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Advocard [28]
3 years ago
5

-3x^2 + 2y^2 + 5xy - 2y + 5x^2 - 3y^2 x = 2 , y = -1

Mathematics
1 answer:
rewona [7]3 years ago
5 0
X=2 Y=-1 plug them into the equation
-3(2)^2 + 2(-1)^2 + 5(2)(-1) -2(-1) + 5(2)^2 -3(-1)^2

36+4-10+2+100+9

40-10+2+100+9

30+2+100+9

132+9

141
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one pump can empty the pool in 5 days, whereas a second pump can empty the pool in 7 days. how long it will take the two pumps,
PtichkaEL [24]
4 days jfjdhsbsiegebehehebeihrhe
7 0
3 years ago
Solve the following differential equations or initial value problems. In part (a), leave your answer in implicit form. For parts
shepuryov [24]

Answer:

(a) (y^5)/5 + y^4 = (t^3)/3 + 7t + C

(b) y = arctan(t(lnt - 1) + C)

(c) y = -1/ln|0.09(t + 1)²/t|

Step-by-step explanation:

(a) dy/dt = (t^2 + 7)/(y^4 - 4y^3)

Separate the variables

(y^4 - 4y^3)dy = (t^2 + 7)dt

Integrate both sides

(y^5)/5 + y^4 = (t^3)/3 + 7t + C

(b) dy/dt = (cos²y)lnt

Separate the variables

dy/cos²y = lnt dt

Integrate both sides

tany = t(lnt - 1) + C

y = arctan(t(lnt - 1) + C)

(c) (t² + t) dy/dt + y² = ty², y(1) = -1

(t² + t) dy/dt = ty² - y²

(t² + t) dy/dt = y²(t - 1)

(t² + t)/(t - 1)dy/dt = y²

Separating the variables

(t - 1)dt/(t² + t) = dy/y²

tdt/(t² + t) - dt/(t² + t) = dy/y²

dt/(t + 1) - dt/(t(t + 1)) = dy/y²

dt/(t + 1) - dt/t + dt/(t + 1) = dy/y²

Integrate both sides

ln(t + 1) - lnt + ln(t + 1) + lnC = -1/y

2ln(t + 1) - lnt + lnC = -1/y

ln|C(t + 1)²/t| = -1/y

y = -1/ln|C(t + 1)²/t|

Apply y(1) = -1

-1 = ln|C(1 + 1)²/1|

-1 = ln(4C)

4C = e^(-1)

C = (1/4)e^(-1) ≈ 0.09

y = -1/ln|0.09(t + 1)²/t|

8 0
3 years ago
Complete the following statements.
stiv31 [10]

Answer:

A soda bottle contains 2 liters of liquid. Therefore:

The soda bottle contains  67.62 fluid ounces of liquid.

The soda bottle contains 0.525  gallons of liquid.

2) A milk jug contains 2 gallons of milk. Therefore:

The milk jug contains 8  quarts of milk.

The milk jug contains 7.6 liters of milk.

Step-by-step explanation:

We need to complete the statements.

1)

A soda bottle contains 2 liters of liquid. Therefore:

The soda bottle contains -------  fluid ounces of liquid.

  • Converting Liters to fluid ounces

We know that 1 liter = 33.81 fluid ounces

So,  2 liter = 2 x 33.81 = 67.62 fluid ounces

The soda bottle contains 67.62  fluid ounces of liquid.

The soda bottle contains  gallons of liquid.

  • Converting liters to gallons

As, we are not given direct conversion from liters to gallons, first we convert liter to quarts and then convert quarts to gallons

We know that

1 liter = 1.05 quarts

2 liters = 2 x 1.05 = 2.1 quarts

4 quarts = 1 gallon

1 quarts = 1/4 gallon

2.1 quarts = 1/4 * 2.1 = 0.525 gallon

The soda bottle contains 0.525  gallons of liquid.

2)

A milk jug contains 2 gallons of milk. Therefore:

The milk jug contains -------- quarts of milk.

  • Converting gallons to quarts

We know:

1 gallon = 4 quarts

2 gallons = 2 x 4 = 8 quarts

The milk jug contains 8 quarts of milk.

The milk jug contains ------  liters of milk.

  • Converting gallons to liters

We know:

1 gallon = 4 quarts

2 gallon = 8 quarts

1.05 quarts = 1 liter

1 quarts = 1/1.05 liter

8 quarts = 1/1.05 * 8 = 7.6 liter

The milk jug contains 7.6 liters of milk.

6 0
2 years ago
What is the slope and y-intrrcept of 5x-3y= -15
Ivahew [28]
<span>5x - 3y= -15
3y = 5x + 15
y = 5/3 x + 5

answer

slope m = 5/3
y intercept = 5</span>
4 0
3 years ago
Read 2 more answers
The sum of 16 and 20 is divided by the product of 6 and 2 , find the result​
kow [346]

The answer is 3

16+20=36

6x2=12

36/12=3

4 0
2 years ago
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