Answer:
The answer is below
Step-by-step explanation:
Find the dimensions of the rectangle of maximum area with sides parallel to the coordinate axes that can be inscribed in the ellipse 4x² + 16y² = 16
Solution:
Given that the ellipse has the equation: 4x² + 16y² = 16
let us make x the subject of the formula, hence:
4x² + 16y² = 16
4x² = 16 - 16y²
Dividing through by 4:
x² = (16 - 16y²)/4
x² = 4 - 4y²
Taking square root of both sides:
The points of the rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Hence the rectangle has length and width of 2x and 2y.
The area of a rectangle inscribed inside an ellipse is given by:
Area (A) = 4xy
A = 4xy
Therefore the length = 2x = 2√2, the width = 2y = 2/√2
Answer:
<h2><u>
j = 38</u></h2>
Explanation:
ʲ⁄₋₂ + 7 = -12
Subtract 7 From Both Sides
ʲ⁄₋₂ + 7 - 7 = -12 - 7
Simplify
ʲ⁄₋₂ = -19
Multiply Both Sides By -2
(-2) ʲ⁄₋₂ = -19 (-2)
<h2><u>j = 38</u></h2>
<span><span> x-4/x3-64</span> </span>Final result :<span> x4 - 64x3 - 4
—————————————
x3 </span>
The value of the unknown variable x by virtue of the geometric sequence given in the task content is; -27.
<h3>What is a geometric sequence and what is the value of x in the sequence given?</h3>
It follows from the task content above that the variable given above is a member of the geometric sequence.
Hence, since it follows from convention that the geometric sequence in discuss has same common difference across each successive term and hence , we have;
3/x = (-1/3) ÷ 3
x = -27.
Therefore, the value of the unknown variable x by virtue of the geometric sequence given in the task content is; -27.
Read more on geometric sequence;
brainly.com/question/1509142
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Putting the square root of 130 in the calculator you would get around 11.4 which if rounded to the next whole number would be 11. The closest whole number to the square root of 130 is 11.
