All categories

2 years ago

What is the vertical asymptote of the graph shown below?

Mathematics

1 answer:

sleet_krkn [62]2 years ago

7 0

Answer:

x = - 1

Step-by-step explanation:

As x → ± ∞, the curve approaches x = - 1

You might be interested in

What is -5x=-2y for slope-intercept form of the equation

julsineya [31]

Answer:

y=(5/2)x

Step-by-step explanation:

Math

7 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

Find the distance between 2-4i and d 6+i

liq [111]

Answer:

7.211

Step-by-step explanation:

-For two points in the complex plane, the distance between the points is the modulus of the of the difference of the two complex numbers.

-Point 2-4i has the coordinates (2,-4)

-Point 6+i has the coordinates (6,1)

#We must find the distance between the two coordinates (2,-4) and (6,1):

$=\sqrt{(6-2)^2+(1--4)^2}\\\\=\sqrt{4^2+6^2}\\\\=\sqrt{52}\\\\=7.211$

Hence, the distance between the two points is 7.211

8 0

2 years ago

Which pair of points have a slope of -3/5?

Allushta [10]

Answer:

No of these answers has a slope of $\frac{-3}{5}$ . My guess is B becasue its close to $\frac{-3}{5}$ unless the 5 is supposed to be negative

Step-by-step explanation:

You have to use the slope formula $\frac{y_{2} - y_{1} }{x_{2} - x_{1} }$

( $x_{1}$ , $y_{1}$ ), ( $x_{2}$ , $y_{2}$ )

(4, 0), (-2, 10) $\frac{10 - 0 }{-2 - 4 }= \frac{10}{6}$ you have to simplfy, the answer will be $\frac{5}{3}$

(10, -2), (0, 4) $\frac{4 - -2 }{0- 10 }= \frac{6}{-10}$ you have to simplfy, the answer will be $\frac{3}{-5}$

(4, 2), (10, 4) $\frac{4 - 2 }{10 - 4 }= \frac{2}{6}$ you have to simplfy, the answer will be $\frac{1}{3}$

(-4, -10),(0, -2) $\frac{{-2- -10} }{0 - -4 }= \frac{8}{4}$ you have to simplfy, the answer will be $\frac{2}{1} =2$

5 0

2 years ago

PLEAASSSE HELP ASAP I WILL MARK →BRAINLIEST← AND 5 STARS!!!

algol13

Answer:Yes she has enough

Step-by-step explanation:

Total ounces=11

1st recipe=6 ounces

2nd recipe=1/4 ounces

1 pound =16 ounces

= 1/4 pounds × 16 ounces/1 pound

= 4 ounces

First recipe + Second recipe

= 6 ounces + 4 ounces

= 10 ounces.

10 ounces of walnuts and Marni has 11

5 0

2 years ago