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Serggg [28]
3 years ago
7

Ind the equation of the tangent line to 9x^2+16y^2=52 through (2, -1)

Mathematics
1 answer:
EastWind [94]3 years ago
6 0
Here are the steps.

In order to get the answer, first we need to get the x and y value of the center of the circle by using the equation of a circle (x^2 + y^2 = r^2)

<span>The center is (-9, -4)</span>

Once you get the center point, find the equation of the line (in a form of a radius) from the center point to point (2, -1). Get the slope.

The slope from center to point (2, -1) is 11/3

Finally, get the negative reciprocal of the slope from the previous step and form the equation using slope-intercept form ( y=mx + b). Then, that's the equation of the tangent line.

The slope of the tangent line is -3/11
The equation is y = -3/11x - 5/11

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PLS help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Darina [25.2K]

9514 1404 393

Answer:

  y = -1

Step-by-step explanation:

Sides marked with the same marking are congruent, so we have two equations:

  • 3x -y = 16
  • 2x +y = 9

Adding the equations gives ...

  5x = 25

  x = 5 . . . . . . divide by 5

Then the second equation tells us ...

  y = 9 -2x = 9 -2(5) = -1

The value of y is -1.

5 0
3 years ago
Complete the following exercises by applying polynomial identities to complex numbers. Factor x2 + 64. Check your work. Factor 1
Mumz [18]
x^2+64=x^2-(8i)^2=(x-8i)(x+8i)

16x^2+49=(4x)^2-(7i)^2=(4x-7i)(4x+7i)

(x+9i)^2=x^2+2x\cdot9i+(9i)^2=x^2+18xi+81i^2=x^2+18xi-81=x^2-81+18xi

(x-2i)^2=x^2-2x\cdot2i+(2i)^2=x^2-4xi+4i^2=x^2-4xi-4=x^2-4-4xi

(x+(3+5i))^2=x^2+2x(3+5i)+(3+5i)^2\\\\=x^2+6x+10xi+3^2+2\cdot3\cdot5i+(5i)^2\\\\=x^2+6x+10xi+9+30i+25i^2=x^2+6x+10xi+9+30i-25\\\\=x^2+6x+10xi+30i-16=x^2+6x-16+(10x+30)i


Used:\\i^2=-1\\\\a^2-b^2=(a-b)(a+b)\\\\(a+b)^2=a^2+2ab+b^2
4 0
3 years ago
Read 2 more answers
Which expression to a+ (c+7)?<br>​
Ann [662]

Answer:

(a + c) + 7

hope this helps

7 0
2 years ago
-3(5x + 6) + 2 = 2(8 + 8x) - 1
bija089 [108]
So first, we multiply out the brackets.
-15x - 18 + 2 = 17 + 16x -1
Then, bring all the terms onto one side so you can solve.
-15x-18+2-17-16x+1=0
Then, we simplify this.
-31x-32=0
Then, isolate x
-31x=32
x=32/-31 or -1.03 (nearest hundredth )
6 0
3 years ago
Find the Circumference of a circle with a Diameter of 9 inches Group of answer choices 9 pi inches 9 pi inches^2 9 pi inches^3 1
katen-ka-za [31]

Answer: 9\pi\ in.

Step-by-step explanation:

Given

The diameter of a circle is d=9\ in.

So, the radius is r=\frac{d}{2}=4.5\ in.

The circumference is given by 2\pi r

Insert the values

\Rightarrow 2\pi \cdot 4.5\\\Rightarrow 9\pi \ in.

Thus, the circumference of the circle is 9\pi\ in.  

8 0
3 years ago
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