The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
<h3>What is the equation of the ellipse associated with the coordinates of the foci?</h3>
By <em>analytical</em> geometry we know that foci are along the <em>major</em> axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the <em>standard</em> form of the equation of the ellipse is of the following form:
(x - h)² / a² + (y - k)² / b² = 1, where a > b (1)
Where:
- a - Length of the major semiaxis.
- b - Length of the minor semiaxis.
Now, we proceed to find the vertex and the lengths of the semiaxes:
a = 10 units.
b = 8 units.
Vertex
V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)
V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)
V(x, y) = (1.5, 1) + (- 4.5, 1)
V(x, y) = (- 3, 2)
The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
To learn more on ellipses: brainly.com/question/14281133
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Fun fact
if f(a)=b then f⁻¹(b)=a
so
if f⁻¹(b)=a then f(a)=b
so we find f(x)=27 and the solve for x
f(x)=3x=27
3x=27
divide both sides by 3
x=9
so if f(9)=27 then f⁻¹(27)=9
problem solved
answer is 9
Answer: 32.35 cm^2
Step by step:
Find the area of the rectangle first.
A= L • W
A= 11 • 4.2
A= 46.2 cm^2
Then find the area of the circle. The formula is A= pi (r)^2. The diameter of the circle is 4.2 cm because looking at the width of the rectangle it fits into the circle as well.
Half of the diameter is 2.1 cm which is the radius.
A= pi (r)^2
A= pi (2.1)^2
A= pi (4.41)
A= 13.85 cm^2
Then you would subtract 13.85 from 46.2 to find the shaded portion.
Hope this helps :))
V= 232 m (8x4x7.25) 232 is the volume
