Both conditions of the alternating series test are satisfied, so the series ∑ (-1)^n a_n converges.
To apply the alternating series test, we need to verify the following two conditions:
The sequence {a_n} = 1/(n^2 - 5) is positive, decreasing, and approaches 0 as n approaches infinity.
The series ∑ (-1)^n a_n = ∑ (-1)^n/(n^2 - 5) converges.
To check the first condition, we can take the derivative of a_n:
a'_n = -2n/(n^2 - 5)^2
Since n ≥ 3, we have n^2 - 5 ≥ 4, so (n^2 - 5)^2 ≥ 16. This implies that a'_n ≤ 0 for n ≥ 3. Therefore, the sequence {a_n} is decreasing.
To check that the sequence approaches 0, we can use the limit comparison test with the convergent p-series ∑ 1/n^2:
lim n→∞ a_n/(1/n^2) = lim n→∞ n^2/(n^2 - 5) = 1
Since the limit is finite and positive, we conclude that {a_n} approaches 0 as n approaches infinity.
Thus, both conditions of the alternating series test are satisfied, so the series ∑ (-1)^n a_n converges.
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solve the system by graphing
x+3y=-3
x-3y=-3
Answer:
This one
1
_
3
1
-_
3
Step-by-step explanation:
The cost c to rent a car for d days is shown in the
table. Which equation represents this function?
Answer:
i would help you but there is no table so, sorryStep-by-step explanation:
am goblin gimme ye pointsgiven teach trig ratio as a fraction in simplest form:sin(N)
Answer:
Choice #1: sq rt 3/2
Step-by-step explanation:
cos N=8/PN
PN=16
tan N=PO/8
PO=13.86
sin N=13.86/16=0.866=sq rt 3/2
Helllllllp
Simplify the expression 43 + 2(3 − 2).
14
16
66
68
Answer:
68
Step-by-step explanation:
Answer:
The answer is 46...i cant find that answer in the choices though
Step-by-step explanation:
In PEMDAS we can see that we have parentheses first so we solve whatever is in the parentheses. which 3-2 = 1....so it should look like this
43 + 2 + 1
Which equals 46
hope this helps. have a good day
brainliest to whoever can answer questions correctly
Answer:
v ~ 32.72
Hope that helps!
5-1(b+2) =
3+4(3m+2n) =
Answer:
5-1(b+2) = 5-b-2=3-b
3+4(3m+2n) =3 +12m +8n
The face of a clock has a circumference of 14π inches. What is its area?
Answer:
A = 49π
Step-by-step explanation:
C = πd
if d = 14 then r = 7
A = πr²
A = π · 7²
A = 49π
What's the equation of a line that passes through point (–1, 3) with a slope of 1?
Answer:
y = 1x + 4
OR
y = x + 4
Step-by-step explanation:
y = 2x + 7
y=2X+7
O one solution
O two solutions
O no solution
O infinitely many solutions
Answer:
Infinitely many solutions
Step-by-step explanation:
The lines overlap one another and this leads to an infinite amount of solutions.
Answer:
one solution is the answer
Can you show me the steps involved in solving this question?
the Great answer to your problem is A
pleade help and show work
9514 1404 393
Answer:
11) x = 9
12) x = 9
Step-by-step explanation:
11) Corresponding segments are proportional, so ...
x/6 = 12/8
x = 6(12)/8 . . . multiply by 6
x = 9
__
12) Similar triangle relationships show you the geometric mean relationship that applies in this case.
long side/short side = x/3 = 27/x
x² = 3·27 . . . . . . cross multiply
x = √(3·27) . . . . geometric mean relationship
x = 9
for what value of m is equivalent to..
Answer:
A
Step-by-step explanation:
because math
I need help on this please:)
Answer:
Step-by-step explanation:
∠x=180-114
=66°
∠p=114 (alt.ext.∠)
Answer:
Although it is not stated... I am assuming line "m" and line "n" are parallel to each other. That's the only way we can solve the problem..
Can someone help me with this problem. I have to show my work. Thank you.
Which of the following is NOT a monomial?
O
x
O -
2x-3
O
155
Answer:
2x -3
Step-by-step explanation:
Answer:
2x-3 isn't monomial. hope u like it
Salesman Scott received $2,792.79 for selling a property. If the gross commission was 6.5 % of the sale price, the listing salesman received 12% of the gross commission and Scott received 45% of the balance, how much did the property sell for?
Answer: The property sold for $5,870.41.
Step-by-step explanation:
Let x be the selling price of the property.
Then, gross commission = 6.5% of x = 0.065x
listing salesman received = 12% of ( 0.065x) = 0.12 (0.065x) = 0.0078 x
Balance = x - ( 0.065x) - (0.0078 x)
= (1+0.065-0.0078)x
= 1.0572x
Scott received = 45% of (1.0572x)
=0.45 (1.0572x)
= 0.47574x
Now, [tex]0.47574x=2,792.79[/tex]
[tex]\Rightarrow\ x=\dfrac{2792.79}{0.47574}\\\\\Rightarrow\ x=5870.41[/tex]
Hence, the property sold for $5,870.41.
4^{3x+2}=
4
3x+2
=
\,\,2^{2x-4}
2
2x−4
Answer:
Dont know
Step-by-step explanation:
Sorryyyyyyyyyyyyyyyyyyyyy
Totally out of points
Need triangle geom help !
Answer:
B. ∠BAC
Step-by-step explanation:
The angle opposite the largest side has the largest angle.
Help I will be marking brainliest!
A. 65.99
B. 70.19
C. 52
D. 65.52
Answer:
65.992
Step-by-step explanation:
LM/PL = RN/QR
LM / 113 = 73/ 125
LM =(73/125) * 113
Step-by-step explanation:
LM =1/2 of 113
56.50
so according to to me it is D) 65.99
High School sold tickets to the winter dance for $3.50 in advanced and $5.00 at the door. If 115 people attended the dance and High School made $470.00, how many students bought their tickets in advance and how many students bought their tickets at the door? (Only an algebraic solution will be accepted)
Answer: 3.5a+5b=470 and a+b=115
Step-by-step explanation:
PLEASE HELP OMG
just put this equation into y = mx + b
7x + 8y = -12
* my answer was y = -7/8x - 12/8
(is there supposed to be two fractions? did i do it right?)
Perform the indicated operation.
f (x) = x2 − 1 g(x) = 3x + 4 Find f (9) − g(9)
Answer:
f(9)=17//g(9)=31
Step-by-step explanation:
substitute- (9)2-1= 18-1=17
substitute and solve- 3(9)+4=27+4=31
Hope this helps
tan^2 30 +tan ^2 45+tan^2 60
Step-by-step explanation:
tan 30 = 1/√3tan 45 = 1tan 60 = √3 = tan² 30 + tan² 45 + tan² 60 = ( 1 /√3 )² + ( 1 )² + ( √3 )² = ( 1 / 3 ) + ( 1 ) + ( 3 ) = ( 1 + 3 + 9 ) ÷ 3 = 13 ÷ 3 = 4.333MARK ME AS BRAINLISTWhat is the rate of change of the proportion y=9x
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The rate of change of the proportion y = 9x is 9.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
y = 4x +2 is an equation.
x + 2x + 3 = 4 is an equation.
We have,
y = 9x
The rate of change of this equation can be calculated by finding its differentiation.
Now,
y = 9x
Differentiating with respect to x we get,
dy/dx = 9dx/dx
dy/dx = 9
Thus,
The rate of change of the proportion y = 9x is 9.
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The graph of a linear function is often a parabola.
True or False
A linear function has a graph as a straight line so the given statement is False.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear function is given by
y = mx + c where m is the slope and constant.
Since it is constant it means it should be a straight line in coordinate geometry.
Therefore a linear function always makes a straight line, not a parabola.
Hence "A linear function has a graph as a straight line so the given statement is False".
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Choose the solution to this inequality.
72≥b+95
Answer:
B. [tex]b \leq 1\frac{7}{10}[/tex]
Step-by-step explanation:
Isolate b in order to solve the inequality. Subtract [tex]\frac{9}{5}[/tex] on both sides of the inequality, then simplify. (You will need to convert the fractions in order to subtract and simplify further.)
[tex]\frac{7}{2} \geq b + \frac{9}{5} \\\frac{7}{2} -\frac{9}{5} \geq b + \frac{9}{5} -\frac{9}{5} \\\frac{35}{10} -\frac{18}{10}\geq b\\\frac{17}{10} \geq b\\1\frac{7}{10} \geq b[/tex]
Thus, [tex]b \leq 1\frac{7}{10}[/tex].
Answer:
b
Step-by-step explanation:
Which costs more per issue, 18-issue subscription for $40.50 or a 12-issue subscription for $33.60?
Answer:
12-issue subscription
Step-by-step explanation:
18-issue sub = $40.50 ÷ 18 = $2.25/issue
12-issue sub = $33.60 ÷ 12 = $2.8/tissue
=> The 12-issue subscription costs more per issue (2.8 > 2.25)
Answer:
so you would divide the cost by the issue
the 18 issue is $2.25 per issue
the 12 issue is $2.80 per issue
the 12 issue costs more
Translate X(2,3) Y(0,0) Z(4,4) 2 units right and 3 units up
Answer:
X(4, 6) Y(2, 3) Z(6, 7)
Step-by-step explanation:
If you want to translate something right on a number line, then you are essentially adding to it. Thus you would just add 2 to each of the x values of the coordinates. The same applies with translating something up, all that really means is that you are adding to each of the y values so all you have to do is add 3 to each of the y values and you get your answer.
Answer:
X:(4,6), Y:(2,3), Z:(6,7)
Step-by-step explanation:
2 units right implies a change on the x-axis, meaning you add 2 units to the x of the coordinate pair (x, y). 3 units up implies a change in Y, you apply the same rule and add 3 to the Y of the pair.
2 units right (add 2 to x pair coordinate)
X: (2,3) --> (4,3)
Y: (0,0) --> (2,0)
Z:(4,4) --> (6,4)
and 3 units up (add 3 to y pair coordinate)
X: (4,3) --> (4,6)
Y: (2,0) --> (2,3)
Z: (6,4) --> (6,7)
A weight of 6 lb stretches a spring a distance of 12 in. Find the constant k for the spring.
Answer:
Let F = the force (6 lbs) and x be the distance that the spring is stretched (12 inches).
F = kx
6 lb = k*(12 in.)
6/12 = k = 0.5 lb/in.
A weight of 6 lb stretches a spring a distance of 12 in. The constant k for the spring will be 0.5 lb/in.
How to obtain acceleration from force applied on an object?If the object is of mass m kg and force applied on it is of F N in the direction of motion, then the acceleration of that object is evaluated as:
a= F/m
Given; A weight of 6 lb stretches a spring a distance of 12 in.
Also,
Let F = the force and x be the distance that the spring is stretched
F = kx
6 lb = k*(12 in.)
6/12 = k = 0.5 lb/in.
Therefore, the constant k for the spring will be 0.5 lb/in.
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which number is composite? 11,2,9,5
Answer:
Answer is 9.
Step-by-step explanation:
Composite number is 9.
I hope it's helpful!