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aleksklad [387]
2 years ago
5

What is an equation of the line that passes through the point(2,−2) and is parallel to the line 5x-2y=4

Mathematics
1 answer:
mixer [17]2 years ago
3 0

Answer:

y = 5/2x - 7

Step-by-step explanation:

5x - 2y = 4

5x - 4 = 2y

y = 5/2x - 2

Slope = 5/2

Point (2,-2)

y-intercept: -2 - (5/2)(2) = -2 - 5

= -7

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Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area: where V = volume (mm3
Alex

Answer:

V = 20.2969 mm^3 @ t = 10

r = 1.692 mm @ t = 10

Step-by-step explanation:

The solution to the first order ordinary differential equation:

\frac{dV}{dt} = -kA

Using Euler's method

\frac{dVi}{dt} = -k *4pi*r^2_{i} = -k *4pi*(\frac {3 V_{i} }{4pi})^(2/3)\\ V_{i+1} = V'_{i} *h + V_{i}    \\

Where initial droplet volume is:

V(0) = \frac{4pi}{3} * r(0)^3 =  \frac{4pi}{3} * 2.5^3 = 65.45 mm^3

Hence, the iterative solution will be as next:

  • i = 1, ti = 0, Vi = 65.45

V'_{i}  = -k *4pi*(\frac{3*65.45}{4pi})^(2/3)  = -6.283\\V_{i+1} = 65.45-6.283*0.25 = 63.88

  • i = 2, ti = 0.5, Vi = 63.88

V'_{i}  = -k *4pi*(\frac{3*63.88}{4pi})^(2/3)  = -6.182\\V_{i+1} = 63.88-6.182*0.25 = 62.33

  • i = 3, ti = 1, Vi = 62.33

V'_{i}  = -k *4pi*(\frac{3*62.33}{4pi})^(2/3)  = -6.082\\V_{i+1} = 62.33-6.082*0.25 = 60.813

We compute the next iterations in MATLAB (see attachment)

Volume @ t = 10 is = 20.2969

The droplet radius at t=10 mins

r(10) = (\frac{3*20.2969}{4pi})^(2/3) = 1.692 mm\\

The average change of droplet radius with time is:

Δr/Δt = \frac{r(10) - r(0)}{10-0} = \frac{1.692 - 2.5}{10} = -0.0808 mm/min

The value of the evaporation rate is close the value of k = 0.08 mm/min

Hence, the results are accurate and consistent!

5 0
3 years ago
What is the length of AD if A is located at (-7,0) and D is located at (8,0)?
Kryger [21]

Answer:

15

Step-by-step explanation:

(-7,0) and (8,0) are on the opposite side of origin of x axis

d = 8 - -7 = 15

6 0
3 years ago
2/3(x+6)=-18 what is the value of x
sladkih [1.3K]

Answer:

x = -33

Step-by-step explanation:

2/3(x+6)=-18

Multiply each side by 3/2

3/2*2/3(x+6)=-18*3/2

x+6 = -27

Subtract 6 from each side

x +6-6 = -27-6

x = -33

4 0
3 years ago
40% written as a decimal
Natasha2012 [34]

40%= 0.40 if you think of the decimal being at the end of the number (40.%) than just move the decimal twice makes it 0.40

8 0
3 years ago
Determine the measure of ∠DBC. answers: 1) 130° 2) 115° 3) 230° 4) 65°
Norma-Jean [14]

Answer:

65 degrees

Step-by-step explanation:

65 degrees

it is 65 because of the vector relationship: 30 + 100 = 130. 130/2=65 degrees

5 0
3 years ago
Read 2 more answers
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