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Romashka-Z-Leto [24]
3 years ago
14

*Please Help!*

Mathematics
1 answer:
trapecia [35]3 years ago
8 0

Answer:

The volume of water that will fill the spa tub is 5.9 cubic meters.

Step-by-step explanation:

Volume of water that would fill the spa tub = volume of semi sphere - (volume of the first cylinder + volume of the second cylinder)

i. volume of first cylinder = \pir^{2}h

where r is the radius and h is the height of the cylinder.

r = \frac{0.75}{2} = \frac{3}{8}

 = 0.375 m

h = 0.80 m

volume of the first cylinder = \frac{22}{7} x (\frac{3}{8} )^{2} x 0.8

                                        = 0.3536 cubic meters

ii. volume of the cylinder underneath = \pir^{2}h

r = \frac{1.25}{2} = \frac{5}{8}

 = 0.625

h = 0.70 m

volume of the cylinder underneath = \frac{22}{7} x (\frac{5}{8}) ^{2} x 0.7

                                                      = 0.8594 cubic meters

iii. volume of the semi sphere = \frac{2}{3} \pir^{3}

where r is the radius = 1.5 m

volume of the semi sphere = \frac{2}{3} x \frac{22}{7} x (1.5)^{3}

                                             = 7.0714 cubic meters

Thus,

volume of the water to fill the spa tub = 7.0714 - (0.3536 + 0.8594)

                                                     = 5.8584

The volume of water that will fill the spa tub is 5.9 cubic meters.

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Type the correct answer in the box
TiliK225 [7]

The expression of X in terms of l is X = √5 l

<h3>How to calculate the diagonal of a rectangle</h3>

According to the given information:

  • Length = w
  • If length<u> l is twice as long </u>as the width, then l = 2w

Determine the diagonal using the Pythagoras theorem:

X² = w²+(2w)²
X² = w² + 4w²

X =√5w²
X = √5 w

Replace w with l

X = √5 l

Hence the expression of X in terms of l is X = √5 l

Learn more on diagonals here: brainly.com/question/26154016

5 0
3 years ago
The government of the Republic of Lemon Island plans to transform their lemon-based economy into a tourism-based economy. They d
NNADVOKAT [17]

Step-by-step explanation:

dy/dt = (A − Be^(-t/5)) y

(a) First, find the general solution by separating the variables and integrating.

dy / y = (A − Be^(-t/5)) dt

dy / y = [A + 5B (-⅕ e^(-t/5))] dt

ln |y| = At + 5B e^(-t/5) + C

y = e^(At + 5B e^(-t/5) + C)

y = Ce^(At + 5B e^(-t/5))

Given that A = 0.06, B = 0.04, and y(0) = 50×10⁶ − 10×10⁶ = 40×10⁶:

40×10⁶ = Ce^(0.06(0) + 5(0.04) e^(-0/5))

40×10⁶ = Ce^(0.2)

C = 40×10⁶ e^(-0.2)

y = 40×10⁶ e^(-0.2) e^(0.06t + 0.2 e^(-t/5))

y = 40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5))

(b) If A = 0.02 and B = 0, and there is no transformation (y(0) = 50×10⁶), then:

50×10⁶ = Ce^(0.02(0) + 0)

50×10⁶ = C

y = 50×10⁶ e^(0.02t)

Comparing to the answer from part (a):

40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5)) = 50×10⁶ e^(0.02t)

e^(-0.2 + 0.04t + 0.2 e^(-t/5)) = 5/4

-0.2 + 0.04t + 0.2 e^(-t/5) = ln(5/4)

-5 + t + 5e^(-t/5) = 25 ln(5/4)

t + 5e^(-t/5) = 5 + 25 ln(5/4)

Solve with a calculator:

t = 9.886

The transformed economy surpasses the untransformed economy in the 10th year.

(c) In year t=5, the size of the transformed economy is:

y = 40×10⁶ e^(-0.2 + 0.06(5) + 0.2 e^(-5/5))

y = 47.6×10⁶

The percent growth is:

(47.6×10⁶ − 40×10⁶) / 40×10⁶ × 100% = 19%

The growth rate is greater than 4%, so the current government can expect to be reelected.

3 0
3 years ago
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