Solve by completing the square. x2 + 12x + 8 = 0

Holly Cuts 3 pans of brownies into eighths. How many 1/8 size brownie pieces does she have?

Anuta_ua [19.1K]

She has 24 pieces, 8x3=24.
Plz rate 5 stars

5 0

3 years ago

Read 2 more answers

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

3 years ago

Please help: Triangle ABC is similar to triangle PQR where

andre [41]

Explanation:

AB=7
AC=9
You are looking for R

7+9=16

So R is 16

6 0

3 years ago

Please help me with this sum I will mark you as brainest

Murljashka [212]

Answer:

Step-by-step explanation:

3/6 x 8

= ( 3 x 8 ) / 6

= 24 / 6

4/7 x 2

= ( 4 x 2 ) / 7

= 8 / 7

9/2 x 3

= ( 9 x 3 ) / 2

= 27 / 2

8/5 x 7

= ( 8 x 7 ) / 5

= 56 / 5

3/9 x 5

= ( 3 x 5 ) / 9

= 15/9

7/4 x 4

= ( 7 x 4 ) / 4

= 28 / 4

6/2 x 6

= ( 6 x 6 ) / 2

= 36 / 2

8/3 x 9

= ( 8 x 9 ) / 3

= 72 / 3

9/4 x 8

= ( 9 x 8 ) / 4

= 72 / 4

5/3 x 6

= ( 5 x 6 ) / 3

= 30 / 3

2/7 x 3

= ( 2 x 3 ) / 7

= 6 / 7

8/4 x 7

= ( 8 x 7 ) / 4

= 72 / 4

6/4 x 2

= ( 6 x 2 ) / 4

= 12 / 4

3 0

3 years ago

Answer...............

aev [14]

In the given graph point B is a relative maximum with the coordinates (0, 2).

The given function is $y=x^{4}-2x^{2} +1$ .

In the given graph, we need to find which point is a relative maximum.

<h3>What are relative maxima?</h3>

The function's graph makes it simple to spot relative maxima. It is the pivotal point in the function's graph. Relative maxima are locations where the function's graph shifts from increasing to decreasing. A point called Relative Maximum is higher than the points to its left and to its right.

In the graph, the maximum point is (0, 2).

Therefore, in the given graph point B is a relative maximum with the coordinates (0, 2).

To learn more about the relative maximum visit:

brainly.com/question/2321623.

#SPJ1

8 0

2 years ago