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NARA [144]
3 years ago
11

There is a rectangular terrain with dimensions "x" and "y". If it is known that its area of ​​is 22m ^ 2 and that x ^ 2 + y ^ 2

= 100, what is the perimeter of said terrain?
Mathematics
1 answer:
Margaret [11]3 years ago
5 0

9514 1404 393

Answer:

  24 m

Step-by-step explanation:

The area formula tells us ...

  22 = xy . . . . . square meters

Adding twice this to the quadratic constraint gives ...

  (x^2 +y^2) +2(xy) = (100) +2(22)

  (x +y)^2 = 144

  x +y = √144 = 12

The perimeter is double this amount, so is ...

  P = 2(x +y) = 2(12) = 24 . . . . meters

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For this case we have the following expression:
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The factored expression is given by:
 
5 ((x + 2y2) (x2 - 2xy2 + 4y4))
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You are in a hot air balloon looking down at two ponds. Pond A which is in front of your balloon, is at an angle of depression t
MatroZZZ [7]

a. See attachment for the labelled diagram

b. Using the sine ratio, distance from the hot air to pond A is 5,038.9 m, while distance from the hot air to pond B is 6,287.1 m.

c. Distance between the two ponds is 1,263.5 m.

<h3>What is the Sine and Tangent Ratios?</h3>

Sine ratio, is: sin ∅ = opposite side/hypotenuse length

Tangent ratio is: tan ∅ = opposite side/adjacent length.

a. The diagram with the appropriate labels is shown in the image attached below.

b. Use the sine ratio to find the distance from the hot air to pond A (CA) and to pond B (CB):

CA = hypotenuse

∅ = 10°

Opposite = 875 m

sin 10 = 875/CA

CA = 875/sin 10

CA ≈ 5,038.9 m (distance from the hot air to pond A)

CB = hypotenuse

∅ = 8°

Opposite = 875 m

sin 8 = 875/CB

CB = 875/sin 8

CB ≈ 6,287.1 m (distance from the hot air to pond B)

c. Distance between the two ponds, BA = BD + DA.

Apply the tangent ratio to find BD and DA

tan 8 = 875/BD

BD = 875/tan 8

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tan 10 = 875/DA

DA = 875/tan 10

DA = 4,962.4 m

Distance between the two ponds = 6,225.9 - 4,962.4 = 1,263.5 m.

Learn more about the sine and tangent ratios on:

brainly.com/question/24137232

#SPJ1

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