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GenaCL600 [577]
3 years ago
10

Find the perimeter of an ellipse if the major axis is 30 millimeters (mm) and the minor axis is 12 mm. Round off your answer to

the nearest whole number A. 49 mm B.72 mm C. 28 mm D. 283 mm
Mathematics
1 answer:
DENIUS [597]3 years ago
3 0
The perimeter of an ellipse is given by:
 P = (2 * pi) * root ((a ^ 2 + b ^ 2) / 2)
 Where,
 a: semi-major axis
 b: Semi-minor axis
 Substituting the values we have:
 P = (2 * 3.14) * root (((30/2) ^ 2 + (12/2) ^ 2) / 2)
 P = 71.74058266
 Round off to the nearest whole number
 P = 72 mm
 Answer:
 
B.72 mm
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A^2 + b^2 + c^2 = 2(a − b − c) − 3. (1) Calculate the value of 2a − 3b + 4c.
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Answer:

2a - 3b + 4c = 1

Step-by-step explanation:

Given

a^2 + b^2 + c^2 = 2(a - b - c) - 3

Required

Determine 2a - 3b + 4c

a^2 + b^2 + c^2 = 2(a - b - c) - 3

Open bracket

a^2 + b^2 + c^2 = 2a - 2b - 2c - 3

Equate the equation to 0

a^2 + b^2 + c^2 - 2a + 2b + 2c + 3 = 0

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a^2 + b^2 + c^2 - 2a + 2b + 2c + 1 + 1 + 1 = 0

Collect like terms

a^2 - 2a + 1 + b^2 + 2b + 1 + c^2  + 2c + 1 = 0

Group each terms

(a^2 - 2a + 1) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

Factorize (starting with the first bracket)

(a^2 - a -a + 1) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

(a(a - 1) -1(a - 1)) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

((a - 1) (a - 1)) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

((a - 1)^2) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

((a - 1)^2) + (b^2 + b+b + 1) + (c^2  + 2c + 1) = 0

((a - 1)^2) + (b(b + 1)+1(b + 1)) + (c^2  + 2c + 1) = 0

((a - 1)^2) + ((b + 1)(b + 1)) + (c^2  + 2c + 1) = 0

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((a - 1)^2) + ((b + 1)^2) + (c^2  + c+c + 1) = 0

((a - 1)^2) + ((b + 1)^2) + (c(c  + 1)+1(c + 1)) = 0

((a - 1)^2) + ((b + 1)^2) + ((c  + 1)(c + 1)) = 0

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By comparison

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(c  + 1)^2 = 0

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Take square root of both sides

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Add 1 to both sides

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Take square root of both sides

b + 1 = 0

Subtract 1 from both sides

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Solving for (c  + 1)^2 = 0

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Subtract 1 from both sides

c + 1 - 1 = 0 - 1

c = -1

Substitute the values of a, b and c in 2a - 3b + 4c

2a - 3b + 4c = 2(1) - 3(-1) + 4(-1)

2a - 3b + 4c = 2 +3  -4

2a - 3b + 4c = 1

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Solution:

we have been asked to find

Which of the given number words represents the numeral 4,056?

Its about the counting.

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on Tenth place we have 5.

on hundredth place we have 0.

On Thousand place we have 4.

so in our number word representation there will be no "Hundreds".

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Hence the given number words representing the numeral 4,056 is Four thousands and fifty six

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