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3 years ago

The height of a tree is 8.194 meters.What is the height rounded to the nearst tenth of a meter?

1 answer:

3 0

SOLUTION:

Height of tree = 8.194 metres

Height of tree = 8.2 metres ( to the nearest tenth of a metre )

Therefore, the answer is:

The height of the tree is 8.2 metres when rounded to the nearest tenth of a metre.

Hope this helps! :)
Have a lovely day! <3

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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

Nina makes $12 per hour at her job. She also earns commission. Last week she earned $78 in commission and made a total of $444.

Vesnalui [34]

Answer:

30.5 hours

Step-by-step explanation:

444-78=366

366/12=30.5

30.5 x 12= 366

7 0

3 years ago

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Bruce's graduation picnic will cost $12 if it has 4 attendees. At most how many attendees can there be if Bruce budgets a total

ASHA 777 [7]

Answer:

6 peaple

Step-by-step explanation:

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3 years ago

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Megan made a paper chain that was 4m long. Mason’s chain was 479 cm long. Who’s was the longest? By how much?

Mekhanik [1.2K]

Answer:

Look below

Step-by-step explanation:

Let's start by converting 4 m into cm:

$4m * \frac{10^{2}cm}{1m}$ $= 4*10^{2}cm=400cm$

Since Megan's chain is only 400 cm long, Mason's chain is longer by 79 cm.

8 0

2 years ago

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Y + 2 =3 (x-6) find the slope and a point on the line

Alex777 [14]

Answer:

slope = 3, point = (6, -2)

Step-by-step explanation:

This is in point-slope form which looks like this : y-y1 = m(x-x1).

m is the slope, an x1 and y1 are the x and y coordinates of the point. Remember to flip the sign of the numbers for the points i.e. the y+2 in the equation becomes -2 for the point.

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3 years ago