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ziro4ka [17]
3 years ago
15

At which points are the tangents drawn to the ellipse x 2 + y 2 = [ a ] x + [ a ] y parallel to

Mathematics
1 answer:
In-s [12.5K]3 years ago
3 0

The given equation of the ellipse is x^2 + y^2 = 2 x + 2 y

At tangent line, the point is horizontal with the x-axis therefore slope = dy / dx = 0

<span>So we have to take the 1st derivative of the equation then equate dy / dx to zero.</span>

x^2 + y^2 = 2 x + 2 y

x^2 – 2 x = 2 y – y^2

(2x – 2) dx = (2 – 2y) dy

(2x – 2) / (2 – 2y) = 0

2x – 2 = 0

x = 1

 

To find for y, we go back to the original equation then substitute the value of x.

x^2 + y^2 = 2 x + 2 y

1^2 + y^2 = 2 * 1 + 2 y

y^2 – 2y + 1 – 2 = 0

y^2 – 2y – 1 = 0

Finding the roots using the quadratic formula:

y = [-(- 2) ± sqrt ( (-2)^2 – 4*1*-1)] / 2*1

y = 1 ± 2.828

y = -1.828 , 3.828

 

<span>Therefore the tangents are parallel to the x-axis at points (1, -1.828) and (1, 3.828).</span>

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PLS ANSWER !!!! <br><br> what is the formula when finding the slope given in two ordered pairs
Katarina [22]

Answer: Since you already know that the ordered pair is in the format of (x, y), then you can label one of the ordered pairs as 1 and kind of distribute it to get 1(x, y) = (x-sub1, y-sub1). Then just use the slope formula (y2-y1)/(x2-x1).

Step-by-step explanation:

5 0
3 years ago
Amélie runs a bakery. She wants to find out whether her cake sales are affected by the weather conditions. She recorded the dail
SVETLANKA909090 [29]

Answer:

Step-by-step explanation:

Daily temp(in F) Cakes sold

 

42 39

45 52

48 31

54 61

59 72

62 35

64 61

65 34

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75 45

84 24

To find whether there is an association between these two let us find the correlation coefficient between these two variables.

r=-0.1975

Since |r|<0.5, correlation is weak.  

Let us test the hypothesis r =0

H0:r=0

Ha:r not equals 0

Test statistic = \frac{r\sqrt{n-2} }{\sqrt{1-r^2} } \\=\frac{-0.1975\sqrt{11-2} }{\sqrt{1-0.1975^2} }\\=\frac{-0.5625}{{0.9803} } \\=-0.5738

p =0.298

Since p value >0.10, at 90% significance level we accept that there is no association.

6 0
3 years ago
Which is the correct solution to the expression 4^8? Use the scientific calculator given in this course.
Rufina [12.5K]
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7 0
3 years ago
The circumference of Circle K is pi. The circumference of Circle L is 4xpi.
dmitriy555 [2]

Answer:

Ratio of circumferences: \displaystyle\frac{1}{4}

Ratio of radii: \displaystyle\frac{1}{4}

Ratio of areas: \displaystyle\frac{1}{16}

Step-by-step explanation:

Hi there!

We are given:

- The circumference of Circle K is \pi

- The circumference of Circle L is 4\pi

Therefore, the ratio of their circumferences would be:

\displaystyle\frac{\pi}{4\pi} ⇒ \displaystyle\frac{1}{4} when simplified

The formula for circumference is C=2\pi r, where <em>r</em> is the radius. To find the ratio of the circles' radii, we must identify their radii through their given circumferences.

If the circumference of Circle K is \pi, or 1\pi, then its radius is \displaystyle\frac{1}{2}.

If the circumference of Circle L is 4\pi, then its radius is \displaystyle\frac{4}{2}, which is 2.

Therefore the ratio their radii would be:

\displaystyle\frac{\frac{1}{2}}{{2}} ⇒ \displaystyle\frac{1}{2}*\frac{1}{2} ⇒ \displaystyle\frac{1}{4} when simplified

The formula for area is:

A=\pi r^2

First, let's find the area of Circle K:

A=\pi (\displaystyle\frac{1}{2})^2\\\\A=\displaystyle\frac{1}{4}\pi

Now, let's find the area of Circle L:

A=\pi (2)^2\\A = 4\pi

Therefore, the ratio of their areas would be:

\displaystyle\frac{\frac{1}{4}\pi}{4\pi} ⇒ \displaystyle\frac{\frac{1}{4}}{4} ⇒ \displaystyle\frac{1}{4} * \frac{1}{4} ⇒ \displaystyle\frac{1}{16} when simplified

I hope this helps!

5 0
2 years ago
Type the expression that results from the following series of steps:
ale4655 [162]

Answer:

y-8.3

Step-by-step explanation:

Y-7÷3±6=

BODMAS  which means brackets ,of, division, multiplication ,addition, subtraction

we start by 7÷3=2.3.....

then 2.3..±6=8.3

then y-8.3 because one is a number and the other one is unknown we will leave it just like that

5 0
3 years ago
Read 2 more answers
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