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3 years ago

Find the missing side lengths

Mathematics

2 answers:

nadya68 [22]3 years ago

8 0

Side a = 17

side b = 17

hichkok12 [17]3 years ago

3 0

Answer:

a = 17

b = 17

Answered by GAUTHMATH

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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

2 years ago

Please help me finish these for summer school :)

ValentinkaMS [17]

13.45 will be the answer

since we are finding the hypotenuse, the formula is a^2 + b^2 = c^2

this will then be 10^2 + 9^2 = c^2

181=c^2

c=13.45 :)

5 0

2 years ago

Read 2 more answers

Enunciado:Si una empresa determina que sus costos obedecen a un modelo lineal y además sabe que si produce $10$ unidades sus cos

const2013 [10]

Responder:

y = 200x + 2000

Explicación paso a paso:

Deje que la ecuación lineal se exprese como y = mx + c

m es la pendiente

c es la intersección

Si la empresa produce $ 10 unidades, sus costos totales son $ 4000 dólares y si produce $ 15 unidades sus costos ascienden a $ 5000 dólares, entonces podemos representar esto como puntos de coordenadas;

(10,4000) y (15,5000)

Conseguir la pendiente

m = 5000-4000 / 15-10

m = 1000/5

m = 200

Obtener la intersección c

Sustituya m = 2000 y el punto (10, 4000) en la fórmula y = MX + c

4000 = 200 (10) + c

4000-2000 = c

c = 2000

Sustituya m = 200 y c = 2000 en la ecuación y = mx + c

y = 200x + 2000

Por tanto, la expresión lineal requerida es y = 200x + 2000

3 0

2 years ago

What is the metric system

Anettt [7]

Answer:

the decimal measuring system based on the meter, liter, and gram as units of length, capacity, and weight or mass. The system was first proposed by the French astronomer and mathematician Gabriel Mouton (1618–94) in 1670 and was standardized in France under the Republican government in the 1790s.

Step-by-step explanation:

7 0

3 years ago

Which value is NOT equivalent to the other values?

Gre4nikov [31]

it's 0.4 while it may look like 4% it's actually 40% of 1

8 0

2 years ago

Read 2 more answers

Find the missing side lengths​

Find the missing side lengths