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3 years ago

Which measurements are equal to 321 decimeters? Check all that apply.

Mathematics

2 answers:

spin [16.1K]3 years ago

6 0

Answer:

The answers are a, c, and d :)

Step-by-step explanation:

allochka39001 [22]3 years ago

5 0

Answer:

a) 32100 millimeters

c) 3,210 centimeters

d)3.21 decameters

Step-by-step explanation:

To find which measurements are equal 321 decimeters, we will follow the steps below:

changing 321 decimeters to millimeters

let x be 321 decimeters in millimeters

1 decimeter = 100 millimeters

321 decimeters = x

cross - multiply

x = 321× 100

x = 32100 millimeters

hence, 321 decimeters = 32100 millimeters

converting 321 decimeters to centimeters

let y be 321 decimeters in centimeters

1 decimeters = 10 centimeters

321 decimeters = y

cross-multiply

y = 321× 10

y = 3210 centimeters

Thus, 321 decimeters = 3210 centimeters

converting decimeter to decameters

let z represent 321 decimeters in decameters

1 decameter = 100 decimeter

z = 321 decimeter

cross-multiply

100 z = 321

divide both-side by 100

100z/100 = 321/100

z=3.21 decameters

therefore, 321 decimeters = 3.21 decameters

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A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material for the sides of the can costs

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Answer:

the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm

Step-by-step explanation:

since the volume of a cylinder is

V= π*R²*L → L =V/ (π*R²)

the cost function is

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C = a* 2*π*R*L + b* 2*π*R²

replacing the value of L

C = a* 2*π*R* V/ (π*R²) + b* 2*π*R² = a* 2*V/R + b* 2*π*R²

then the optimal radius for minimum cost can be found when the derivative of the cost with respect to the radius equals 0 , then

dC/dR = -2*a*V/R² + 4*π*b*R = 0

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R³ = a*V/(2*π*b)

R= ∛( a*V/(2*π*b))

replacing values

R= ∛( a*V/(2*π*b)) = ∛(0.03$/cm² * 600 cm³ /(2*π* 0.05$/cm²) )= 3.85 cm

then

L =V/ (π*R²) = 600 cm³/(π*(3.85 cm)²) = 12.88 cm

therefore the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm

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