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Musya8 [376]
3 years ago
15

The figure below shows a rectangle with a diagonal drawn.

Mathematics
1 answer:
Kipish [7]3 years ago
3 0

Answer:

<u>Option B. sin(s) = cos(u)</u>

Step-by-step explanation:

The rest of the question is the attached figure.

Complementary angles - two angles that add to 90 degrees.

The sine of one of them will be equal to the cosine of other angle.

For the attached figure:

The set all complementary angles are:

  1. angle s and angle t
  2. angle u and angle v
  3. angle s and angle u
  4. angle t and angle v

We will check the options:

A. sin(t) = sin(u)  ⇒(<u>wrong</u>) because t and u are not complementary angles

B. sin(s) = cos(u) ⇒ (<u>True</u>) ⇒ s and u are complementary angles and sine of one of them will be equal to the cosine of other angle.

C. cos(s) = sin(v) ⇒(<u>wrong</u>) because t and u are not complementary angles

D. cos(t) = cos(v) ⇒(<u>wrong</u>) because t and v are complementary angles but sine of one of them should be equal to the cosine of other angle.

<u>The answer is option B. sin(s) = cos(u)</u>

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A community swimming pool is a rectangular prism that is 30 feet long, 12 feet wide, and 5 feet deep. The wading pool is half as
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Answer:

The volume of the community swimming pool is 4 times greaters than the volume of the wading pool.

Step-by-step explanation:

By definition of rectangular prism, we get the respective formulas for the volumes of the community swimming pool and the wadling pool, respectively:

Community swimming pool

V_{c} = l\cdot w\cdot h (1)

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V_{w} = \left(\frac{1}{2}\cdot l \right)\cdot \left(\frac{1}{2}\cdot h\right)\cdot w (2)

Where:

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h – Depth of the swimming pool, measured in feet.

w – Width of the swimming pool, measured in feet.

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V_{w} – Volume of the wading swimming pool, measured in cubic feet.

The ratio of the volume of the community swimming pool to the volume of the wadling pool is:

\frac{V_{c}}{V_{w}} = \frac{l\cdot w \cdot h}{\left(\frac{1}{2}\cdot l \right)\cdot \left(\frac{1}{2}\cdot h\right)\cdot w} (3)

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