The recursive formula to describe a sequence is shown below.
PART A:
State the first four terms of this sequence.
PART B:
Can this sequence be represented using an explicit geometric formula? Justify your answer.
The first four terms of the sequence are 3, 7, 15, and 31. This sequence is represented using an explicit geometric formula.
What is the recursive rule?A rule is defined such that its definition includes itself.
Example:
F(x) = F(x-1) + c
is one such recursive rule.
PART A:
State the first four terms of this sequence.
[tex]a_1 = 3\\\\a_n = 1+ 2a_{n-1}[/tex]
[tex]a_2 = 1+ 2a_{2-1}\\\\a_2 = 1+ 2a_{1}\\\\a_2 = 7\\\\a_3 = 1+ 2a_{2}\\\\a_3 = 15\\\\a_4 = 1+ 2a_{3}\\\\a_4 = 31\\[/tex]
PART B:
This sequence is represented using an explicit geometric formula.
Learn more about the recursive rule and explicit rule here:
https://brainly.com/question/12620593
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Michelle invested $10,000 for one year, part at 8% interest and the rest at 12% annual interest. Her total interest for the year was $944. How much money did she invest at 12% interest?
Step by step please.
Answer:
Michelle invested $ 6,400 at 8% and $ 3,600 at 12%.
Step-by-step explanation:
Given that Michelle invested $ 10,000 for one year, part at 8% interest and the rest at 12% annual interest, and her total interest for the year was $ 944, to determine how much money did she invest at 12% interest, the following calculation must be done:
10,000 x 0.08 + 0 x 0.12 = 800
8,000 x 0.08 + 2,000 x 0.12 = 880
4,500 x 0.08 + 5,500 x 0.12 = 1,020
6,000 x 0.08 + 4,000 x 0.12 = 960
6,500 x 0.08 + 3,500 x 0.12 = 940
6,400 x 0.08 + 3,600 x 0.12 = 944
Therefore, Michelle invested $ 6,400 at 8% and $ 3,600 at 12%.
How much almond milk does James use per teaspoon of cashew butter
Evaluate (xy) ^-6 if x = 3 and y = -1.
A. 3
B. -1/729
C. 1/73
D. 1/729
If David walks 1/2 mile in 1/4 hour, then how fast does David walk in one hour? (In other words, what is David's "unit rate"?)
A trained stunt diver is diving off a platform that is 15 m high into a pool of water that is 45 cm deep. The height, h, in meters, of the stunt diver above the water, is modeled by h=-4.9t^2+12t+5, where t is the time in seconds after starting the dive.
a) How long is the stunt diver above 15 m?
b) How long is the stunt diver in the air?
Answer:
a) 0 seconds.
b) The stunt diver is in the air for 2.81 seconds.
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
Height of the diver after t seconds:
[tex]h(t) = -4.9t^2 + 12t + 5[/tex]
a) How long is the stunt diver above 15 m?
Quadratic equation with [tex]a < 0[/tex], so the parabola is concave down, and it will be above 15m between the two roots that we found for [tex]h(t) = 15[/tex]. So
[tex]h(t) = -4.9t^2 + 12t + 5[/tex]
[tex]15 = -4.9t^2 + 12t + 5[/tex]
[tex]-4.9t^2 + 12t - 10 = 0[/tex]
Quadratic equation with [tex]a = -4.9, b = 12, c = -10[/tex]. Then
[tex]\Delta = 12^{2} - 4(-4.9)(-10) = -52[/tex]
Negative [tex]\Delta[/tex], which means that the stunt diver is never above 15m, so 0 seconds.
b) How long is the stunt diver in the air?
We have to find how long it takes for the diver to hit the ground, that is, t for which [tex]h(t) = 0[/tex]. So
[tex]h(t) = -4.9t^2 + 12t + 5[/tex]
[tex]0 = -4.9t^2 + 12t + 5[/tex]
[tex]-4.9t^2 + 12t + 5 = 0[/tex]
Quadratic equation with [tex]a = -4.9, b = 12, c = 5[/tex]. Then
[tex]\Delta = 12^{2} - 4(-4.9)(5) = 242[/tex]
[tex]x_{1} = \frac{-12 + \sqrt{242}}{2*(-4.9)} = -0.36[/tex]
[tex]x_{2} = \frac{-12 - \sqrt{242}}{2*(4.9)} = 2.81[/tex]
Time is a positive measure, so we take 2.81.
The stunt diver is in the air for 2.81 seconds.
HELP NEEDED ASAP!! Find the sine of B
Complete the synthetic division to find the quotient of 3x^3-25x^2+12x-32 and x-8
Answer:
Explanation:
Hey there!
Please see your required solution in picture.
Quotient Q(X) = 3x²-x+4
Hope it helps!
Answer:
see image
Step-by-step explanation:
Plato/Edmentum
Plz solve this question correctly.
Show the steps needed to solve it.
Answer: 378y^3
Step-by-step explanation:
the formula for volume is V = L * w * h , where V=volume, L=length, W=width, and H=height
if we plug the numbers from the picture in, the formula would look like this:
V = 9y * 7y * 6y
to solve you just multiply them together
V = 378 y^3
CAN SOMEONE HELP ME OUT WITH THIS PLEASE AND THINK YOU
Answer:
[tex]10\frac{7}{18}[/tex]
Step-by-step explanation:
First revert it to improper fraction.
[tex]\frac{13}{2} +\frac{35}{9} \\\\[/tex]
Now put them to a common denominator.
[tex]\frac{187}{18}[/tex]
=> [tex]10\frac{7}{18}[/tex]
I need help, please!! I'll give a brainliest
Answer:
metals or metalloids
Step-by-step explanation:
I'm built different i dont know if im right about the question. im just not sure if i understood the question correctly
please help me 2 The two lines shown below are perpendicular. If the slope of the red line is 5 what is the slope of the green line? Use a slash mark (/) as a fraction bar if necessary. 15 O A. O OB. 5 min O c. O c tole D. O
Answer:
-5/2
Step-by-step explanation:
Perpendicular slope is always the negative reciprical. This basically means the opposite sign and the nubers are flipped.
Play the four digit 3,5,7,and 9 into the boxes pure in the position that would give the greatest results in the true numbers are multiplied
- 73X95
- 79X53
-97X35
-93X75
- 9 3 x 7 5
Step-by-step explanation:To get the combination that would yield the greatest result if the true number are multiplied,
i. multiply each given combination
73 x 95 = 6935
79 x 53 = 4187
97 x 35 = 3395
93 x 75 = 6975
ii. get the largest result from the results calculated above in (i)
The greatest of the results is 6975, therefore the digits should be placed like so;
9 3
7 5
simplify the question
Answer:
=−4√2
I got this when simplified.
Louise begins factoring the polynomial, which has four terms. 8x3+24x2+10x+30 2(4x3+12x2+5x+15) 2[4x2(x+3)+5(x+3)] Which is the completely factored form of her polynomial? 8x2(x + 3)2 2x(4x2 + 5) 2(4x2 + 5) (x + 3) 2(4x2 + 5) (x + 3)2
Answer:
[tex]8x3+24x2+10x+30= 2[(4x^2+5)(x+3)][/tex]
Step-by-step explanation:
Given
[tex]8x3+24x2+10x+30= 2(4x^3+12x^2+5x+15)[/tex]
[tex]8x3+24x2+10x+30= 2[4x^2(x+3)+5(x+3)][/tex]
Required
The complete factored form
We have:
[tex]8x3+24x2+10x+30= 2[4x^2(x+3)+5(x+3)][/tex]
Factor out x + 3
[tex]8x3+24x2+10x+30= 2[(4x^2+5)(x+3)][/tex]
The above represents the completely factored form
Answer:
C on edge
Step-by-step explanation:
I took the test
The present ages of hero and hero in the ratio 3 is to 4 5 years from now their ratio of their ages will be 4 is 25 find the present ages
Answer:
Presently; Veeru is 15 and Neeru is 20
Step-by-step explanation:
Given
See comment for proper format of question
Let their present ages be x and y
So:
[tex]x : y = 3 : 4[/tex]
5 years time, the ratio will be:
[tex]x + 5: y + 5= 4 : 5[/tex]
Required
Their present ages
Express both ratios as fractions
[tex]x : y = 3 : 4[/tex] becomes
[tex]\frac{x}{y} = \frac{3}{4}[/tex]
and
[tex]x + 5: y + 5= 4 : 5[/tex] becomes
[tex]\frac{x+5}{y+5} = \frac{4}{5}[/tex]
Make x the subject in: [tex]\frac{x}{y} = \frac{3}{4}[/tex]
[tex]x = \frac{3}{4}y[/tex]
[tex]x = 0.75y[/tex]
Cross multiply in [tex]\frac{x+5}{y+5} = \frac{4}{5}[/tex]
[tex]5(x + 5) = 4(y + 5)[/tex]
Substitute [tex]x = 0.75y[/tex]
[tex]5(0.75y + 5) = 4(y + 5)[/tex]
Open brackets
[tex]3.75y + 25 = 4y + 20[/tex]
Collect like terms
[tex]3.75y -4y = -25 + 20[/tex]
[tex]-0.25y = -5[/tex]
Divide by -0.25
[tex]y = 20[/tex]
Substitute [tex]y = 20[/tex] in [tex]x = 0.75y[/tex]
[tex]x = 0.75 * 20[/tex]
[tex]x = 15[/tex]
Two friends Vicky and Micky start a business together. They decided to share their capitals depending up on the variable expenditure. The capital of the two partners together is given by polynomial 6x² + 11x – 35 which is the product of their individual share factors.
a-The value of x, when their total share is equal to 0?
b-The total expenditure of Vicky and Micky when x = 10 is (in Rs
c-The sum of their expenditure is
Answer:
a- x = 5/3, or x = -7/2
b- 675
c - 5·x + 2
Step-by-step explanation:
The polynomial representing the capital of the two partners = 6·x² + 11·x - 35
a. The total share is the capital of the two partners together = 6·x² + 11·x - 35
∴ When their total share is equal to 0, we have;
6·x² + 11·x - 35 = 0
Factorizing the above equation with a graphing calculator gives;
(3·x - 5)·(2·x + 7)
Therefore;
x = 5/3, or x = -7/2
b- The total expenditure, when x = 10 is given by substituting the value of x in the polynomial 6·x² + 11·x - 35, as follows;
When x = 10
6·x² + 11·x - 35 = 6 × 10² + 11 × 10 - 35 = 675
The total expenditure of Vicky and Micky when x = 10 is 675
c - The sum of their expenditure is (3·x - 5) + (2·x + 7) = 5·x + 2
А
E
F
B1
2
2x
135°
750
2x -15°
12
G
H
I
C3
D
Determine the value of x.
i wonder this is math problem or code word for treasure
Answer:
Step-by-step explanation:
(2x-15) = 45
Step-by-step explanation:
When two angles lie on a straight line, they are supplementary
what this mean is that the add up to equal 180 degrees
Mathematically, we have this as:
(2x-15) + 135 = 180
(2x-15) = 180-135
(2x-15) = 45
log2 1 is defined
True
False
Answer: True
Through the change of base formula, we can say,
[tex]\log_{2}(1) = \frac{\log(1)}{\log(2)} = \frac{0}{\log(2)} = 0[/tex]
So in short,
[tex]\log_{2}(1)=0[/tex]
It turns out that
[tex]\log_{b}(1) = 0[/tex]
for real numbers b such that b > 0 and [tex]b \ne 1[/tex]
PLZ HELP ILL GIVE BRAINLIEST IF RIGHT!!!
Rosa has already written 11 pages ,and she expects to write 3 pages for every additional hour spent writing. How many hours will Rosa have to spend writing this week in order to have written a total of 47 pages?
Answer:
12 hours
Step-by-step explanation:
pages total = pages written + pages per hour * number of hour
47 = 11 + 3*h
Subtract 11 from each side
47 -11 = 11 +3h -11
36 = 3h
Divide by 3
36/3 = 3h/3
12 = h
HELP PLZ
Possible values for the area A of the rectangle shown are 12 - As 36. Write and
solve a compound inequality to find the possible values of x. Are these values all
viable in this situation?
2x + 1
3
Answer:
i had the exact same question as this, dm me on discord so i can screenshare my answer
Step-by-step explanation:
jey0001 is my discord
Help me with this question too
Answer:
The one on the right
Step-by-step explanation:
Because it is 4 then 3
Answer:
the second one (the one to the right)
Step-by-step explanation:
Find the equation of the line with slope -2 which goes through the point (9,-7).
Give your answer in slope-intercept form y = mx + b.
6. A bought 3 3 by 2 kg of wheat and 2 1 by 2kg of rice. Find the total weight of wheat and rice
bought.......
please answer the question proccesfuly.
the answer which is the best I will mark it as braunlist.
Answer:
Step-by-step explanation:544
Answer:
total weight of wheat and rice is 8 kg
Step-by-step explanation:
rice = [tex]3\frac{3}{2}[/tex]
=3*2+3/2
=9/2
wheat = [tex]2\frac{1}{2}[/tex]
=2*2+1/2
=5/2
total weight of wheat and rice = [tex]\frac{7}{2} + \frac{9}{2}[/tex]
since their denominator are same u can add numerators.
=7 +9/2
=16/2
=8
Calculus 2. Please help
Answer:
[tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}}} \, dx = \infty[/tex]
General Formulas and Concepts:
Algebra I
Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Calculus
Limits
Right-Side Limit: [tex]\displaystyle \lim_{x \to c^+} f(x)[/tex]Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integrals
Definite IntegralsIntegration Constant C
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
U-Solve
Improper Integrals
Exponential Integral Function: [tex]\displaystyle \int {\frac{e^x}{x}} \, dx = Ei(x) + C[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integral] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \int\limits^1_0 {\frac{e^{-x^2}}{x} \, dx[/tex][Integral] Rewrite [Improper Integral]: [tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \int\limits^1_a {\frac{e^{-x^2}}{x} \, dx[/tex]Step 3: Integrate Pt. 2
Identify variables for u-substitution.
Set: [tex]\displaystyle u = -x^2[/tex]Differentiate [Basic Power Rule]: [tex]\displaystyle \frac{du}{dx} = -2x[/tex][Derivative] Rewrite: [tex]\displaystyle du = -2x \ dx[/tex]Rewrite u-substitution to format u-solve.
Rewrite du: [tex]\displaystyle dx = \frac{-1}{2x} \ dx[/tex]Step 4: Integrate Pt. 3
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} -\int\limits^1_a {-\frac{e^{-x^2}}{x} \, dx[/tex][Integral] Substitute in variables: [tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} -\int\limits^1_a {\frac{e^{u}}{-2u} \, du[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}\int\limits^1_a {\frac{e^{u}}{u} \, du[/tex][Integral] Substitute [Exponential Integral Function]: [tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(u)] \bigg| \limits^1_a[/tex]Back-Substitute: [tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(-x^2)] \bigg| \limits^1_a[/tex]Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(-1) - Ei(a)][/tex]Simplify: [tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{Ei(-1) - Ei(a)}{2}[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \infty[/tex]∴ [tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx[/tex] diverges.
Topic: Multivariable Calculus
An unknown number y is 10 more than an unknown number x. The number y is also x less than 3. The equations to find x and y are shown
below.
y = x + 10
y=-x+3
Which of the followine statements is a correct step to find x and y?
A add the equations to eliminate x
B multiply the equations to eliminate y
C write the points where the groans of the equation intersect the x axis
D write the points where the graphs equation intersect the y axis
Answer:
a. add the equations to eliminate x
Step-by-step explanation:
this is called process of elimination
Can someone help me? Which of the following verifies that triangle YXZ is similar to triangle QPR?
Answer:
a
Step-by-step explanation:
How many cups of chocolate would Linda need for 2 cups of cream
căn bậc hai của (x^2-2x-3)
[tex]heres \: the \: answer \: i \: hope \: it \: help[/tex]
Which ordered pair is a solution of the equation y = -7x + 2
A. (1,2)
B. (8, -54)
C. (5, -35)
D. (1, -7)
Answer:
B. (8, -54)
Step-by-step explanation:
y = -7x + 2
Check to see if the point makes the equation true
A. (1,2) 2 = -7(1)+2 = -7+2 = 5 False
B. (8, -54) -54 = -7(8)+2 = -56+2 = -54 True
C. (5, -35) -35 = -7(5) +2 = -35+2 = -33 False
D. (1, -7) -7 =-7(1)+2 = --7+2 = -5 False