Answer:
15 degrees
Step-by-step explanation:
Draw a horizontal segment approximately 4 inches long. Label the right endpoint A and the left endpoint C. Label the length of AC 4.2 meters. That is the horizontal distance between the eye and the blackboard.
At the right endpoint, A, draw a vertical segment going up, approximately 1 inch tall. Label the upper point E, for eye. Label segment EA 1 meter since the eye is 1 meter above ground.
At the left endpoint of the horizontal segment, point C, draw a vertical segment going up approximately 2 inches. Label the upper point B for blackboard. Connect points E and B. Draw one more segment. From point E, draw a horizontal segment to the left until it intersects the vertical segment BC. Label the point of intersection D.
The angle of elevation you want is angle BED.
The length of segment BC is 2.1 meters. The length of segment CD is 1 meter. That means that the length of segment BD is 1.1 meters.
To find the measure of angle BED, we can use the opposite leg and the adjacent leg and the inverse tangent function.
BD = 1.1 m
DE = 4.2 m
tan <BED = opp/adj
tan <BED = 1.1/4.2
m<BED = tan^-1 (1.1/4.2)
m<BED = 15
Answer: 15 degrees
Answer:
(a) 0.367
(b) 0.544
(c) 0.616
(d) 0.792
(e) 1.087
Step-by-step explanation:
The transition matrix T multiplying the vector ...
{freshmen, sophomores, juniors, seniors, graduates, dropouts}
can be written as
(a) Then the 4th power of this matrix (1st attachment) will tell the number of freshmen graduating in 4 years. That will be ...
__
(b) Then the 5th power of this matrix (2nd attachment) will tell the number of freshmen graduating in 5 years. That will be ...
__
(c) The Nth power of matrix T as N approaches infinity (3rd attachment) will tell the numbers of students of each class who eventually graduate. For freshmen, that fraction is ...
__
(d) As in part (c), the desired fraction is ...
__
(e) The expected number of years spent in school is the sum of the products of time in school and the probability of taking that time. The expected value in years is ...
Answer:
A. at (8,7) the maximum value is 98
Step-by-step explanation:
First draw the region, that is bounded by all
inequalities. This is the triangle with vertices
(6,1), (2,5) and (8,7).
Now you can see where the line f(x,y)=7x+6y
intersect this region. The maximum value will be
at endpoints of this region:
• at (6,1), f(6,1)=7-6+6-1=42+6=48;
·
at (2,5), f(2,5)=7·2+6.5=14+30=44;
• at (8,7), f(8,7)=7.8+6-7=56+42=98.
Thus, the maximum value of the function is 98 at
the point (8,7).
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Answer:
First statement is correct
Step-by-step explanation:
Segment AB is tangent to circle C because