Mathematics, 17.07.2019 06:30 lllizzas

In this picture the measure of angle theta is 1 radian

Answers: 2

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Answer from: leshayellis1591

True.

Step-by-step explanation:

Answer from: uh8hardiek

To solve this, we are going to use the formula for the area of the sector of a circle: $A= \frac{1}{2} r^2 \alpha$
where

is the area of the circular sector.

is the radius of the circle.
$\alpha$ is the central angle in radians.

We know form our problem that that the measure of the central angle is 1 radian, so $\alpha =1$ . We can also infer from the picture that the radius of the circle is 3in, so r=3in

. Lets replace those values in our formula to find

:
$A= \frac{1}{2} r^2 \alpha$
$A= \frac{1}{2} (3in)^2(1)$
A=4.5in^2

We can conclude that the area of the circular sector in the picture is 4.5 square inches.

To prove that the arc length is indeed 3 inches, we are going to use the formula: $A_{L}=r \alpha$
where
$A_{L}$ is the arc length.

us the radius of the circle.
$\alpha$ is the central angle.

We know from our problem that r=3in

, and $\alpha =1$ , so lets replace those values in our formula:
$A_{L}=r \alpha$
$A_{L}=(3in) \alpha$
$A_{L}=3in$

We can conclude that the length of the arc is indeed 3 inches.

Answer from: Quest

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

=3x+1

=3(2)+1

since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

=x+1

=2+1

now, let's find g(2)g(2):

g(x)

g(2)

=2x

=2⋅2

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

Answer from: Quest

many reason,

step-by-step explanation:

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