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3 years ago

Which of the following is a convex polygon?

Mathematics

1 answer:

AlladinOne [14]3 years ago

7 0

Answer:

option b is the correct answer

Step-by-step explanation:

in convex polygon, none of the interior angle is greater than 180deg.

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Intersection point of Y=logx and y=1/2log(x+1)

GalinKa [24]

Answer:

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

The Problem:

What is the intersection point of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ ?

Step-by-step explanation:

To find the intersection of $y=\log(x)$ and $y=\frac{1}{2}\log(x+1)$ , we will need to find when they have a common point; when their $x$ and $y$ are the same.

Let's start with setting the $y$ 's equal to find those $x$ 's for which the $y$ 's are the same.

$\log(x)=\frac{1}{2}\log(x+1)$

By power rule:

$\log(x)=\log((x+1)^\frac{1}{2})$

Since $\log(u)=\log(v)$ implies $u=v$ :

$x=(x+1)^\frac{1}{2}$

Squaring both sides to get rid of the fraction exponent:

$x^2=x+1$

This is a quadratic equation.

Subtract $(x+1)$ on both sides:

$x^2-(x+1)=0$

$x^2-x-1=0$

Comparing this to $ax^2+bx+c=0$ we see the following:

$a=1$

$b=-1$

$c=-1$

Let's plug them into the quadratic formula:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{1 \pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$x=\frac{1 \pm \sqrt{1+4}}{2}$

$x=\frac{1 \pm \sqrt{5}}{2}$

So we have the solutions to the quadratic equation are:

$x=\frac{1+\sqrt{5}}{2}$ or $x=\frac{1-\sqrt{5}}{2}$ .

The second solution definitely gives at least one of the logarithm equation problems.

Example: $\log(x)$ has problems when $x \le 0$ and so the second solution is a problem.

So the $x$ where the equations intersect is at $x=\frac{1+\sqrt{5}}{2}$ .

Let's find the $y$ -coordinate.

You may use either equation.

I choose $y=\log(x)$ .

$y=\log(\frac{1+\sqrt{5}}{2})$

The intersection is $(\frac{1+\sqrt{5}}{2},\log(\frac{1+\sqrt{5}}{2})$ .

6 0

3 years ago

Please help with math again! ToT (10 points, link = report to moderators)

ycow [4]

Answer:

10.D

Step-by-step explanation:

A=2(wl+hl+hw)

7 0

3 years ago

Read 2 more answers

Select the equation that contains the point (4, -8), and in which the graph of the line has a positive slope.

BaLLatris [955]

Okay, let me just make this a little clearer. Hopefully, this is what you meant:

A. y - 8 = -4(x + 4)
B. y - 8 = 4(x + 4)
C. y + 8 = 4(x - 4)
D. y + 8 = -4(x - 4)

--

This can also be written as y2 - y1 = m(x2 - x1).

Your M is your slope.

Both A and D have their m as a negative 4. Because you are looking for a positive slope, immediately cancel those answers.

* note that you could have also put them in a more standard form and discovered m which is the x in bx.

Now, you are looking for an equation that contains (4,-8).

Because it is written as y2-y1, your y's are actually points if you were to find another slope or something. This part is a bit hard to explain, but -8 is only found in the y coordinate place in answer B. Your answer would be B. For more explanation on that, there's this great site called coolmath.com and if you search for finding the equation of two points, it explains it much better on there, but I would not want to plagiarize.

The answer is B.

5 0

3 years ago

In a direct variation, y = 18 when x = 6. Write a direct variation equation that

inysia [295]

Step-by-step explanation:

y =kx(where k is constant)

18 = 6k

divide both side by 6

k = 6

The relationship between x and y

y = kx

y =3x

8 0

3 years ago

I need help <br> Simplify. (x³)⁵

pshichka [43]

The answer would be X^15

7 0

3 years ago

Which of the following is a convex polygon? ​

Which of the following is a convex polygon?