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4 years ago

Prince is 6n years old. jordan is (3n + 10) years older than prince

1 answer:

4 0

A. 6n+3n+10= 9n+10. Jordan is 9n+10 years old.

B. 6n+9n+10= 15n+10. The total age of Prince and Jordan is 15n+10.

C. 6n-9. Kimberly is 6n-9 years old.

D. (6n+9n+10)+6n-9 = 15n+10+6n-9 = 15n+6n+10-9 = 21n+1. The total age of Prince, Jordan and Kimberly is 21n+1

E. 21•(4)+1=84+1=85. The total age of Prince, Jordan and Kimberly is 85 years.

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Which equation represents a proportional relationship that has a constant of proportionality equal to –10?

aksik [14]

Answer:

y = - 10x

Step-by-step explanation:

The equation representing a proportional relationship is

y = kx ← k is the constant of proportionality

y = - 10x ← is the only equation in this form

Thus the equation is y = - 10x with k = - 10

4 0

4 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

What's the best definition of the word "ratio?"

ololo11 [35]

Answer:

Compare

Step-by-step explanation:

Or relation I believe so...

7 0

4 years ago

Jada bought 3 shirts that cost $19.99 each before discount. What was her total after the discount? The percentage discount at a

Alex777 [14]

Total after the discount would be $77.96

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4 years ago

Find the unknown angle measure by solving for the given variable. Supplementary angles

likoan [24]

Step-by-step explanation:

Given that,

∠PSQ = 13x+7

∠QSR = 42x+8

We need to find the measure of angles.

We can use the property of linear pair. ATQ,

13x+7 + 42x+8 = 180 (Linear pair)

Taking like terms,

13x+42x = 180 - 7-8

55x = 165

x = 3

So,

∠PSQ = 13x+7 = 13(3) + 7 = 46°

∠QSR = 42x+8 = 42(3) + 8 = 134°

Hence, this is the required solution.

3 0

3 years ago