Given:-
;
, where a is any positive real number.
Consider the helix parabolic equation :

now, take the derivatives we get;

As, we know that two vectors are orthogonal if their dot product is zero.
Here,
are orthogonal i.e, 
Therefore, we have ,




take t common in above equation we get,

⇒
or 
To find the solution for t;
take 
The number
determined from the coefficients of the equation 
The determinant 

Since, for any positive value of a determinant is negative.
Therefore, there is no solution.
The only solution, we have t=0.
Hence, we have only one points on the parabola
i.e <1,0>
Answer:
Mrs. Snitch will leave a tip of $8.40.
Step-by-step explanation:
$8.40 is 15% 0f 56.00.
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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Answer: go dnejsheur kejru I didn't do this
Step-by-step explanation:
Answer:
The answer is -2/3.
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