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Vinvika [58]
3 years ago
7

Last week, Jamie counted the number of rice grains in his plate, and found he had 250

Mathematics
1 answer:
Reil [10]3 years ago
4 0

30% decrease
175 divided by 250 = 0.7
1 - 0.7 = 0.3
0.3 = 30%
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Diameter=10.5 in . Determine the area of each circle. Use 3.14 or 22/7 for pie . Round to the nearest tenth.
zloy xaker [14]

Answer:

86.5 square inches

Step-by-step explanation:

Area of circle: pi*r^2

  • first find the radius

10.5in /2= 5.25in

  • find the square

5.25^2=27.5625

  • multiply with pi

27.5625*3.14=86.54625

rounded 86.5 in

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3 years ago
Solve for x<br> 510<br> (2x + 3)<br> 65%<br> 60°<br> 64°<br> 43<br> (3x - 1)º
marshall27 [118]

Answer:

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3 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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3 years ago
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answer: 12x^9+15x^8-8x^6-10x^5

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F(x) should be shifted right 3 units.
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3 years ago
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