Describe a way in which the diagram above illustrates the unique plane postulate.

Please help and show work it helps a lot thanks

Vinvika [58]

Me to I was doing the work but just lost it I will try again

8 0

2 years ago

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

2 years ago

using two of the number cards from the list, fill in the gaps so that the values are in ascending order

Mademuasel [1]

The two gaps of the series are 236 % and 2.41.

The series is 2(32/100) _, _ , 247/100.

We are given that the series is in ascending order.

Let the missing numbers be x and y respectively.

We know that 2(32/100) = 2.32 in decimal form and 247/100 is 2.47 in decimal form.

Hence, we can write,

2.32 < x < y < 2.47

The given options are:-

231 % = 231/100 = 2.31 < 2.32

Hence, it is not the answer.

0.42 < 2.31

Hence, it is not the answer.

236 % = 236/100 = 2.36 > 2.31

Hence, this is one of the answers.

34 % = 0.34

0.34 < 2.31

Hence, it is not the answer.

0.237 < 2.31

Hence, it is not the answer.

2.41 > 2.32

Hence, this is one of the answers.

24.2 % = 24.2/100 = 0.242 < 2.31

Hence, it is not the answer.

0.36 < 2.31

Hence, it is not the answer.

As, 2.36 < 2.41, hence,

x = 2.36 or 236 % and,

y = 2.41

To learn more about series, here:-

brainly.com/question/15415793

#SPJ1

6 0

1 year ago

Which of the following equations is not a linear equation?

ElenaW [278]

Answer:

its a

Step-by-step explanation:

Since x=5 is a vertical line, there is no y-intercept and the slope is undefined.

7 0

3 years ago

Read 2 more answers

1 Negative numbers do not need the<br>negative sign (-) in front of them.<br>O True<br>O False

katrin [286]

Answer:

The answer is False

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers