How do you do this question?

Mathematics

1 answer:

tensa zangetsu [6.8K]2 years ago

3 0

Answer:

18 ln(9) − ¹⁰⁴/₉

Step-by-step explanation:

∫₁⁹ √y ln(y) dy

If u = ln(y), then du = dy/y.

If dv = √y dy, then v = ⅔ (y)^³/₂.

∫ u dv = uv − ∫ v du

= ln(y) (⅔ (y)^³/₂) − ∫ (⅔ (y)^³/₂) (dy/y)

= ln(y) (⅔ (y)^³/₂) − ∫ (⅔ (y)^½) dy

= ln(y) (⅔ (y)^³/₂) − ⁴/₉ (y)^³/₂ + C

= (⅔ (y)^³/₂) (ln(y) − ⅔) + C

Evaluate between y=1 and y=9.

[(⅔ (9)^³/₂) (ln(9) − ⅔)] − [(⅔ (1)^³/₂) (ln(1) − ⅔)]

[18 (ln(9) − ⅔)] − [(⅔) (-⅔)]

18 ln(9) − 12 + ⁴/₉

18 ln(9) − ¹⁰⁴/₉

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Natasha_Volkova [10]

Answer:Cost per box: $95.94 ÷ (b)

Cost per tile: [$95.94 ÷ (b)]÷ (t)

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6 0

2 years ago

Solve the following equation simultaneously 1/x-5/y=7, 2/x+1/y=3

maria [59]

Answer:

(x, y) = (1/2, -1)

Step-by-step explanation:

Subtracting twice the first equation from the second gives ...

(2/x +1/y) -2(1/x -5/y) = (3) -2(7)

11/y = -11 . . . . simplify

y = -1 . . . . . . . multiply by y/-11

Using the second equation, we can find x:

2/x +1/-1 = 3

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x = 1/2 . . . . . . . multiply by x/4

The solution is (x, y) = (1/2, -1).

_____

Additional comment

If you clear fractions by multiplying each equation by xy, the problem becomes one of solving simultaneous 2nd-degree equations. It is much easier to consider this a system of linear equations, where the variable is 1/x or 1/y. Solving for the values of those gives you the values of x and y.

A graph of the original equations gives you an extraneous solution of (x, y) = (0, 0) along with the real solution (x, y) = (0.5, -1).