A geometric sequence is given by the recursive rule $a_1=\frac{2}{3},\ a_n=3a_{n-1}$ . Give an explicit rule for the nth term of the sequence $b_1,\ b_2,\ b_3,\ \dots\ ,$ given that $b_1=a_1,\ b_2=a_3,\ b_3=a_5,\ \dots$ .
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]
en una granja sembraron 20 parcelas de locotes, con 40 plantas en cada una ¿Cuántas plantas de locotes se tienes?
Answer:
800
Step-by-step explanation:
20 x 40 = 800
Two trains on opposite tracks leave the same station at the same time. One train travels at an average speed of 80 kilometres per hour and the other travels at an average speed of 70 kilometres per hour. How long after they leave the station will they be 50 km apart?
Answer:
1/3 hr or 20 min.
Step-by-step explanation:
Call the trains A and B
Remember d = rt
Distance train A travels is 80t
Distance train B travels is 70t
Now, 80t + 70t = 50
150t = 50
t = 50/150 = 1/3 hr or 20 min.
Quadrilaterals must have exactly 4 sides. The shapes in ___ must have 2 pairs of parallel sides, 4 right angles, and 4 sides of equal length. The shapes in ___ must have at least one pair of parallel sides. The shapes in Group D must have 2 pairs of parallel sides and 4 sides of equal length. The shapes in ___ must have 2 pairs of parallel sides and 4 right angles. The shapes in ___ must have exactly 2 pairs of parallel sides.
Answer:
1) Square
2) Trapezoid
3) Rectangle
4) Parallelogram
Step-by-step explanation:
Quadrilaterals must have exactly 4 sides.
The shapes in a square must have 2 pairs of parallel sides, 4 right angles, and 4 sides of equal length.
The shapes in a trapezoid must have at least one pair of parallel sides. The shapes in Group D must have 2 pairs of parallel sides and 4 sides of equal length.
The shapes in a rectangle must have 2 pairs of parallel sides and 4 right angles.
The shapes in Parallelogram must have exactly 2 pairs of parallel sides.
Answer:
yoooo
Step-by-step explanation:
Find the value of x. Round your answer to the nearest tenth.
Answer:
+4√5
Step-by-step explanation:
Note that this is a right triangle. Therefore, the lengths of the three sides are related through the Pythagorean Theorem: a^2 + b^2 = c^2, where c is the length of the hypotenuse.
Thus, x^2 + 19^2 = 21^2, or, after solving this for x^2,
x^2 = 441 - 361 = 80
x is therefore +√80, or +4√5.
Choose Yes or No to tell if the fraction 58 will make each equation true. 815−□=37 Yes □−516=58 No 78−12=□ No 34−18=□ Yes
Answer:
815−58=37 False
58−516=58 False
78−12=58 False
34−18=58 False
Step-by-step explanation:
i just did them all on my algebra calculator and they all said false. brainliest please?
The store brought a pair of shoes for 40$ and sold it for 50$. What percentage was the markup?
Answer:
20%
Step-by-step explanation:
You would do 40/50 and then 40/50 is also 80/100. Then you'd take the remainder and that'd be the mark up price.
HELP NO WRONG ANSWER PLS
it's π 11²-π 3²
π(121-9)
3.14(112)
=351.68cm²
round off yourself (╥﹏╥)
Which triangle is similar to triangle T
Answer:
2nd one from the left.
Step-by-step explanation:
it has the same angle measures.
PLEASE HELP ASAP PLEASE WILL GIVE BEST RATE AND BRAINLEST PLEASE
Answer:
I think it's 145.225 sq in.
Step-by-step explanation:
2.5 x 2 x 3.14 = 15.7
15.7 x 9.25 = 145.225
Answer:
its the second one
Step-by-step explanation:
2.5 x 2 x 3.14 = 15.7 because 3.14 is pi
and then do
15.7 x 9.25 = 145.225 so there you go
Can some one help me answer this.
Answer: y= 0.0025
Step-by-step explanation:
Answer:
y= 0.0025
Step-by-step explanation:
every number in the y place is mutipled by four so to find y you need to divide 0.01 by 4
Please help I'll mark brainliest ASAP (NO LINKS)
Answer:
see belowStep-by-step explanation:
4)for question 1 there is only a constant terms 2
hence, our answer choice is
a)25)Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5, ... (and so on)
hence our answer choices are
a)31b)06) degree of a expression means the exponent of the expression
since there's no number 3 as exponent
our answer choice is
False7) The Standard Form for writing down a polynomial is to put the terms with the highest degree first
hence our answer choice is
Dto simplify the expression
remember, law of exponent i.e [tex]\displaystyle x^m\times x^n=x^{m+n}[/tex]
[tex]\displaystyle (5x ^{2} y)(3x ^{3} y ^{4} )[/tex]
simplify:
[tex]\displaystyle 15x ^{2 + 3} y ^{4 + 1} [/tex]
[tex]\displaystyle 15x ^{5} y ^{5} [/tex]
hence, our answer choice is
[tex]C)15x ^{5} y ^{5} [/tex]Step-by-step explanation:
4.constant term=2
2.whole no : 31&0
5.false
7.15x^5y^5
6.standard form =2x^5-8x⁴y³+3x²y
what is the answer to this question?
qeta ssbeni rpnedjo e
adwdaee icsoch
Please can someone help I don’t understand the question if it’s right I’ll give more plsssssesssssssssssddsd
Answer:
x = 33°
Step-by-step explanation:
From the figure attached,
FB and FC are two secants intersecting each other at point F outside the circle.
Measure of angles between the secants measures half of the difference between the intercepted arcs.
x° = [tex]\frac{1}{2}(\text{arc BC}-\text{arc DE})[/tex]
x° = [tex]\frac{1}{2}(108-42)[/tex]
x = 33°
Please I need this quick !!!
Answer:
81
Step-by-step explanation:
First we go with exponents, 2x2=4 and 5x2=25. Now we go with what's inside the parentheses so, 4 (Originally 2x2) plus 4 plus 6, which equals 14. Now we multiply 4 and 14, which equals 56. Then we add 56 and 25 which equals 81.
PLEASE HELP ASAP I WILL GIVE BRAINLILIST
Let () = −3(2)^ and () = − 14.
Complete the table to determine the solutions of () = −3(2)^ = () = − 14.
The solution of () = −3(2)
= () = − 14 is = ______
Step-by-step explanation:
-3. 2
-2. 1
-7. 6
i did my best.
Blank minus 1/10 equals 1/2
if the difference (3x2 - 2x + 5) – (x2 + 3x - 2) is multiplied by 1/2x^2,
what is the result, written in standard form?
The result of the given equation [tex](3x^2 - 2^x + 5) -(x^2 + 3x - 2)\\[/tex] is [tex]4x^4-10x^3 + 14x^2[/tex]
What is cubic polynomial ?"Cubic polynomial is a type of polynomial based on the degree i.e. the highest exponent of the variable. Hence, a cubic polynomial is a polynomial with the highest power of the variable or degree is 3. A polynomial is an algebraic expression with variables and constants with exponents as whole numbers"
"The general form of a cubic polynomial is p(x): ax3 + bx2 + cx + d, a ≠ 0, where a, b, and c are coefficients and d is the constant with all of them being real numbers. An equation involving a cubic polynomial is called a cubic equation. "
The given equation is given as[tex](3x^2 - 2^x + 5) - (x^2 + 3^x - 2)[/tex]
Solving it ,we get [tex]2x^2 - 5x +7[/tex]
Now multiplying it by [tex]1/2x^2[/tex] gives us [tex]4x^4-10x^3 + 14x^2[/tex]
Hence the answer is [tex]4x^4-10x^3 + 14x^2[/tex]
To know more about cubic polynomial here
https://brainly.com/question/12726811
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What is the value of 3^2+4(2+4)x6 divided by 8+4
Answer:
its 31
Step-by-step explanation:
the first three terms of sequence are given round the nearest thousandth if necessary
12,15,18,..
Find the 32nd term
Answer:
105
Step-by-step explanation:
It is increasing by 3 everytime.
So you just use that and write down all numbers in order ascending to the 32nd term.
I'd list them all but I don't think you wanna read all of it.
Hope this helps.
i got the last one wrong , pls give me the right answer i need atleast a 75%
How do you say I am sleepy in spanish?
Answer:
tengo sueño
Step-by-step explanation:
Answer:
To say I am sleepy in spanish you say: tengo sueño
Step-by-step explanation:
Hope this helped!
in the pic below help me please
Answer:
comet is the on the other side the 3rd one down and crater is the 4th one down meteor is the second one down and meteorite is the 5th on down which is the last one. Asteroid is the first one.
Find the solution to this equation - 3x + 32 - 7x = -2 (5x + 10)
Remember the steps
1. Distribute
2. Combine like terms on the left side
3 Pick sides variables = constants
4 Move terms that don't belong by doing the opposite operations
5 Decide what the statement means If it's always true write "infinitely many solutions." If it's always false, write "no solutions."
Answer:
[tex]x =\frac{-26}{3}[/tex]
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3x+32−7x=−2(5x+10)
3x+32+−7x=(−2)(5x)+(−2)(10)(Distribute)
3x+32+−7x=−10x+−20
(3x+−7x)+(32)=−10x−20(Combine Like Terms)
−4x+32=−10x−20
−4x+32=−10x−20
Step 2: Add 10x to both sides.
−4x+32+10x=−10x−20+10x
6x+32=−20
Step 3: Subtract 32 from both sides.
6x+32−32=−20−32
6x=−52
Step 4: Divide both sides by 6.
6x
6
=
−52
6
x=
−26
3
Will give brainliest to whoever figures this out :(
Step-by-step explanation:
I think it's 8.9932×10⁶
Answer:
8,993,200
Step-by-step explanation:
10^3 is 1000
8993.2 * 1000
=
8,993,200
please help!!!! find the value of x
Answer:
The answer is x+2=7,
Step-by-step explanation:
because x is a variable
I need this for bonus points !
Find the lateral surface area of the triangular prism.
A) 420 cm2
B) 480 cm2
C) 540 cm2
D) 620 cm2
Answer:
620
Step-by-step explanation:
other dood is wrong lol i did the math and took the test AND got it right
The lateral surface area of the triangular prism is 480 square cm,
option (B) is correct.
It is given that the triangular prism has a 10 cm height and its sides are 16 cm, 12 cm, and 20 cm respectively.
It is required to find the lateral surface area.
What is the lateral surface area?It is defined as the surface area of an object excluding its top and base areas, it is different from the total area.
We know that,
The lateral surface area of triangular prism = perimeter of the
base×height
= (a + b + c ) × h
We have, a = 16, b = 20 cm, c = 12 cm, and h =10 cm.
Putting these values in the above formula, we get:
[tex]\rm = (16+20+12) \times10\\\\\rm = 48\times 10\\\\\rm = 480 \ cm^2[/tex]
Thus, the lateral surface area of the triangular prism is 480 square cm,
option (B) is correct.
Learn more about the lateral surface area here:
https://brainly.com/question/14001755
pls help asap for brainlest
Answer:
the answer is C ik its right because i did this two days ago so im sure its C
Step-by-step explanation:
Find the approximate radius of a circle with a circumference of 198 centimeters. Use 3.14
for it Round to the nearest hundredth.
A. 63.06
B. 31.53
C. 621.72
D. 310.86
The radius of the circle is around 31.65 cm. Choice B
The formula C = 2πr , where C is the circle's circumference and r is its radius, yields the circumference of a circle. In this illustration, the circle's circumference is given as 198 cm
C = 2πr
The formula to calculate the radius can be revised as follows:
r = C / (2π)
r = 198 / (2 * 3.14)
To perform the calculation, divide the numbers:
r ≈ 198 / 6.28
r ≈ 31.65
The circle's estimated radius is 31.65 centimetres as a result.
So, rounded to the closest hundredth, the estimated radius of the circle with a circumference of 198 centimetres is 31.65 centimetres.
The closest option to 31.65 in the list of possible answers is B. 31.53. It's crucial to keep in mind that choosing 3.14 as an approximation for involves some mistake and that the precise radius number might change slightly.
When rounded to the next hundredth, the radius is 31.65. This result can be compared to the other solutions to show that:
B. 31.53.
For more such questions on radius visit;
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