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3 years ago

15

A circle has a sector with area 27pie and central angle of 120

1 answer:

yaroslaw [1]3 years ago

3 0

Answer:

Step-by-step explanation:

27π= 120°/360°* πr^2

81=r^2

r=9

Area of circle=πr^2

Area of circle=254.34 or 81π

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goblinko [34]

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3 0

3 years ago

Function f is an exponential function. It predicts the value of a famous painting, in thousands of dollars, as a function of the

nalin [4]

Answer:

$y=8 \cdot (\frac{5}{4})^x$

$f(x)=8 \cdot (\frac{5}{4})^x$

or

$f(x)=8 \cdot (1.25)^x$

Step-by-step explanation:

We are going to see if the exponential curve is of the form:

$y=a \cdot b^x$ , ( $b\neq 0$ ).

If you are given the $y-$ intercept, then $a$ is easy to find.

It is just the $y-$ coordinate of the $y-$ intercept is your value for $a$ .

(Why? The $y-$ intercept happens when $x=0$ . Replacing $x$ with 0 gives $y=a \cdot b^0=a \cdot 1=a$ . This says when $x=0 \text{ that} y=a$ .)

So $a=8$ .

So our function so far looks like this:

$y=8 \cdot b^x$

Now to find $b$ we need another point. We have two more points. So we will find $b$ using one of them and verify for our resulting equation works for the other.

Let's do this.

We are given $(1,10)$ is a point on our curve.

So when $x=1$ , $y=10$ .

$10=8 \cdot b^1$

$10=8 \cdot b$

Divide both sides by 8:

$\frac{10}{8}=b$

Reduce the fraction:

$\frac{5}{4}=b$

So the equation if it works out for the other point given is:

$y=8 \cdot (\frac{5}{4})^x$

Let's try it. So the last point given that we need to satisfy is $(2,12.5)$ .

This says when $x=2$ , $y=12.5$ .

Let's replace $x$ with 2 and see what we get for $y$ :

$y=8 \cdot (\frac{5}{4})^2$

$y=8 \cdot \frac{25}{16}$

$y=\frac{8}{16} \cdot 25$

$y=\frac{1}{2} \cdot 25}$

$y=\frac{25}{2}$

$y=12.5$

So we are good. We have found an equation satisfying all 3 points given.

The equation is $y=8 \cdot (\frac{5}{4})^x$ .

4 0

3 years ago

d1i1m1o1n [39]

Step-by-step explanation:

$x^{2} - 4x - 7 = 0$

First, let's move the $7$ to the right-hand side so we can determine what constant we'll need on the left-hand side to complete the square:

$x^{2} - 4x = 7$

From here, since the coefficient of the $x$ term is $-4$ , we know the square will be $(x - 2)$ (since $-2$ it's half of $-4$ ).

To complete this square, we will need to add $(-2)^{2}$ to both sides of the equation:

$x^{2} - 4x + (-2)^2 = 7 + ^{-2}$

$x^{2} - 4x + 4 = 7 + 4$

$(x - 2)^{2} = 11$

Now we can take the square root of both sides to figure out the solutions to $x$ :

$x - 2 = \pm \sqrt{11}$

$x = 2 \pm \sqrt{11}$

7 0

3 years ago

If u bring 10 empty bottles to the bottle shop, the bottle shop will change 10 empty bottles for a drink. If u bring 100 bottles

lakkis [162]

100 divided by 10 is ten, so they would give you ten bottles!

7 0

3 years ago

Read 2 more answers

Joshua has more than 250 toy soldiers. When he tries to arrange them in rows of 3, there are 2 left over. When he tries to arran

Vikentia [17]

Don't look at this comment.. I messed up the first time so, yeah.

6 0

2 years ago