9514 1404 393
Answer:
- cable length: 300.2 ft
- anchor distance: 193.0 ft
Step-by-step explanation:
The side given is opposite the given angle. We want to find both the hypotenuse and the adjacent side in the right triangle that models the geometry.
Sin = Opposite/Hypotenuse
sin(50°) = (230 ft)/h
h = (230 ft)/sin(50°) ≈ 300.24 ft
The length of the cable must be about 300.2 feet.
__
Tan = Opposite/Adjacent
tan(50°) = (230 ft)/d
d = (230 ft)/tan(50°) ≈ 192.99 ft
The cable must be anchored about 193.0 ft from the tower.
The sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5
Given,
18th term of an arithmetic sequence = 8.1
Common difference = d = 0.25.
<h3>What is an arithmetic sequence?</h3>
The sequence in which the difference between the consecutive term is constant.
The nth term is denoted by:
a_n = a + ( n - 1 ) d
The sum of an arithmetic sequence:
S_n = n/2 [ 2a + ( n - 1 ) d ]
Find the 18th term of the sequence.
18th term = 8.1
d = 0.25
8.1 = a + ( 18 - 1 ) 0.25
8.1 = a + 17 x 0.25
8.1 = a + 4.25
a = 8.1 - 4.25
a = 3.85
Find the sum of 20 terms.
S_20 = 20 / 2 [ 2 x 3.85 + ( 20 - 1 ) 0.25 ]
= 10 [ 7.7 + 19 x 0.25 ]
= 10 [ 7.7 + 4.75 ]
= 10 x 12.45
= 124.5
Thus the sum of the first 20 terms of an arithmetic sequence with the 18th term of 8.1 and a common difference of 0.25 is 124.5
Learn more about arithmetic sequence here:
brainly.com/question/25749583
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The number of students who do not like puzzles and ride the bus to school is 205
To find the answer it is necessary to do the following procedure:
To find out how many people the 2/5 traveling by bus are equivalent to, divide the total number (2000) of people by 5, and then multiply that value by 2.
- 2000 ÷ 5 = 400
- 400 × 2 = 800
From the above, it can be established that 800 people travel by bus to school. Now, to know how many people travel by bus and do not like puzzles, the following operation must be done.
Subtract the number of students who do like puzzles and ride the bus (595) from the total number of students who ride the bus (800)
So the answer is 205 students ride the bus and they don't like puzzles.
Learn more at: brainly.com/question/24558946
Step-by-step explanation:
use the formula: (a+b)³ = a³+3a²b+3ab²+b³
and place the corresponding values.
15 round by the nearest 10 is 20.
