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2 years ago

What is an equation of the line that passes through the points (-7,3) and (-4,3)?

Mathematics

1 answer:

sammy [17]2 years ago

3 0

Answer:

Step-by-step explanation:

Slope = 0

y-y1=m(x-x1)

y-3=0

y = 3

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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

How is 23 written as a fraction

Ierofanga [76]

It would be 23/100.
C. Is the answer

3 0

2 years ago

Read 2 more answers

Solve by finding the square root 2x^2=32

Cerrena [4.2K]

2x^2=32 so divide by 2 to make x^2=16 and the square root so x=4

8 0

2 years ago

Read 2 more answers

What is the sum of the polynomials?

lesya [120]

Add the like terms:

8x2+x2=9x2

-9y2-3y2=-12y2

-4x-7x=-11x

Combine each term:

9x2-12y2-11x

Hope this helps!!

5 0

3 years ago

An executive board consists of a president (P) and three vice-presidents ( V 1 , V 2 , V 3 ) . For a motion to pass it must have

Crank

Answer:

[P, V1, V2]

[P, V1, V3]

[P, V2, V3]

Step-by-step explanation:

From the question, the executive board has 4 persons.

P = president

V1 = vice president 1

V2 = vice president 2

V3 = vice president 3

The president must be part of three members formed from these 4 to vote yes for a motion to pass

The weighted system can be represented as

[P, V1, V2]

[P, V1, V3]

[P, V2, V3]

These are the 3 possibilities.

7 0

2 years ago