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1 year ago

Identify the slope of the line y−1=−6(x−3).

Mathematics

2 answers:

geniusboy [140]1 year ago

7 0

Answer:

The slope of the line is -5

olga nikolaevna [1]1 year ago

4 0

The slope is -6.

In the point-slope form, y - y1 = m(x - x1):

“(x1, y1)” represents (3, 1) coordinate
“m” represents the slope, -6

Therefore, the slope of the point-slope form, y - 1 = -6(x - 3), is -6.

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eimsori [14]

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2 years ago

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

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

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2 years ago

accoridng to byu idaho entorllemtn statistic there are 12000 femailes student here on camputes during any given semster of those

nordsb [41]

Answer:

so this as a fraction is 3500/12000 which is equivalent to

0.29166666666 we multiply this by 100

29.166666666

so about 29.1% or the students are female and have served a mission

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4 0

2 years ago

How to find slope using a graph. <br>

Pani-rosa [81]

Answer:

See below.

Step-by-step explanation:

Find two points on the graph that are easy to read.

Start at one point. You must now go to the other point, but you can only move vertically (up and down) and horizontally (right and left.)

Move vertically toward the other point. Count the number of units you moved. Up is positive, and down is negative. This is the rise.

Now move horizontally to the second point and count the units. Right is positive and left is negative. This is the run.

slope = rise/run

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jasenka [17]

Answer: just use phot math

Step-by-step explanation:

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