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2 years ago

Find the gradient of the line segment between the points (2,3) and (4,7)

Mathematics

1 answer:

belka [17]2 years ago

5 0

Answer:

Step-by-step explanation:

The gradient or slope of a straight line which is found between two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Where y2 = 7

y1 = 3

x2 = 4

x1 = 2

=> m = (7 - 3) / (4 - 2)

m = 4 / 2 = 2

The gradient is 2.

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Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)

vfiekz [6]

Answer:

Step-by-step explanation:

given a point $(x_0,y_0)$ the equation of a line with slope m that passes through the given point is

$y-y_0 = m(x-x_0)$ or equivalently

$y = mx+(y_0-mx_0)$ .

Recall that a line of the form $y=mx+b$ , the y intercept is b and the x intercept is $\frac{-b}{m}$ .

So, in our case, the y intercept is $(y_0-mx_0)$ and the x intercept is $\frac{mx_0-y_0}{m}$ .

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph $(x_0,\frac{1}{x_0})$ . Which means that $y_0=\frac{1}{x_0}$

The slope of the tangent line is given by the derivative of the function evaluated at $x_0$ . Using the properties of derivatives, we get

$y' = \frac{-1}{x^2}$ . So evaluated at $x_0$ we get $m = \frac{-1}{x_0^2}$

Replacing the values in our previous findings we get that the y intercept is

$(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}$

The x intercept is

$\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0$

The triangle in consideration has height $\frac{2}{x_0}$ and base $2x_0$ . So the area is

$\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2$

So regardless of the point we take on the graph, the area of the triangle is always 2.

6 0

2 years ago

Find two numbers that up to 158. The greater number is 40 more than the lesser number.

snow_tiger [21]

99 and 59

X=big number
X-40 = small

X+ x-40 =158
2X -40=158
2X =198
X=99. Big number is 99
99-40 =59

99+59=158

3 0

2 years ago

A school principal has to choose randomly among the six best students in each grade to be the school captain every month. For th

schepotkina [342]

Answer: It's an unfair method because two or more students could get the same results./ D

Step-by-step explanation: hope this helps

4 0

2 years ago

Read 2 more answers

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TiliK225 [7]

Which equation am I looking at

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2 years ago

How do i do this??Please help due tomorrow

Klio2033 [76]

For the range:
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2 years ago