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2 years ago

Find the equation of the tangent to the circle x2 + y2 = 109 at point (-10,3)

Mathematics

1 answer:

konstantin123 [22]2 years ago

4 0

Answer:

10x - 3y = -109 .

Step-by-step explanation:

x^2 + y^2 = 109

Implicit Differentiation:

2x + 2y.y' = 0

y' = -2x/2y = -x/y

So at the point (-10,3) the gradient of the tangent is -(-10)/3 = 10/3.

Equation of the tangent:

y - y1 = m(x - x1)

y - 3 = 10/3(x + 10)

y - 3 = 10/3 x + 100/3

3y - 9 = 10x + 100

-109 + 3y = 10x

10x - 3y = -109

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3 years ago

Read 2 more answers

What is the difference between these two integers? −14 − (+6) =

sladkih [1.3K]

Answer:

-14-6=-20

Step-by-step explanation:

the negative sign gives you a negative 6, which you can subtract from -14, giving you -20.

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2 years ago

Graph f(x) =-2x^+16x-30 by factoring to find the solutions, then find the coordinates of the vertex, and the axis of symmetry. I

fredd [130]

Answer:

Observe attached image

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

Axis of symmetry:

 $x =4$ 

Step-by-step explanation:

First factorize the function

$f (x) = -2x ^ 2 + 16x-30$

Take -2 as a common factor.

$-2(x ^ 2 -8x +15)$

Now factor the expression $x ^ 2 -8x +15$

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.

These numbers are -5 and -3

Then we can factor the expression in the following way:

$f (x) = -2(x-5)(x-3)$

The quadratic function cuts the x-axis at x = 3 and at x = 5.

Now we find the coordinates of the vertex.

For a function of the form $ax ^ 2 + bx + c$ the x coordinate of its vertex is:

$x = \frac{-b}{2a}$

In the function $f (x) = -2x ^ 2 + 16x-30$

$a = -2\\b = 16\\c = 30$

Then the vertice is:

$x = \frac{-16}{2(-2)}\\\\x = 4$

The y coordinate of the symmetry axis is

$y = f (4) = -2 (4) ^ 2 +16 (4) -30\\\\y = 2$

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.

Then the axis of symmetry is the line

$x = 4$

The solutions and the vertice written as ordered pairs are:

Function zeros:

(3, 0), (5, 0)

Vertex:

(4, 2)

6 0

2 years ago

Find an expression which represents the sum of (7x - 8y) and (-6x - 6y) in simplest terms.

grigory [225]

Answer:

$\displaystyle (7x - 8y) + (-6x - 6y) = x - 14y$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle (7x - 8y) + (-6x - 6y)$

Step 2: Simplify

Combine like terms (x): $\displaystyle (7x - 8y) + (-6x - 6y) = x - 8y - 6y$
Combine like terms (y): $\displaystyle (7x - 8y) + (-6x - 6y) = x - 14y$

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2 years ago

Maria is making a stained glass window in the form of a kite. the width of the window must be 15 in., and she only has enough st

NeTakaya

Kite Area = (Diagonal 1 * Diagonal 2) / 2
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2 years ago