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3 years ago

5

What is the radius of the circle who’s equation is x^2 + y^2 = 9

1 answer:

Svetllana [295]3 years ago

8 0

Answer:

r=3

Step-by-step explanation:

The equation of a circumference is $(x-a)^2+(y-b)^2=r^2$ .
Then , in this case $r^2=9$ , and then to know the value of r we just simply have to calculate the square root of 9, which is 3.

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Can someone help me with this please? I'll give you brainliest :)

andreev551 [17]

Step-by-step explanation:

(2*5)*4 = 10*4 = 40

2*(5*4) = 2*20 = 40

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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 sum (3x^2+5x-8)+(5x^2-13x-5)

Radda [10]

<span>8x^2-8x-13 is the correct answer </span>

3 0

2 years ago

Read 2 more answers

Solve the inequality.<br> |3x+7| <_ 4

n200080 [17]

Answer:

Using ∣x∣>a⇒x<−a or x>a, we get

∣3x−7∣>4⇒3x−7<−4 or 3x−7>4

⇒3x<3 or 3x>11⇒x<1 or x>

3

11

⇒x∈(−∞,1)∪(

3

11

,∞).

3 0

2 years ago

Read 2 more answers

The radius of a circle is 20 cm. Find its area in terms of π π.

natulia [17]

Answer:

A = $400\pi cm^2$

Step-by-step explanation:

Area of a circle is:

A = πr²

We are given a radius of 20 cm.

A = πr²

A = π(20)²

A = π400

<em>A = 400πcm²</em>

Hope this helps.

4 0

2 years ago