<img src="https://tex.z-dn.net/?f=%20%20%5Cfrac%7B6%7D%7B%20%5Csqrt%7B54%7D%20%7D%20" id="TexFormula1" title=" \frac{6}{ \sqrt{

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suter [353]

2 years ago

54} } " alt=" \frac{6}{ \sqrt{54} } " align="absmiddle" class="latex-formula">
can someone simplify this for me?

Mathematics

1 answer:

IgorC [24]2 years ago

5 0

Square root 54 and you get 7.35 and then you do 6/7.35 then you should get 0.82

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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

3 years ago

So, Christian has a collection of 18 shark teeth. He identified them as 6 tiger shark teeth, 8 sand shark teeth, and the rest as

svetoff [14.1K]

Answer:

So, the question means that if we add the number of tiger shark teeth and the sand shark teeth and subtract it from the total number of teeth, we will get the number of bull shark teeth. And, the number of bull shark teeth is 4.

Step-by-step explanation:

So, the question means that if we add the number of tiger shark teeth and the sand shark teeth and subtract it from the total number of teeth, we will get the number of bull shark teeth.

Since Christian has 18 shark teeth, and 6 are tiger shark teeth, 8 are sand shark teeth and the rest are bull shark teeth.

Let x represent the number of bull shark teeth.

So, total number of shark teeth = number of tiger shark teeth + number of sand shark teeth + number of bull shark teeth.

18 = 6 + 8 + x

18 = 14 + x

subtracting 14 from both sides, we have

18 - 14 = 14 - 14 + x

4 = 0 + x

4 = x

x = 4

So, the number of bull shark teeth is 4.

4 0

3 years ago

What am I doing wrong?

Angelina_Jolie [31]

You didn't put x in !

3 0

3 years ago

To find the distance across a lake, a

Nesterboy [21]

The distance across the lake, a is 611 yards

<h3>Right angle triangle:</h3>

Right angle triangle have one of its angles as 90 degrees. Therefore, the side a can be found using trigonometric ratios,

Therefore,

tan 47° = opposite / adjacent

tan 47° = a / 570

cross multiply

a = 570 tan 47°

a = 570 × 1.07236871002

a = 611.250164714

a = 611 yards

learn more on right triangle here: brainly.com/question/18450490

6 0

2 years ago

Read 2 more answers

Please can anyone help answer this question? It would be greatly appreciated!!! :)

Ray Of Light [21]

Answer:

0.667

Step-by-step explanation:

Angle in a circle = 360°

Area of total shaded parts = 60 + 60 = 120°

Area of total unshaded parts = 360-120 = 240°

Probability that a random selected point within the circle falls in the unshaded area

= 240/360

= 2/3

≈ 0.667

I apologize in advance if I made a mistake.

7 0

3 years ago

Read 2 more answers