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2 years ago

It was a 5ft. by 5ft. sandbox. how many square feet would mr. potato head be able to walk inside the box?

Mathematics

1 answer:

AnnZ [28]2 years ago

5 0

25 square feet would mr. potato head be able to walk inside the box.

<h3>What is square ?</h3>

A square is a 2D figure in which all the sides are of equal measure.
Since all the sides are equal, the area would be length times width, which is equal to side × side.
Hence, the area of a square is side square.
Each side of square is 90° .

Given,

length and breadth of sandbox is 5 ft.

Now, We apply formula of area of square.

5 × 5 = 25 ft²

Therefore, 25 ft² would mr. potato head be able to walk inside the box.

Learn more about Area of square

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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

the height in feet above the ground of an arrow after it is shot can be modeled by y=-16r^2+63r+4.Can the arrow pass over a tree

miss Akunina [59]

Answer:

yes

Step-by-step explanation:

y=-16r^2+63r+4

maximum value of y :

y'=0

-32r +63=0

r= 63/32

y = -16(63/32)²+63(63/32)+4

= -4 + 124 + 4 = 124 ft

124 > 68

the Arrow can pass over the tree

7 0

3 years ago

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Sidana [21]

Answer:

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Step-by-step explanation:

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3 years ago

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Damm [24]

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3 years ago

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Savatey [412]

Answer:

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Step-by-step explanation:

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3 years ago