Please solve with explanation

Mathematics

1 answer:

OverLord2011 [107]2 years ago

8 0

Real life scenarios of acute angles are:

Sighting a ball from the top of a building at an angle of 55 degrees.
The angle between two adjacent vanes of a fan that has 6 vanes

<h3>What are acute angles?</h3>

As a general rule, an acute angle, x is represented as: x < 90

This means that acute angles are less than 90 degrees.

<h3>The real life scenarios</h3>

The real life scenarios that involve acute angles are scenarios that whose measure of angle is less than 90 degrees.

Sample of the real life scenarios that satisfy the above definition are:

Sighting a ball from the top of a building at an angle of 55 degrees.
The angle between two adjacent vanes of a fan that has 6 vanes

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The region r is enclosed by the curves y=4-4x2 and y=0

Misha Larkins [42]

The region r is enclosed by the curves y₁ = 4 - 4x² and y₂ = 0 is 16/3 or 5.333 square units.

<h3>What is an area bounded by the curve?</h3>

When the two curves intersect then they bound the region is known as the area bounded by the curve.

The region r is enclosed by the curves y₁ = 4 - 4x² and y₂ = 0

The intersection points will be

y₁ = y₂

4 - 4x² = 0

x = ±1

Then the area bounded by the curves will be

$\rm Area = \int _{-1}^1 (y_1- y_2) dx\\\\Area = \int _{-1}^1 (4 - 4x^2) dx\\\\Area = \left [ 4x - \dfrac{4x^3}{3} \right ]_{-1}^1\\\\Area = 4 \left ( 1 + 1 \right ) - \dfrac{4}{3} \left ( 1^3 - (-1)^3 \right )\\\\Area = 8 - \dfrac{8}{3}\\\\Area = \dfrac{16}{3} = 5.333 \$