Evalute p-4 for p=24

The scale factor of rectangle JKLM to rectangle QRST

tiny-mole [99]

1) 4

2) 48

3) 8

4) same

5) square of the

stan twice

5 0

3 years ago

Read 2 more answers

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NemiM [27]

Answer: base times height divided by two

4 0

3 years ago

The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find

9966 [12]

Answer:

The particular integral of given differential equation

$y_{p} = \frac{1}{4} ( x - (\frac{-5}{4} ) (1))$

General solution of given differential equation

$y = y_{c} + y_{p}$

$Y (x) = C_{1} e^{x} + C_{2} e^{4x} + \frac{1}{4} ( x + (\frac{5}{4} ))$

Step-by-step explanation:

Step(i):-

Given Differential equation y'' − 5 y' + 4 y = x

Given equation in operator form

D²y - 5 Dy + 4 y = x

⇒ ( D² - 5 D + 4 ) y =x

⇒ f(D) y = Q

where f(D) = D² - 5 D + 4 and Q(x) = x

The auxiliary equation f(m) =0

m²-5 m + 4 =0

m² - 4 m - m + 4 =0

m ( m -4 ) -1 ( m-4) =0

(m - 1) =0 and ( m-4) =0

m = 1 and m =4

The complementary function

$Y_{c} = C_{1} e^{x} + C_{2} e^{4x}$

Step(ii):-

particular integral

Particular integral

$y_{p} = \frac{1}{f(D)} Q(x) = \frac{1}{D^{2} - 5 D + 4} X$

taking common '4'

$= \frac{1}{4(1 + (\frac{D^{2} - 5 D}{4} ))} X$

$=\frac{1}{4} (1 + (\frac{D^{2} -5D}{4})^{-1} )} X$

applying binomial expression

( 1 + x )⁻¹ = 1 - x + x² - x³ +.....

$=\frac{1}{4} (1 - (\frac{D^{2} -5D}{4}) +((\frac{D^{2} -5D}{4})^{2} -...} )X$

Now simplifying and we will use notation D = $\frac{dy}{dx}$

$=\frac{1}{4} (x - (\frac{D^{2} -5D}{4})x +((\frac{D^{2} -5D}{4})^{2}(x) -...}$

Higher degree terms are neglected

$=\frac{1}{4} (x - (\frac{ -5 D}{4}) x)$

The particular integral of given differential equation

$y_{p} = \frac{1}{4} ( x - (\frac{-5}{4} ) (1))$

Final answer:-

General solution of given differential equation

$y = y_{c} + y_{p}$

$Y (x) = C_{1} e^{x} + C_{2} e^{4x} + \frac{1}{4} ( x + (\frac{5}{4} ))$

4 0

3 years ago

Figure ABCD is a parallelogram, if point C lies on the line x = -1, what is the y value of point c?

brilliants [131]

Answer:

y = 0

Step-by-step explanation:

A parallelogram is a quadrilateral with opposite sides parallel. Then segment CD must be parallel to AB, and CB must be parallel to DA. Two different segments are parallel if they have the same slope.

slope of DA = (yA - yD)/(xA - xD) = (4 - 2)/(1 - (-1)) = 1

slope of CB = (yB - yC)/(xB - xC) = (2 - yC)/(1 - (-1)) = 1

(2 - yC) = 2 * 1

2 - 2 = yC

0 = yC

Note: coordinates of A are (xA, yA), of B are (xB, yB), of C are (xC, yC) and of D are (xD, yD)

6 0

3 years ago

The world population is estimated to be nearly 9 billion by the year 2050.

Olin [163]

The world population is estimated to be nearly 9 billion by the year 2050.

Africa- 20%

What is the estimated population of Africa in the year 2050?

9 billion x 0.2 = 1.8 billion

5 0

3 years ago