Answer:
The radius is
or 2.866
Step-by-step explanation:
Given
Central angle = 120
Length of arc = 6
Required
The radius
To solve this question, we'll apply the formula of length of an arc.
The length of an arc is calculated as follows;
![L = \frac{theta}{360} * 2\pi r](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7Btheta%7D%7B360%7D%20%2A%202%5Cpi%20r)
Where theta = central angle = 120
L = length of the arc = 6.
By substituting these values in the formula above, we have
![6 = \frac{120}{360} * 2\pi r](https://tex.z-dn.net/?f=6%20%3D%20%5Cfrac%7B120%7D%7B360%7D%20%2A%202%5Cpi%20r)
![6 = \frac{1}{3} * 2\pi r](https://tex.z-dn.net/?f=6%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2A%202%5Cpi%20r)
Multiply both sides by 3
![3 * 6 =3 * \frac{1}{3} * 2\pi r](https://tex.z-dn.net/?f=3%20%2A%206%20%3D3%20%2A%20%20%5Cfrac%7B1%7D%7B3%7D%20%2A%202%5Cpi%20r)
![18 = 2\pi r](https://tex.z-dn.net/?f=18%20%3D%202%5Cpi%20r)
Divide both sides by ![2\pi](https://tex.z-dn.net/?f=2%5Cpi)
![\frac{18}{2\pi} = \frac{2\pi r}{2\pi}](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7B2%5Cpi%7D%20%3D%20%5Cfrac%7B2%5Cpi%20r%7D%7B2%5Cpi%7D)
![r = \frac{18}{2\pi}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B18%7D%7B2%5Cpi%7D)
![r = \frac{9}{\pi}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B9%7D%7B%5Cpi%7D)
Leaving the answer in terms of
, the radius is calculated as ![\frac{9}{\pi}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B%5Cpi%7D)
However, if we're to solve further
Taking
as 3.14
![r = \frac{9}{3.14}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B9%7D%7B3.14%7D)
![r = 2.866](https://tex.z-dn.net/?f=r%20%3D%202.866)
The radius is 2.866
I think you mean "a set of three points". What I would do is take one point, find the slope from that point to another one, and then find the slope from the same starting point to the third one. If the (absolute values of the) slopes from the same starting point to each of the others are equal, then the three points are collinear.
Answer:
$18.
Step-by-step explanation:
$9:8= 1.125 $ per pound.
16 x 1.125 =18$
The points on the graph of the parabola other than the vertex and x-intercepts where the equation of the parabola is given as t(x) = -x^2 + 4x - 3 are (10, -63) and (5, -8)
<h3>How to determine the points on the graph of the parabola other than the vertex and x-intercepts?</h3>
The equation of the parabola is given as:
t(x) = -x^2 + 4x - 3
The vertex of the parabola is the point where the graph is at the maximum or the minimum
While the x-intercept is the point where the graph crosses the x-axis i.e when y = 0
Having said that, we have the equation of the parabola to be
t(x) = -x^2 + 4x - 3
Set x = 5.
So, we have:
t(5) = -5^2 + 4 * 5 - 3
Evaluate the exponents
t(5) = -25 + 4 * 5 - 3
Evaluate the products
t(5) = -25 + 20 - 3
Evaluate the sum and the difference
t(5) = -8
Set x = 10.
So, we have:
t(10) = -10^2 + 4 * 10 - 3
Evaluate the exponents
t(10) = -100 + 4 * 10 - 3
Evaluate the products
t(10) = -100 + 40 - 3
Evaluate the sum and the difference
t(10) = -63
Hence, the points on the graph of the parabola other than the vertex and x-intercepts where the equation of the parabola is given as t(x) = -x^2 + 4x - 3 are (10, -63) and (5, -8)
Read more about parabola at:
brainly.com/question/4061870
#SPJ1
Answer:
Kaitlin's account will have 72% of the money initially invested, that is, about $ 6,192.
Step-by-step explanation:
Given that last year Kaitlin opened an investment account with $ 8,600, and at the end of the year, the amount in the account had decreased by 28%, to determine the year-end amount in terms of the original amount both in whole numbers and in decimals, the following calculation must be performed:
100 - 28 = 72
8,600 x 0.72 = X
6.192 = X
Thus, Kaitlin's account will have 72% of the money initially invested, that is, about $ 6,192.