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Paul [167]
3 years ago
5

a sequence is defined recursively by the formula f(n 1) = f(n) 8 . the first term of the sequence is 6. what is the next term in

the sequence? there are no options.
Mathematics
1 answer:
Mariulka [41]3 years ago
8 0
F(2) = f(1 + 1) = f(1) + 8 = 6 + 8 = 14
You might be interested in
The reciprocal of 1/2
12345 [234]

Answer:

2

Step-by-step explanation:

When you "flip" the fraction, switching the numerators and denominators, you get 2/1 which is just 2.  

6 0
3 years ago
Read 2 more answers
An airplane pilot can see the top of a traffic control tower at a 20 degree angle of depression. the airplane is 5,000 feet away
daser333 [38]

The given question describes a right triangle with with one of the angles as 20 degrees and the side adjacent to the angle 20 degrees is of length 5,000 feet. We are looking for the length of the side opposite the angle 20 degrees.

Let the required length be x, then

\tan{20^o}=\cfrac{opp}{hyp}=\cfrac{x}{5,000}\\ \\ \Rightarrow x=5,000\tan{20^o}=1,819.85

Therefore, the height of the airplane above the tower is 1,819.85 feet.

8 0
3 years ago
Read 2 more answers
1. Consider the right triangle ABC given below.
lbvjy [14]
#1) 
A) b = 10.57
B) a = 22.66; the different methods are shown below.
#2)
A) Let a = the side opposite the 15° angle; a = 1.35.
Let B = the angle opposite the side marked 4; m∠B = 50.07°.
Let C = the angle opposite the side marked 3; m∠C = 114.93°.
B) b = 10.77
m∠A = 83°
a = 15.11

Explanation
#1)
A) We know that the sine ratio is opposite/hypotenuse.  The side opposite the 25° angle is b, and the hypotenuse is 25:
sin 25 = b/25

Multiply both sides by 25:
25*sin 25 = (b/25)*25
25*sin 25 = b
10.57 = b

B) The first way we can find a is using the Pythagorean theorem.  In Part A above, we found the length of b, the other leg of the triangle, and we know the measure of the hypotenuse:
a²+(10.57)² = 25²
a²+111.7249 = 625

Subtract 111.7249 from both sides:
a²+111.7249 - 111.7249 = 625 - 111.7249
a² = 513.2751

Take the square root of both sides:
√a² = √513.2751
a = 22.66

The second way is using the cosine ratio, adjacent/hypotenuse.  Side a is adjacent to the 25° angle, and the hypotenuse is 25:
cos 25 = a/25

Multiply both sides by 25:
25*cos 25 = (a/25)*25
25*cos 25 = a
22.66 = a

The third way is using the other angle.  First, find the measure of angle A by subtracting the other two angles from 180:
m∠A = 180-(90+25) = 180-115 = 65°

Side a is opposite ∠A; opposite/hypotenuse is the sine ratio:
a/25 = sin 65

Multiply both sides by 25:
(a/25)*25 = 25*sin 65
a = 25*sin 65
a = 22.66

#2)
A) Let side a be the one across from the 15° angle.  This would make the 15° angle ∠A.  We will define b as the side marked 4 and c as the side marked 3.  We will use the law of cosines:
a² = b²+c²-2bc cos A
a² = 4²+3²-2(4)(3)cos 15
a² = 16+9-24cos 15
a² = 25-24cos 15
a² = 1.82

Take the square root of both sides:
√a² = √1.82
a = 1.35

Use the law of sines to find m∠B:
sin A/a = sin B/b
sin 15/1.35 = sin B/4

Cross multiply:
4*sin 15 = 1.35*sin B

Divide both sides by 1.35:
(4*sin 15)/1.35 = (1.35*sin B)/1.35
(4*sin 15)/1.35 = sin B

Take the inverse sine of both sides:
sin⁻¹((4*sin 15)/1.35) = sin⁻¹(sin B)
50.07 = B

Subtract both known angles from 180 to find m∠C:
180-(15+50.07) = 180-65.07 = 114.93°

B)  Use the law of sines to find side b:
sin C/c = sin B/b
sin 52/12 = sin 45/b

Cross multiply:
b*sin 52 = 12*sin 45

Divide both sides by sin 52:
(b*sin 52)/(sin 52) = (12*sin 45)/(sin 52)
b = 10.77

Find m∠A by subtracting both known angles from 180:
180-(52+45) = 180-97 = 83°

Use the law of sines to find side a:
sin C/c = sin A/a
sin 52/12 = sin 83/a

Cross multiply:
a*sin 52 = 12*sin 83

Divide both sides by sin 52:
(a*sin 52)/(sin 52) = (12*sin 83)/(sin 52)
a = 15.11
3 0
3 years ago
Read 2 more answers
a school musical soild 353 tickets. $5 for adults and $3.50 for students. the school made $1500 how many adult tickets were sold
IrinaVladis [17]

Answer:

177 Students

176 Adults

Step-by-step explanation:

Adult - (A) $5

Student - (S) $3.50

Equation 1: A+S = 353 tickets

Equation 2: 5A + 3.50S = $1500

Sub equation 1 into 2:

5A + 3.50(353 - A) = 1500

Multiply: 5A + 1235.50 -3.50A =1500

Subtract 1235.50 and -3.50A from both sides: 1.50A = 264.50 and then divide:

264.50/1.50 = 176 Adults

Sub into equation 1:

176 +S = 353

Solve: 353 - 176 = 177 Students

Check: 5(176) + 3.50(177) = $1500

1499.5 rounded = 1500 = 1500 ✔

I hope this helped!

3 0
3 years ago
A certain number was divided by 3 and 3 was added to the result. The final answer was 8 what was the number​
nevsk [136]

Answer:

15

Step-by-step explanation:

x/3 + 3 = 8

x/3 + 9/3 = 8

x + 9 = 24

x = 15

5 0
2 years ago
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