Answer:
Step-by-step explanation:
Given radius and arc length
.
Divide. Use place-value blocks or area models to help.
1 answer:
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Answer:
Circumcenter =(-1,0)
Orthocenter =(2,-3)
Step-by-step explanation:
Given : Points A = (2,3), B = (-4,-3), C = (2,-3)
Formula used :
→Mid point of two points-
→Slope of two points -
→Perpendicular of a line =
Circumcenter- The point where the perpendicular bisectors of a triangle meets.
Orthocenter-The intersecting point for all the altitudes of the triangle.
To find out the circumcenter we have to solve any two bisector equations.
We solve for line AB and AC
So, mid point of AB =
Slope of AB =
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of the perpendicular bisector = -1
Equation of AB with slope -1 and the coordinates (-1,0) is,
(y – 0) = -1(x – (-1))
y+x=-1………………(1)
Similarly, for AC
Mid point of AC =
Slope of AC =
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of the perpendicular bisector = 0
Equation of AC with slope 0 and the coordinates (2,0) is,
(y – 0) = 0(x – 2)
y=0 ………………(2)
By solving equation (1) and (2),
put y=0 in equation (1)
y+x=-1
0+x=-1
⇒x=-1
So the circumcenter(P)= (-1,0)
To find the orthocenter we solve the intersections of altitudes.
We solve for line AB and BC
So, mid point of AB =
Slope of AB =
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of CF = -1
Equation of AB with slope -1 and the coordinates (-1,0) gives equation CF
(y – 0) = -1(x – (-1))
y+x=-1………………(3)
Similarly, mid point of BC =
Slope of AB =
Slope of the bisector is the negative reciprocal of the given slope.
So, the slope of AD = 0
Equation of AB with slope 0 and the coordinates (-1,-3) gives equation AD
(y-(-3)) = 0(x – (-1))
y+3=0
y=-3………………(4)
Solve equation (3) and (4),
Put y=-3 in equation (3)
y+x=-1
-3+x=-1
x=2
Therefore, orthocenter(O)= (2,-3)
Answer:
The percentage of people should be seen by the doctor between 13 and
17 minutes is 68% ⇒ 2nd term
Step-by-step explanation:
* Lets explain how to solve the problem
- Wait times at a doctor's office are typically 15 minutes, with a standard
deviation of 2 minutes
- We want to find the percentage of people should be seen by the
doctor between 13 and 17 minutes
* To find the percentage we will find z-score
∵ The rule the z-score is z = (x - μ)/σ , where
# x is the score
# μ is the mean
# σ is the standard deviation
∵ The mean is 15 minutes and standard deviation is 2 minutes
∴ μ = 15 , σ = 2
∵ The people should be seen by the doctor between 13 and
17 minutes
∵ x = 13 and 17
∴ z =
∴ z =
- Lets use the standard normal distribution table
∵ P(z > -1) = 0.15866
∵ P(z < 1) = 0.84134
∴ P(-1 < z < 1) = 0.84134 - 0.15866 = 0.68268 ≅ 0.68
∵ P(13 < x < 17) = P(-1 < z < 1)
∴ P(13 < x < 17) = 0.68 × 100% = 68%
* The percentage of people should be seen by the doctor between
13 and 17 minutes is 68%