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3 years ago

What is the slope, and what is the y-intercept of the line?

1 answer:

4 0

$General\ equation\ for\ line\ in\ slope\ intercept\ form:
\\\\y=ax+b\\
 a-slope\\ 
b-intercept\\\\ 
y=\frac{5}{4}x+9\\\\
slope=\frac{5}{4}\\\\intercept=9$

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HELPPP WILL MARK BRAINLYIST IF RIGHT

Bingel [31]

Answer:

550.92

Step-by-step explanation:

plz mark brainliest even if im wrong, i really need this, and if im wrong tell me im wrong so I cant correct it

7 0

3 years ago

Use undetermined coefficient to determine the solution of:y"-3y'+2y=2x+ex+2xex+4e3x

Kitty [74]

First check the characteristic solution: the characteristic equation for this DE is

r ² - 3r + 2 = (r - 2) (r - 1) = 0

with roots r = 2 and r = 1, so the characteristic solution is

y (char.) = C₁ exp(2x) + C₂ exp(x)

For the ansatz particular solution, we might first try

y (part.) = (ax + b) + (cx + d) exp(x) + e exp(3x)

where ax + b corresponds to the 2x term on the right side, (cx + d) exp(x) corresponds to (1 + 2x) exp(x), and e exp(3x) corresponds to 4 exp(3x).

However, exp(x) is already accounted for in the characteristic solution, we multiply the second group by x :

y (part.) = (ax + b) + (cx ² + dx) exp(x) + e exp(3x)

Now take the derivatives of y (part.), substitute them into the DE, and solve for the coefficients.

y' (part.) = a + (2cx + d) exp(x) + (cx ² + dx) exp(x) + 3e exp(3x)

… = a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)

y'' (part.) = (2cx + 2c + d) exp(x) + (cx ² + (2c + d)x + d) exp(x) + 9e exp(3x)

… = (cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

Substituting every relevant expression and simplifying reduces the equation to

(cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

… - 3 [a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)]

… +2 [(ax + b) + (cx ² + dx) exp(x) + e exp(3x)]

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

… … …

2ax - 3a + 2b + (-2cx + 2c - d) exp(x) + 2e exp(3x)

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

Then, equating coefficients of corresponding terms on both sides, we have the system of equations,

x : 2a = 2

1 : -3a + 2b = 0

exp(x) : 2c - d = 1

x exp(x) : -2c = 2

exp(3x) : 2e = 4

Solving the system gives

a = 1, b = 3/2, c = -1, d = -3, e = 2

Then the general solution to the DE is

y(x) = C₁ exp(2x) + C₂ exp(x) + x + 3/2 - (x ² + 3x) exp(x) + 2 exp(3x)

4 0

2 years ago

A card is drawn at random out of a well-shuffled deck of 52 cards. Find the probability of drawing a six comma seven comma or e

Rina8888 [55]

Answer: $\frac{3}{13}$ , or ~23.07%

Step-by-step explanation:

There are 52 cards in your average deck.

For this question, you need the numbers of the cards in the deck. There are four of each number from 2 through 10, and four aces, jacks, queens, and kings.

Considering there are four 6s, four 7s, and four 8s, there are 12 cards that fit the description.

Divide 12 by the total number of cards in the deck, 52, to get your answer.

8 0

3 years ago

Mark Brainliest .........

Gwar [14]

Answer:

work is shown and pictured

6 0

3 years ago

What is the complete factorization of 36y2 − 1?

ludmilkaskok [199]

Answer:

36y² - 1

Factorize

We have the final answer as

$(y - \frac{1}{6} )(36y + 6)$

Hope this helps you

3 0

3 years ago