Answer:
50.24 cm
Step-by-step explanation:
A = pi r^2
A = 3.14 (4^2)
A = 3.14 (16)
A = 50.24 cm
Answer:
X+4=8
Step-by-step explanation:
X+4=8 has an equal sign. Equations have equal signs, not expressions.
Answer:
4
Step-by-step explanation:
Using the nth term formula
a₁ = 2(1) - 5 = 2 - 5 = - 3
a₆ = 2(6) - 5 = 12 - 5 = 7
Then
a₁ + a₆ = - 3 + 7 = 4
The width and height of the rectangle inscribed in the right triangle have a measure of 3.529 units.
<h3>How to find the dimensions of the rectangle of maximum area by optimization</h3>
In this problem we must use <em>critical</em> values and <em>algebraic</em> methods to determine to determine the dimensions of the rectangle such that the area is a <em>maximum</em>. The equation of the quadrilateral is formed by definition of the area of a rectangle:
A = w · h (1)
Where:
- w - Width of the rectangle.
- h - Height of the rectangle.
And the area of the entire triangle is:
0.5 · (5) · (12) = w · h + 0.5 · w · (12 - h) + 0.5 · (5 - w) · h
30 = w · h + 6 · w - 0.5 · w · h + 2.5 · h - 0.5 · w · h
30 = 6 · w + 2.5 · h
2.5 · h = 30 - 6 · w
h = 12 - 2.4 · w (2)
The quadrilateral of <em>maximum</em> area is always a square, then we must solve for w = h:
w = 12 - 2.4 · w
3.4 · w = 12
w = 3.529
Then, the width and height of the rectangle inscribed in the right triangle have a measure of 3.529 units.
To learn more on optimizations: brainly.com/question/15319802
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