Answer:
[tex]b_n = \frac{2}{27} (9^n)[/tex]
Step-by-step explanation:
Given
[tex]a_1=\frac{2}{3},\ a_n=3a_{n-1}.[/tex]
Required
An explicit rule for [tex]b_1,\ b_2,\ b_3,\ \dots[/tex]
Where [tex]b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots[/tex]
We have:
[tex]a_1=\frac{2}{3},\ a_n=3a_{n-1}.[/tex]
Calculate a2
[tex]a_2 = 3a_{2-1}[/tex]
[tex]a_2 = 3a_1[/tex]
[tex]a_2 = 3 * \frac{2}{3}[/tex]
[tex]a_2 = 2[/tex]
Calculate a3
[tex]a_3 = 3a_{3-1}[/tex]
[tex]a_3 = 3a_2[/tex]
[tex]a_3 = 3 *2[/tex]
[tex]a_3 = 6[/tex]
Calculate a4
[tex]a_4 = 3a_{4-1}[/tex]
[tex]a_4 = 3a_3[/tex]
[tex]a_4 = 3*6[/tex]
[tex]a_4 = 18[/tex]
Calculate a5
[tex]a_5 = 3a_{5-1}[/tex]
[tex]a_5 = 3a_4[/tex]
[tex]a_5 = 3*18[/tex]
[tex]a_5 = 54[/tex]
So:
[tex]b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots[/tex]
[tex]a_1=\frac{2}{3}[/tex] [tex]a_3 = 6[/tex] [tex]a_5 = 54[/tex]
The above sequence form a geometric sequence.
Calculate common ratio (r)
[tex]r = \frac{b_3}{b_2}[/tex]
[tex]r = \frac{a_5}{a_3}[/tex]
[tex]r = \frac{54}{6}[/tex]
[tex]r = 9[/tex]
So, the explicit formula is:
[tex]b_n = b_1 * r^{n-1[/tex]
[tex]b_1=a_1[/tex], so:
[tex]b_n = a_1 * r^{n-1[/tex]
[tex]a_1=\frac{2}{3}[/tex], so:
[tex]b_n = \frac{2}{3} * 9^{n-1[/tex]
Split:
[tex]b_n = \frac{2}{3} * \frac{9^n}{9}[/tex]
[tex]b_n = \frac{2}{3*9} (9^n)[/tex]
[tex]b_n = \frac{2}{27} (9^n)[/tex]
The explicit rule is: [tex]b_n = \frac{2}{27} (9^n)[/tex]
estimate the product then find the product
Answer:
1 5/6 = 11/6
7 1/3 = 22/3
11/6 + 22/3 = 11/6 + 44/6 = 55/6 ≈ 9.16
1 5/6 = 11/6
11/6 - 1/10
55/30 - 3/30 = 52/30 ≈ 1.73
9.16 x 1.73 = 15.8468
So, 15.8468 is the result.
I hope this is helpful. :)
Please, do me Brainliest!
Write an equation for the hanger diagram and then us the sketch to show how to solve the equation algebraically.
Step-by-step explanation:
Since there are 3 w's and a 1 on one side and 7 1's on the other and the hanger diagram shows they are even, we can set them equal to each other.
3w + 1 = 7 Subtract 1 from both sides
3w = 6 Divide 3 from both sides
w = 2
V= u +at U=2 A=-5 T=1/2 Work out the value of v
Answer:
v =-1/2 hope it may help u
Step-by-step explanation:
v =u+at
v=2 -5/2
v=4-5/2
v=-1/2/2
Answer:
Step-by-step explanation:
Given
u = 2 , a = - 5 t = 1/2
Now
v = u + at
= 2 + (-5) * 1/2
= ( 4 - 5) /2
= - 1/2
Omar painted half of a heart on a piece of paper.
While the paint was still wet, he folded the paper in half and pressed the sides
together
Which transformation did Omar use to complete the heart?
A Slide
B Translation
C Dilation
D Reflection
Answer:
D reflection
Step-by-step explanation:
think of it like a mirror when u look at the mirror its an exact match to what u are seeing
please would you be so kind and help me with problems four through 12?
I will do 4 and 5 only. Also, post one problem at a time.
Question 4
Measure of arc GJ = measure of the central angle, which in this case is 90 degrees. So, the measure of arc GJ = 90°.
Question 5
The measure of diameter HJ = 180 degrees.
We need to find the adjacent angle which I will call angle x.
So, x = 180° - 151° = 29 degrees.
Just like Question 4 above, the measure of 29 degrees is the central angle for arc HI.
As you know, HI = the measure of the central angle. So, the measure of arc HI = 29°.
Try the rest on your own.
As you do the rest, keep in mind that the measure of a circle in terms of degrees is 360 degrees. This will help you do the rest of the questions for circle B.
If 6 pounds of grapes costs $1.89, how much would 15 pounds of grapes cost?
find the value of given expression
[tex] \sqrt{63 \times 63} [/tex]
Answer:
± 63Step-by-step explanation:
[tex]\sqrt{63*63} = \sqrt{63^2} =[/tex] ± 63Answer:
√(63×63)=√63²=±63 is your answer
The area of a rectangular parking lot is 8051 m ^2 . If the length of the parking lot is 97 m, what is its width?
Answer:
Width of rectangle = 83 meter
Step-by-step explanation:
Given:
Area of rectangle = 8,051 m²
Length of rectangle = 97 m
Find:
Width of rectangle
Computation:
Area of rectangle = Length of rectangle x Width of rectangle
97 x Width of rectangle = 8,051
Width of rectangle = 8,051 / 97
Width of rectangle = 83 meter
The proper height of a highway guardrail is 27 inches, but 3 inches higher or lower is acceptable. Which inequality represents the acceptable heights, h, of a highway guardrail?
A.|h+27|≤3
B.|h−3|≤27
C.|h+3|≤27
D.|h−27|≤3
Answer:
Step-by-step explanation:
27 is the "center" of a range of measurements of the height of the guard rail. The height could be as much as 30 inches or as little as 24 inches. The absolute value operator encloses "x - 27," where 27 is the "center." The acceptable excess or acceptable deficiency is 3 inches.
So now we can eliminate possible answers B and C, in both cases because 27 is inappropriately greater than 3.
Narrowing down our choices, we have h + 27 and h - 27 inside the absolute value operator. 27 is a positive quantity (height of the guard rail), so the inequality showing +27 as the "center" is correct; that is
D: |h - 27| ≤ 3 (measurements in inches).
The area of the parallelogram below is ____ square meters.
Answer:
63
Step-by-step explanation:
9 * 7 = 63
What is the radius of 18 circle?
What is the equation from this graph?
PLEASE HELP IF POSSIBLE :)
Answer:
JM = 20
Step-by-step explanation:
Find the value of JM
Using similar triangles;
MJ/HN = GJ/HK
GJ+JM/HN = GJ/HK
15+JM/12+16 = 15/12
15+JM/28 = 15/12
Cross multiply
12(15+JM) = 15*28
180+12JM = 420
12JM = 420 - 180
12JM = 240
JM = 240/12
JM = 20
Hence the length of JM is 20
find the value of given expression
[tex] \sqrt{213 \times 213} [/tex]
Answer:
213 Answer ..............
Answer:
√{213×213}=√213²=±213 is your answer
A hollow ball is made of rubber that is 2 centimeter thick. The ball has a diameter of 20 centimeters at the outside surface.
What is the exact volume of rubber used to make the ball?
Please explain how to find the volume and i will mark brainliest
Answer:
628.57CM²
Step-by-step explanation:
20/2=10
VOLUME OF CYLINDER=PIR^2H
22/7*10*10*2=628.57
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
268.083
Step-by-step explanation:
volume of a sphere = 4/3 times pi times r^3. 4/3(pi)(4^3) = 268.083
hellp me pls i need to pass this class or my parents will kill me for not passing
Answer:
hello wat is the matter how can I help I am a tutor I can teach you
PLEASE HELP
A number b increased by 4 is greater than or equal to 15.
Answer:
b ≥ 11
Step-by-step explanation:
b + 4 ≥ 15
b ≥ 15 - 4
b ≥ 11
Anyone help please god lord please
here are the answers:
#1
#2=11
#3=-2
#4=70
What is the solution for -4x - 10 ≤ 2?
Answer:
x>=-3
Step-by-step explanation:
-4x-10<=2
-4x<=2+10
-4x<=12
x<=12/-4
x<=-3
x>=-3
lec types 3/5 of a paragraph in 2/3 minute. If he continues at the same rate, what fraction of a paragraph can Alec complete in 1 minute?
Answer:
ik you in MS 118 but still the answer is 9/10
Step-by-step explanation:
multiply by the reciprocal 3/2.
3/5x3/2=9/10
Determine whether the measures for the figure shown are proportional.
a. the length of a side and the perimeter
b. the length of a side and the area
A researcher begins an experiment with 50 bacteria. She notices each bacterium triples every hour. Which equation best represents this scenario?
A. y=3(50)x
B. y=3x+50
C. y=50(3)x
D. y=3x+50
Answer:
A. y=3(50)x
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The Martinez Family has driven 240 miles so far. Their total trip is 300 miles. What percentage of the trip have they already driven?
Factor 18r+15s escribe tu respuesta como un producto con un número entero >1?
At a zoological garden, 3 people ride the tram for every 4 people who don't ride it. Write the ratio of people who ride the tram to all people in three ways. Write the ratio of all people to people who don't ride the tram in three ways. Write the ratio of people who ride the tram to all people in three ways.
Answer:
= 3 to 7
= 3 : 7
= 3/7
Step-by-step explanation:
Number of people who ride the tram = 3
Number of people who does not ride the tram = 4
Total people = 3 + 4 = 7
Ratio of people who ride the tram to all people in three ways.
= 3 to 7
= 3 : 7
= 3/7
Ratio of all people to people who don't ride the tram in three ways.
= 7 to 4
= 7 : 4
= 7/4
Ratio of people who ride the tram to all people in three ways.
= 3 to 7
= 3 : 7
= 3/7
Select all that are equivalent to a^2/a^9
Assume a \= 0
1
1
DONE
A coat is on sale for 30% off the original price of 120$.what is the amount of discount
Answer:
36
Step-by-step explanation:
You do 120 multiplied by .3 to get 36. This makes the discount amount is $36 which also means you only pay $84 for the coat.
a pilot is flying an airplane at an elevation of 17,500 feet. she is increasing her elevation at a rate of 2,500 feet per minute. which number line shows the solution set for the number of minutes the pilot could increase her elevation and be above 25,000 feet?
Answer:
y= *greater than or equal to sign* 2500x+17500
The answer is: A
Step-by-step explanation:
Hope this help :)
Answer:
It's C
Step-by-step explanation:
I put in A for my exam but it said it was incorrect and it said the answer was C :')
Write down the x-coordinate of the point where y=x2-x and y=x+1 cross