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myrzilka [38]
3 years ago
9

The slope field for the differential equation dy/dx=(3y)/(xy+5x) will have vertical segments when

Mathematics
1 answer:
Inessa05 [86]3 years ago
3 0

Answer:

E) x=0 or y=-5

Step-by-step explanation:

The slope field will have vertical segments when dy/dx is undefined, that is, dy/dx is a division by 0.

We have that

dy/dx=(3y)/(xy+5x)

So the slope field will have vertical segments when

xy + 5x = 0

x(y + 5) = 0

This is when x = 0 or y = -5.

So the correct answer is:

E) x=0 or y=-5

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Solve this equation.
Anika [276]

Answer:

Answer:  b = 58/5  or 11 3/5 or 11.6 decimal

Step-by-step explanation:

Solve for b:

b - (3 + 2/5) = 8 + 1/5

Put 3 + 2/5 over the common denominator 5. 3 + 2/5 = (5×3)/5 + 2/5:

b - (5×3)/5 + 2/5 = 8 + 1/5

5×3 = 15:

b - (15/5 + 2/5) = 8 + 1/5

15/5 + 2/5 = (15 + 2)/5:

b - (15 + 2)/5 = 8 + 1/5

15 + 2 = 17:

b - 17/5 = 8 + 1/5

Put each term in b - 17/5 over the common denominator 5: b - 17/5 = (5 b)/5 - 17/5:

(5 b)/5 - 17/5 = 8 + 1/5

(5 b)/5 - 17/5 = (5 b - 17)/5:

(5 b - 17)/5 = 8 + 1/5

Put 8 + 1/5 over the common denominator 5. 8 + 1/5 = (5×8)/5 + 1/5:

(5 b - 17)/5 = (5×8)/5 + 1/5

5×8 = 40:

(5 b - 17)/5 = 40/5 + 1/5

40/5 + 1/5 = (40 + 1)/5:

(5 b - 17)/5 = (40 + 1)/5

40 + 1 = 41:

(5 b - 17)/5 = 41/5

Multiply both sides of (5 b - 17)/5 = 41/5 by 5:

(5 b - 17)/(5 1/5) = 1/5×1/(1/5) 41

1/5×1/(1/5) = 1:

5 b - 17 = 1/5×1/(1/5) 41

1/5×1/(1/5) = 1:

5 b - 17 = 41

Add 17 to both sides:

5 b + (17 - 17) = 17 + 41

17 - 17 = 0:

5 b = 41 + 17

41 + 17 = 58:

5 b = 58

Divide both sides of 5 b = 58 by 5:

(5 b)/5 = 58/5

5/5 = 1:

Answer:  b = 58/5  or 11 3/5 or 11.6 decimal


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