Find the point at which the rightmost vertical tangent line touches the ellipse. The rightmost vertical tangent line touches the ellipse at the point

The missing part of the question showing the figure and other earlier questions has been attached.

A) dy/dx = (2x + y)/(-x - 2y)

B) the lower horizontal tangent line is defined by the equation: y = -⅔√15

C) the right most tangent is; x = ⅔√15

D) point at which the rightmost vertical tangent line touches the Ellipse is y = -⅓√15.

Tangent point is at: (⅔√15, -⅓√15)

Step-by-step explanation:

We are given the equation as:

x² + xy + y² = 5. Looking at this equation and the image given, we can see that it is an Ellipse.

A) Using implicit differentiation, we have;

2x(dx) + y(dx) + x(dy) + 2y(dy) = 0

Collecting like terms and rearranging gives us;

(2x + y)dx = (-x - 2y)dy

Thus;

dy/dx = (2x + y)/(-x - 2y)

b) The horizontal tangent will be the point where dy/dx = 0

Thus;

(2x + y)/(-x - 2y) = 0

Therefore,

2x + y = 0

y = -2x

Now, since the horizontal tangent has y to be a constant, then x = -y/2

Putting -y/2 for x in the initial Ellipse equation gives;

(-y/2)² + (-y/2)y + y² = 5

¼y² - ½y² + y² = 5

¾y² = 5

y² = 20/3

y = √(20/3)

y = ± ⅔√15

Therefore,the lower horizontal tangent line is defined by the equation: y = -⅔√15

c) The vertical tangent is gotten by equating the denominator of dy/dx to 0

Thus;

(-x - 2y) = 0

Or when rearranging gives; x + 2y = 0

From symmetry, we can say that the solution is x = ± ⅔√15, with the right most tangent being x = ⅔√15

d) The point at which the right most tangent touches the Ellipse is at;

y = -x/2

Since x = ⅔√15 from C above, then;

y = -(⅔√15)/2

y = -⅓√15

Therefore,the tangent point is at; (⅔√15, -⅓√15)

the answer is 200

step-by-step explanation:

the way the question is worded, it seems to imply the $264 interest is simple interest, not compound interest.

the simple interest for 2 years is $264; the simple interest for 1 year is $132.

$132 interest on a $600 investment means an interest rate of (132/600)*100 = 22%.

the value of $200 at 22% interest compounded annually for three years is

200%281.22%29%5e3

the amount of interest is that value, minus the original $200.

555.99.

step-by-step explanation:

hope this