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2 years ago

PLEASE HELP!!!!!!!What is the standard form of the equation of the circle in the graph?

Mathematics

2 answers:

Juliette [100K]2 years ago

5 0

X^2+y^2=9

because it is at the origin and radius is 3

Aneli [31]2 years ago

5 0

Hi there!
The standard form of the equation of a circle is: $(x-a)^{2} + (y-b)^{2} = r^{2}$

With (a, b) representing the centre and r representing the radius of the circle. Since the centre of the circle is (0, 0) and the radius is 3, we get the following equation:
$(x-0)^{2} + (y-0)^{2} = 9 \\ x^{2} + y^{2} = 9$

~ Hope this helps you!

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2 years ago

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!

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2 years ago

A classroom is 30 feet long and 30 feet wide. The ceiling is 10 feet above the floor. What is the volume of the classroom?

ser-zykov [4K]

If you would like to know the volume of the classroom, you can calculate this using the following steps:

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The correct result would be 9000 ft^3.

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3 years ago