain bikes and 15 trail bikes.

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6 0

2 years ago

I need help with this ​

I need help with this