Find the length of AB.A140/6 inAB = [ ? ]inBRound your answer to the nearest hundredth.
![Find The Length Of AB.A140/6 InAB = [ ? ]inBRound Your Answer To The Nearest Hundredth.](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/jicRXjNRdbDIFkJGCLsM8uPSW5jrFa0Y.jpeg)
Answers
The length of AB is given by:
AB = θ*r
Basically AB = L
Where:
L = Arc length of the minor sector.
Now:
r = 6 in
θ = 140° = 7/9 π
Therefore:
AB = (7/9 π) * 6 = 14/3 π ≈ 14.66 in
Related Questions
Math sequence 1,2,4,7,__
Answers
Maths sequence :
1+1 = 2
2+2 =4
4+3 =7
7+4 =11
11+5 = 16
16 +6 = 22
22+7 = 29......
rule : add the answer with the next number to .
sequence is that the pattern rule.
The governor of state A earns $48,430 more than the governor of state B . If the total of their salaries is $279,100, find the salaries of each
Answers
For the first part, we can write
[tex]B+48430=A[/tex]where A is the salary for governor A and B is the salary for governor B.
From the second part, we can write
[tex]A+B=279100[/tex]Then, we have 2 equations in 2 unknows.
Solving by substitution method.
If we substitute the firs equation into the second one ,we get
[tex](B+48430)+B=279100[/tex]which gives
[tex]2B+48430=279100[/tex]If we move 48430 to the right hand side as -48430, we have
[tex]\begin{gathered} 2B=279100-48430 \\ 2B=230670 \end{gathered}[/tex]then, B is equal to
[tex]\begin{gathered} B=\frac{230670}{2} \\ B=115335 \end{gathered}[/tex]Finally, by substituting this result into our first equation, we obtain
[tex]\begin{gathered} A+115335=279100 \\ A=279100-115335 \\ A=163765 \end{gathered}[/tex]This means that governo A earns $163,765 and gobernor B earns $115,335
HELP)1-47.Which of the relationships below are functions? If a relationship is not a function, give a reason to support yourconclusion. Homework Helpb.input (a) output (y)&-3195191900-37input (2)- 2074c.d.output (y)1001030**INSERT PICTURES OF YOUR WORK HERE.
Answers
According to the given data, from the relationship seen in the image, the ones that are functions are the following:
b. This is a function becuase there is exactly one output for every input.
Picture of work:
Input output
-3 __________ 19
5 __________ 19
19 __________ 0
0 __________ -3
c. This is a function becuase there is exactly one output for every input.
Input output
7 __________ 10
-2 __________ 0
0 __________ 10
7 __________ 3
4_____________ 0
what is the value of 6n-2whenn=3
Answers
To find the value of an expression we only need to plug the value of the variable in said expression.
In this case we have:
[tex]6n-2[/tex]If, n=3, then:
[tex]6(3)-2=18-2=16[/tex]Therefore, the value of the expression when n=3 is 16.
A rectangular paperboard measuring 33 in long and 21 in wide has a semicircle cut out of it as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.)
Answers
Explanation
The question wants us to obtain the perimeter of the paperboard that remains after the semicircle has been removed
To do so, we will follow the steps below:
Step1: Find the Perimeter of the rectangle
The perimeter of a rectangle is simply the sum of all its sides
So in our case, we will have to sum sides A as given below
[tex]Perimeter\text{ of rectangle= 21 +33+33= 87 inches}[/tex]Step 2: Find the perimeter of the semi-circle
The perimeter of a semi-circle is given by:
[tex]\begin{gathered} \frac{\pi D}{2} \\ where \\ \pi=3.14 \\ D=diameter\text{ of the semicircle =21 inches} \end{gathered}[/tex]Simplifying
[tex]Perimeter\text{ of semicircle=}\frac{3.14\times21}{2}=32.97\text{ inches}[/tex]Step 3: Find the sum of the perimeters of the rectangle and semicircle
Therefore, the perimeter of the paperboard that remains after the semicircle is removed will be
[tex]\begin{gathered} perimeter\text{ }of\text{ }the\text{ }rectangle+\text{ perimeters of the semicircle =87inches + 32.97 inches} \\ perimeter\text{ }of\text{ }the\text{ }rectangle-\text{ perimeters of the semicircle =119.97 inches} \end{gathered}[/tex]Hence, the perimeter of the paperboard that remains after the semicircle is removed will be 119.97 in
The time spent waiting in the line is approximately normally distributed. The mean waiting time is 6 minutes and the variance of the waiting time is 9. Find the probability that a person will wait for between 10 and 12 minutes. Round your answer to four decimal places.
Answers
The probability that a person will wait for between 10 and 12 minutes is 0.069.
What is meant by z score?z-score is defined as the number of standard deviations by which the value of a raw score is above or below the mean value of what is being measured or observed. It tells where the score lies on a normal distribution curve. It is a numerical measurement that describes a values relationship to the mean of a group of values.
z = (raw score - mean) / standard deviation
Given,
The mean waiting time is 6 minutes and variance waiting time is 9 minutes.
Standard deviation = √variance = √9 = 3minutes
For between 10 and 12 minutes, the probability is
z = (10- 6)/3 = 1.333 and z=(12-6)/3=2
p(z≤1.3333)=0.982
p(z≤2)=0.9772
Probability that a person will wait for between 10 and 12 minutes is,
|0.9082-0.9772|= 0.069
To know more about z-score, visit:
https://brainly.com/question/15016913
#SPJ1
denominator of a fraction is 2 more than the numerator . if both numerator and denominator are increased by 10 , a simplified result is 9/10. Find the original fraction. Do not simplify
Answers
Let the numerator = x
The denominator of a fraction is 2 more than the numerator
So, the denominator = x + 2
if both numerator and denominator are increased by 10, a simplified result is 9/10.
So,
[tex]\frac{x+10}{(x+2)+10}=\frac{9}{10}[/tex]Solve for x:
[tex]\begin{gathered} \frac{x+10}{x+12}=\frac{9}{10} \\ \\ 10(x+10)=9(x+12) \\ 10x+100=9x+108 \\ 10x-9x=108-100 \\ x=8 \end{gathered}[/tex]so, the original fraction will be = 8/10
So, the answer will be = 8/10
Find the angle between the vectors (-9, -8) and (-9,5). Carry your intermediate computations to at least 4 decimalplaces. Round your final answer to the nearest degree.| 。x 6 ?
Answers
The vector for (-9,-8) is,
[tex]u=-9\hat{i}-8\hat{j}[/tex]The vector for (-9,5) is,
[tex]v=-9\hat{i}+5\hat{j}[/tex]The formula for the angle between vector u and vector v is,
[tex]\cos \theta=\frac{u\cdot v}{|u\mleft\Vert v\mright|}[/tex]Determine the angle between vectors.
[tex]\begin{gathered} \cos \theta=\frac{(-9\hat{i}-8\hat{j)}\cdot(-9\hat{i}+5\hat{j})}{\sqrt[]{(-9)^2+(-8)^2}\cdot\sqrt[]{(-9)^2+(5)^2}} \\ =\frac{81-40}{\sqrt[]{145}\cdot\sqrt[]{106}} \\ =\frac{41}{\sqrt[]{15370}} \\ \theta=\cos ^{-1}(0.3307) \\ =70.688 \\ \approx71 \end{gathered}[/tex]So angle between the vector is 71 degree.
Simplify each expression by using The Distributive Property and combine like terms to simplify the expression.4(3х - 2)
Answers
The given expression is
[tex]undefined[/tex]Find the minimum or maximum value of the function f(x)=10x^2+x−5. Give your answer as a fraction.
Answers
In order to find the minimum or maximum value of the function f(x),
[tex]f\mleft(x\mright)=10x^2+x-5[/tex]First, we have to find out at which value of x the function takes it. For example:
In order to find the value of x when it takes the maximum of minimum, we are going to analyze the derivative of the function. Then we are going to be following the next step-by-step:
STEP 1: finding the derivative of the function
STEP 2: analysis of the derivative of the function.
STEP 3: minimum or maximum value of the function
STEP 1: finding the derivative of the functionWe have that the derivative of the function is given by f'(x):
[tex]\begin{gathered} f\mleft(x\mright)=10x^2+x^1-5 \\ \downarrow \\ f^{\prime}(x)=2\cdot10x^{2-1}+1\cdot x^{1-1} \\ f^{\prime}(x)=20x^{2-1}+1\cdot x^0 \\ f^{\prime}(x)=20x^1+1\cdot1 \\ f^{\prime}(x)=20x^{}+1 \end{gathered}[/tex]Then, the derivative of f(x) is:
f'(x) = 20x + 1
STEP 2: analysis of the derivative of the function.We have that the function has a maximum or a minimum when its derivative takes a value of 0:
[tex]\begin{gathered} f^{\prime}\mleft(x\mright)=0 \\ 0=20x+1 \end{gathered}[/tex]when this happens, then, x has a value of:
[tex]\begin{gathered} 0=20x+1 \\ \downarrow\text{ taking -1 and 20 to the left side} \\ -1=20x \\ -\frac{1}{20}=x \end{gathered}[/tex]When x=-1/20, the function takes its minimum or maximum
STEP 3: minimum or maximum value of the functionNow, we can replace in the equation of f(x), to see what is the value of the function when x= -1/20:
[tex]\begin{gathered} f\mleft(x\mright)=10x^2+x-5 \\ \downarrow\text{ when x=}-\frac{1}{20} \\ f(-\frac{1}{20})=10(-\frac{1}{20})^2+(-\frac{1}{20})-5 \end{gathered}[/tex]Solving f(-1/20):
[tex]\begin{gathered} f(-\frac{1}{20})=10(-\frac{1}{20})^2+(-\frac{1}{20})-5 \\ \downarrow\sin ce(-\frac{1}{20})^2=\frac{1}{400} \\ =10(\frac{1}{400})-\frac{1}{20}-5 \\ =-\frac{201}{40} \end{gathered}[/tex]Then, the minimum value of the function is
[tex]f\mleft(x\mright)=\frac{-201}{40}[/tex]Answer: -201/40Select the correct choice below and fill in the answer
Answers
Step 1:
Write the function
[tex]g(x)=x^5-16x^3[/tex]Step 2:
Write an inequality equation where g(x) > 0
[tex]\begin{gathered} x^5-16x^3\text{ > 0} \\ \text{Factorize the left hand side of the equation} \\ x^3(x^2\text{ - 16) > 0} \\ x^3(x\text{ - 4)(x + 4) > 0} \end{gathered}[/tex]Step 3:
Identify the intervals
- 4 < x < 0 or x > 4
[tex]\text{Answer in interval notation: }(\text{ - 4 , 0 ) }\cup\text{ ( 4 , }\infty\text{ )}[/tex]Find the formula for an exponential equation that passes through the points, (0,5) and (1,2). The exponential equation should be of the form y = ab^x
Answers
Answer:
[tex]y=5\cdot(\frac{2}{5})^x[/tex]Explanation:
The exponential equation has the form
[tex]y=a\cdot b^x[/tex]Since it passes through the point (0, 5). Let's replace (x, y) by (0, 5) to find the value of a
[tex]\begin{gathered} 5=a\cdot b^0 \\ 5=a\cdot1 \\ 5=a \end{gathered}[/tex]Then, the equation is
[tex]y=5\cdot b^x[/tex]To find the value of b, we will use the point (1, 2), so replacing x = 1 and y = 2, we get:
[tex]\begin{gathered} 2=5\cdot b^1 \\ 2=5\cdot b \\ \frac{2}{5}=\frac{5\cdot b}{5} \\ \frac{2}{5}=b \end{gathered}[/tex]Then, the exponential equation is:
[tex]a=5\cdot(\frac{2}{5})^x[/tex]Answer:
Step-by-step explanation: the answer is a= 5(2/5)^x
The model shows the expression 21 + 9. Which expression is equivalent to this sum? O 317+3) 0 31+ 3 0 3+7+3 O 763+3)
Answers
Given data:
The given expression is (21+9).
The given expression can be written as,
[tex](21+9)=3(7+3)[/tex]Thus, the first option is correct.
Given: CD⎯⎯⎯⎯⎯⎯ is an altitude of △ABC.Prove: a2=b2+c2−2bccosAFigure shows triangle A B C. Segment A B is the base and contains point D. Segment C D is shown forming a right angle. Segment C D is labeled h. Segment A B is labeled c. Segment B C is labeled a. Segment A C is labeled b. Segment A D is labeled x. Segment D B is labeled c minus x. Select from the drop-down menus to correctly complete the proof.Statement ReasonCD⎯⎯⎯⎯⎯⎯ is an altitude of △ABC. Given△ACD and △BCD are right triangles. Definition of right trianglea2=(c−x)2+h2a2=c2−2cx+x2+h2Square the binomial.b2=x2+h2cosA=xbbcosA=xMultiplication Property of Equalitya2=c2−2c(bcosA)+b2a2=b2+c2−2bccosA Commutative Properties of Addition and Multiplication
Answers
Solution:
The equation below is given as
[tex]a^2=(c-x)^2+h^2[/tex]This represents the
PYTHAGOREAN THEOREM
The second equation is given below as
[tex]b^2=x^2+h^2[/tex]This represents the
PYTHAGOREAN THEOREM
The third expression is given below as
[tex]\cos A=\frac{x}{b}[/tex]This represents
Definition of cosine
The fourth expression is given below as
[tex]a^2=c^2-2c(bcosA)+b^2[/tex]This represents
Substitution property of equality
find each measure 113° 23°x=?
Answers
We have that a vertex outside a circle is just the half of the difference of the angles:
Then, in this case:
[tex]x=\frac{113-23}{2}=\frac{90}{2}=45[/tex]Answer: x = 45º
Fallington Fair charges an entrance fee of $10 and $1.00 per ticket for the rides. Levittown Fair charges $5 entrance fee and $2 per ticket. Write an equation/inequality to show when Fallington Fair and Levittown Fair will cost the same.
Answers
Information given
Fallington Fair charges an entrance fee of $10 and $1.00 per ticket for the rides. Levittown Fair charges $5 entrance fee and $2 per ticket. Write an equation/inequality to show when Fallington Fair and Levittown Fair will cost the same.
Solution
Let's put some notation for this case, let x the number of rides and we can set up the following equation:
[tex]\text{Fallington}=\text{Levitown}[/tex][tex]10+x=5+2x[/tex]And now we can solve for x on the following way:
10-5= 2x-x
5=x
So then Fallington Fair and Levittown Fair will cost the same at 5 rides
For z1 = 9cis 5pi/6 and z2=3cis pi/3, find z1/z2 in rectangular form
Answers
We have the following:
are the complex number
[tex]\begin{gathered} z_1=9cis\frac{5\pi}{6}_{} \\ z_2=3\text{cis}\frac{\pi}{3} \\ \frac{z_1}{z_2} \end{gathered}[/tex]So magnitudes are r₁ = 9, and r₂ = 3 and arguments are ∅₁ = 5π/6, and ∅₂ = π/3
[tex]\frac{z_1}{z_1}=\frac{r_1}{r_2}\cdot\text{cis(}\emptyset_1\cdot\emptyset_{2})[/tex]replacing:
[tex]\begin{gathered} \frac{z_1}{z_2}=\frac{9}{3}\cdot\text{cis}(\frac{5\pi}{6}-\frac{\pi}{3}) \\ \frac{z_1}{z_2}=3\cdot\text{cis}(\frac{5\pi}{6}-\frac{2\pi}{6}) \\ \frac{z_1}{z_2}=3\cdot\text{cis}(\frac{3\pi}{6}) \\ \frac{z_1}{z_2}=3\cdot\text{cis}(\frac{\pi}{2})\rightarrow\text{cis}(\frac{\pi}{2})=\cos \mleft(\frac{\pi}{2}\mright)+3i\sin \mleft(\frac{\pi}{2}\mright) \\ \frac{z_1}{z_2}=3\cdot\lbrack\cos (\frac{\pi}{2})+i\sin (\frac{\pi}{2})\rbrack \\ \frac{z_1}{z_2}=3\cdot\lbrack0+i\cdot1)\rbrack \\ \frac{z_1}{z_2}=3\cdot0+3\cdot i \\ \frac{z_1}{z_2}=3i \end{gathered}[/tex]Therefore, the answer is option D 3i
You deposit $ 1,821 in an account earning 3 % interest compounded monthly. How much will you have in the account in 1 years?$__________ (Give your answer accurate to 2 decimal places)
Answers
Using the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = Amount
P = Principal = $1821
r = Interest rate = 3% = 0.03
n = Number of times interest is compounded per year = 12
t = Time = 1
So:
[tex]\begin{gathered} A=1821(1+\frac{0.03}{12})^{12\cdot1} \\ A\approx1876.39 \end{gathered}[/tex]Answer:
$1876.39
8+7i/4-6iI need the answer and how to solve asap!
Answers
ANSWER
[tex]\frac{1}{52}(-10\text{ + 76i) or }\frac{1}{26}(-5\text{ + 38i)}[/tex]EXPLANATION
We are given the fraction of complex numbers:
[tex]\frac{\text{8 + 7i}}{4\text{ - 6i}}[/tex]To simplify this, we will find the conjugate of the denominator and then multiply that with the numerator and denomiator.
The conjugate is gotten by changing the sign of the denominator. That is:
4 + 6i
So, we have:
[tex]\begin{gathered} \frac{\text{8 + 7i}}{4\text{ - 6i}}\cdot\text{ }\frac{4\text{ + 6i}}{4\text{ + 6i}} \\ =\text{ }\frac{(8\text{ + 7i) (4 + 6i)}}{(4\text{ - 6i) (4 + 6i)}} \\ =\frac{(8\cdot\text{ 4) + (8 }\cdot\text{ 6i) + (7i }\cdot\text{ 4) + (7i }\cdot\text{ 6i)}}{(4\cdot\text{ 4) + (6i }\cdot\text{ 4) - (6i }\cdot\text{ 4) - (6i }\cdot\text{ 6i)}} \\ We\text{ know that i = }\sqrt{i},\text{ so i }\cdot\text{ i = -1:} \\ \Rightarrow\text{ }\frac{\text{ }32\text{ + 48i + 28i - 42}}{16\text{ + 24i - 24i + 36}} \\ =\text{ }\frac{-10\text{ + 76i}}{16\text{ + 36}}\text{ = }\frac{-10\text{ + 76i}}{52} \\ =\text{ }\frac{1}{52}(-10\text{ + 76i) or }\frac{1}{26}(-5\text{ + 38i)} \end{gathered}[/tex]That is the answer.
3 3/10 divied by 1 4/7 in lowest terms
Answers
Answer:
Step-by-step explanation:
The answer is [tex]\frac{21}{10}[/tex] or 2 [tex]\frac{1}{10}[/tex] or 2.1.
Depending on what form your answer needs to be in, it can be one of those.
Explanation:
Turn both the mixed numbers into improper fractions. To do this, take the outside number and multiply it by the denominator. Then, add that number to the numerator. For this specific question, you would take 3×10 (because 10 is the denominator) and add it to the numerator, 3, giving the improper fraction [tex]\frac{33}{10}[/tex]. Doing the same to the divisor, you would get [tex]\frac{11}{4}[/tex].Next, take the divisor ([tex]\frac{11}{7}[/tex]) and turn it into the reciprocal ("flip" the fraction), making it [tex]\frac{7}{11}[/tex].Now, simply multiply the dividend ([tex]\frac{33}{10}[/tex]) to the reciprocal of the divisor ([tex]\frac{4}{11}[/tex]).So, your new equation is a much easier [tex]\frac{33}{10}[/tex]×[tex]\frac{7}{11}[/tex]=[tex]\frac{231}{110}[/tex]. These both are reducable by 11, therefore giving you the final answer of [tex]\frac{21}{10}[/tex].
Note: Upon reaching this step, you can simplify 33 into 3×11, then divide out the 11 from the numerator and the denominator making it a much easier problem to simplify. Hope this helps!
Do not round ant intermediate computations, and round your final answers to the nearest cent
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
PART ONE;
a) Find the interest that will be owed after 78 days:
[tex]Simple\text{ Interest = }\frac{Principal\text{ x Rate x Time}}{100}[/tex][tex]Simple\text{ Interest =}\frac{15,600\text{ x 3. 6 x }\frac{78}{365}}{100}=\text{ \$ 120.01}[/tex]PART TWO:
Assume that she doesn't make any payment, the amount owed after 78 days:
[tex]\begin{gathered} Amount\text{ = Principal + Simple Interest} \\ Amount\text{ = \$15600 + \$ 120.01} \\ Amount\text{ = \$ 15,720.01} \end{gathered}[/tex]A bag of fertilizer covers 2,000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn that is 29400 square feet.
Answers
Okay, here we have this:
Considering the provided information, we are going to calculate how many bags of fertilizer should be purchased to cover a rectangular lawn that is 29400 square feet, so we obtain the following:
Number of bags=Total space / Space per bag
Number of bags=29400ft² / 2000ft²
Number of bags=14.7
Number of bags≈15 bags of fertilizer.
Finally we obtain that rounded to the nearest unit, 15 bags of fertilizer are needed.
i have to use interval notation and i’m stuck on it
Answers
Given two sets of real numbers:
[tex]\begin{gathered} D=\mleft\lbrace w\mright|w\ge4\} \\ E=\mleft\lbrace w\mright|w<8\} \end{gathered}[/tex]we will write the given sets as intervals
so,
[tex]\begin{gathered} D=\lbrack4,\infty) \\ E=(-\infty,8) \end{gathered}[/tex]The intersections and the union of the sets will be as follows:
[tex]\begin{gathered} D\cap E=\lbrack4,8) \\ \\ D\cup E=(-\infty,\infty) \end{gathered}[/tex]10x the nunber adds to 5 is the same as 9 times the number is what
Answers
Answer:
-5
Step-by-step explanation:
5+10x=9x
clt
5=9x-10x
5=-x
x=-5
Each vertical cross-section of the triangular prism shown below is an isosceles triangle.4What is the slant height, s, of the triangular prism?Round your answer to the nearest tenth.The slant height isunits
Answers
The length of the diagonal of a cube can be calculated by the formula
[tex]\begin{gathered} d=a\sqrt[]{3} \\ \text{where a is one side of the cube} \\ a=60 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} d=60\sqrt[]{3}\text{ units} \\ d=103.92\text{ units (2 decimal place)} \end{gathered}[/tex]3. The Hill family rented a car for the weekend. The rental agency charged a weekend fee of $35.00 and $0.12 per mile. Their final bill was $44,36, Which equation could be used to discover how many miles the family drove (A) 44.36 - 12y = 35 (B) 12x + 35 = 44.36 (C) 35 +0.12% = 44.36 (D) 44.36 + 35 = 0.127
Answers
ANSWER:
C)
[tex]35+0.12x=44.36[/tex]STEP-BY-STEP EXPLANATION:
With the help of the statement, we can conclude that the equation is the following because the value of 0.12 must go together with the x, and that the total value must be 44.36
[tex]\begin{gathered} 35+0.12x=44.36 \\ \text{where x is the number of miles the familly drove} \end{gathered}[/tex]Select three points: one above the line, one below it, and one on it. Substitute each into the inequality and show the results.Select the words from the drop-down lists to correctly complete the sentences.The point (−5, 5) is on, below, above the line and is, is not a solution to the inequality. The point (0, 10) is on, below, above the line and is, is not a solution to the inequality. The point (0, 0) is on, below, above the line and is not, is a solution to the inequality.(0, 0) is on, below, above the line and is now, is a solution to the inequality.
Answers
EXPLANATION
Since we have the given graph, the points that we can use are the following:
The points (-5,5) is above the line and is not a solution to the inequality.
The point (0,10) is on the line and is not a solution to the inequality.
The point (0,0) is below the line and is a solution to the inequality.
evaluate this expression using the quotient rule 9^7 divided by 9^2
Answers
Using the method of Quotient rule:
[tex]\begin{gathered} \text{Which says} \\ \frac{x^{n^{}}}{x^m}=x^{n-m} \\ \end{gathered}[/tex][tex]\begin{gathered} \frac{9^7}{9^2}=9^{7-2}=9^5 \\ \\ 9^5=\text{ 9}\times9\times9\times9\times9 \\ 9^5=\text{ 59049} \\ \text{The answer is 59049} \end{gathered}[/tex]Hence the answer is 59,049.
1. find the sum of the first 7 terms of the following sequence round to the nearest hundredth if necessary 18,-6,22. Find the sum of the first 6 terms of the following sequence to the nearest hundredth:324, 54, 9
Answers
You can find the sum of the first n terms of a geometric sequence using the formula:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]1. First, let's calculate r:
[tex]\begin{gathered} r_1=18-(-6)=24 \\ r_2=-6-2=-8 \\ r=-\frac{8}{24}=-\frac{1}{3} \end{gathered}[/tex]Replacing the values in the formula, (n=7 , r=-1/3) we get that:
[tex]S_n=13.51[/tex]2. Let's calculate r:
[tex]\begin{gathered} r_1=324-54=270 \\ r_2=54-9=45 \\ r=\frac{r_2}{r_1}=\frac{45}{270}=\frac{1}{6} \end{gathered}[/tex]Using the formula with the data we have, (n=6 , r=1/6) we get that
[tex]S_n=388.79[/tex]can you help me with my work
Answers
1. the initial value of A is 50 and B is 25 so a is bigger so A>B
2. A hits the grond on 6.53 and B on 10.477 so A is less , so A
3. A grows to 2.5 and B to 5 so A
4. the maximum of a is 2.5 and B is 5 so A
5. the maximum height of A is 81.25 and B 150 so A>B