Answer:
31.9617 rounded to 32
Step-by-step explanation:
set up is sin24=13/x
Answer:
5.83 miles
Step-by-step explanation:
Bill's net distance west of his starting point is -4+7 = 3 miles. His net distance north of his starting point is 5 miles. The straight-line distance will be the hypotenuse of a right triangle with legs 3 miles and 5 miles. That distance is given by the Pythagorean theorem:
d² = (3 mi)² +(5 mi)² = 34 mi²
d = √34 mi ≈ 5.83 mi
Bill is 5.83 miles on a direct line from his starting point.
_____
The attached calculator screenshot shows the sum of the travel distances. The angles are bearings measured clockwise from north. The angle of the sum indicates Bill is about 31° west of north relative to his starting point.
Given:
The figure.
To find:
The value of a.
Solution:
We know that, in a right angled triangle
![\tan \theta =\dfrac{Perpendicular}{Base}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%20%3D%5Cdfrac%7BPerpendicular%7D%7BBase%7D)
In the given triangle,
![\tan (38^\circ) =\dfrac{6}{a}](https://tex.z-dn.net/?f=%5Ctan%20%2838%5E%5Ccirc%29%20%3D%5Cdfrac%7B6%7D%7Ba%7D)
Multiply both sides by a.
![\tan (38^\circ)\times a=6](https://tex.z-dn.net/?f=%5Ctan%20%2838%5E%5Ccirc%29%5Ctimes%20a%3D6)
Divide both sides by ![\tan (38^\circ)](https://tex.z-dn.net/?f=%5Ctan%20%2838%5E%5Ccirc%29)
![a =\dfrac{6}{\tan (38^\circ)}](https://tex.z-dn.net/?f=a%20%3D%5Cdfrac%7B6%7D%7B%5Ctan%20%2838%5E%5Ccirc%29%7D)
The value of a is
.
Therefore, the correct option is b.
Answer:
The 6th term of the sequence is 6144/243
Step-by-step explanation:
From what we have, we can see that the sequence might be geometric
to confirm this, we have to check if the common ratio is the same all through
To know this, we have to divide the succeeding term by the preceding term and check if the results for two sets are equal
thus, we have it that;
32/3 * 1/8 = 8/6
= 4/3 = 4/3
We can confirm that the sequence is thus geometric
Now, to find the nth term of a geometric sequence, we have it that;
Tn = ar^(n-1)
where a is the first term, given as 6
r is the common ratio given as 4/3
n is the term number given as 6
Thus, we have this as:
T6 = 6 * (4/3)^(6-1)
T6 = 6 * (4/3)^5
T6 = 6144/243