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3 years ago

15

HELP PLZ RN<3 which graph displays a rate of change of 2.5?

1 answer:

Ilya [14]3 years ago

3 0

Answer:

The second graph.

Step-by-step explanation:

The first graph has a negative slope, so that can't be the right answer.

The last graph isn't steep enough to show a rate of 2.5.

This leaves us with the middle graph which is correct.

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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

Two equations are given below:

Ostrovityanka [42]

A - 3b = 4 . . . . (1)
a = b - 2 . . . . . (2)
Putting (2) into (1), we have
b - 2 - 3b = 4
-2b = 4 + 2 = 6
b = 6/-2 = -3
From (1), a = b - 2 = -3 - 2 = -5
Hence, solution = (-5, -3)

3 0

2 years ago

Using the graph , determine the coordinates of the vertex of the parabola

aivan3 [116]

Answer:

(-4,-4)

Step-by-step explanation:

Delta math

3 0

2 years ago

Solve each equation mentally.

larisa [96]

Answer:

1) 1/17

2) 1/111

3) 1/15

They're all fractions

Hope that helped, just divide the result with the number available

Example :

1÷17 =1/17

4 0

2 years ago

What is the answer to this problom

arsen [322]

2,373divide3=791 i hope this help

7 0

3 years ago