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3 years ago

15

(6x - 4) – 8x+ = -28

1 answer:

igomit [66]3 years ago

6 0

Answer:

12

im in a rush, bt i hope it helps :)

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Consider the circle of radius 5 centered at (0, 0). Find an equation of the line tangent to the circle at the point (3, 4) in sl

Wittaler [7]

Answer:

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

Step-by-step explanation:

The equation of a circle of radius $5$ centered at $(0,0)$ is:

$x^{2} + y^{2} = 5^{2}$ .

$x^{2} + y^{2} = 25$ .

Differentiate implicitly with respect to $x$ to find the slope of tangents to this circle.

$\displaystyle \frac{d}{dx}[x^{2} + y^{2}] = \frac{d}{dx}[25]$

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(y^{2}) = 0$ .

Apply the power rule and the chain rule. Treat $y$ as a function of $x$ , $f(x)$ .

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(f(x))^{2} = 0$ .

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}(2f(x)\cdot f^{\prime}(x)) = 0$ .

That is:

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}\left(2y \cdot \frac{dy}{dx}\right) = 0$ .

Solve this equation for $\displaystyle \frac{dy}{dx}$ :

$\displaystyle \frac{dy}{dx} = -\frac{x}{y}$ .

The slope of the tangent to this circle at point $(3, 4)$ will thus equal

$\displaystyle \frac{dy}{dx} = -\frac{3}{4}$ .

Apply the slope-point of a line in a cartesian plane:

$y - y_0 = m(x - x_0)$ , where

$m$ is the gradient of this line, and
$(x_0, y_0)$ are the coordinates of a point on that line.

For the tangent line in this question:

$\displaystyle m = -\frac{3}{4}$ ,
$(x_0, y_0) = (3, 4)$ .

The equation of this tangent line will thus be:

$\displaystyle y - 4 = -\frac{3}{4} (x - 3)$ .

That simplifies to

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

3 0

3 years ago

(-10m^4n^7)(-3m^4n)<br><br> the answer should be a simplified monomial

Brilliant_brown [7]

(-10m^4n^7)(-3m^4n)

= -10*-3 m^4*m^4 * n^7* n^1

= 30m^8n^8

3 0

2 years ago

Which proportional relationship has the greatest rate of change?

slavikrds [6]

Answer:

The answer is A.

Step-by-step explanation:

A- slope is 7

B- slope is 3

C- slope is 4

D- slope is 6

3 0

2 years ago

Read 2 more answers

At a restaurant, 36%

Gekata [30.6K]

Answer:

128

Step-by-step explanation:

72 people are vegetarians so 200-72=128

3 0

2 years ago

Calculate a and b if

const2013 [10]

Notice that

$7^{2014} - 7^{2012} = 7^{2012} \bigg(7^2 - 1\bigg) = 7^{2012} \times 48 = 2^4 \times 3 \times 7^{2012}$

$12=2^2\times3$ , so

$\dfrac{7^{2014}-7^{2012}}{12} = 2^2 \times 7^{2012}$

Then taking the positive square root gives

$\sqrt{\dfrac{7^{2014}-7^{2012}}{12}} = \sqrt{2^2 \times 7^{2012}} = 2\times7^{1006}$

so $\boxed{a=2}$ and $\boxed{b=1006}$ .

4 0

1 year ago