10) Using Limit Comparison Test (LCT), the following series
+00
M:
-1 + 2n5
n6 + 1
n=1
Answers
Compare to the divergent series,
[tex]\displaystyle\sum_{n=1}^\infty\frac1n[/tex]
Then by the limit comparison test, the given series also diverges, since the limit
[tex]\displaystyle\lim_{n\to\infty}\frac{\frac{2n^5-1}{n^6+1}}{\frac1n} = \lim_{n\to\infty}\frac{2n^6-n}{n^6+1}=\lim_{n\to\infty}\frac{2-\frac1{n^5}}{1+\frac1{n^6}}=2[/tex]
is positive and finite.
Related Questions
A scuba diver is swimming 28 feet below the water’s surface. The diver swims up slowly at a rate of 0.3 feet per second for 6 seconds. Then they swim back down for 4 seconds at a rate of 0.3 feet per second. What is the diver’s new depth?
Answers
Answer:
27.4 feet down deep
Step-by-step explanation:
28 feet down, swins up for 0.3 feet times 6 or 1.8 feet up
leaving a total of 26.2 under the sea and he swims back down at 0.3 feet times 4 or 1.2 feet down. and the new total is 26.2 + 1.2 which equals 27.4 feet down in the deep sea
Answer:
27.4 feet
Step-by-step explanation:
.3 ft per sec for 6 sec = 1.8 feet
.3 ft per sec for 4 sec = 1.2 feet
28 - 1.8 + 1.2 = 27.4
Solve the solution as an ordered pair
X + 9 = y
X = 4y - 6
Answers
Answer:
-10, -1
Step-by-step explanation:
See Image below:)
Express 0.02 as a percent.
Answers
Answer:
2 Percent or %
Step-by-step explanation:
The decimal 0.02 would be equivalent to 2 percent, or 2 per hundred.
Answer:
0.02 is 2 percent as a percent
Will mark Brainlest please answer. find the value of a,b.
,p,q from the equal order pairs
Answers
Step-by-step explanation:
Question-1:by order pair we obtain:
[tex] \displaystyle \begin{cases} \displaystyle 3p = 2p - 1 \dots \dots i\\2q - p = 1 \dots \dots ii\end{cases}[/tex]
cancel 2p from the i equation to get a certain value of p:
[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\2q - p = 1 \end{cases}[/tex]
now substitute the value of p to the second equation:
[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\2q - ( - 1) = 1 \end{cases}[/tex]
simplify parentheses:
[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\2q + 1= 1 \end{cases}[/tex]
cancel 1 from both sides:
[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\2q = 0\end{cases}[/tex]
divide both sides by 2:
[tex] \displaystyle \begin{cases} \displaystyle p = - 1 \\q = 0\end{cases}[/tex]
question-2:by order pair we obtain:
[tex] \displaystyle \begin{cases} \displaystyle 2x - y= 3 \dots \dots i\\3y= x + y \dots \dots ii\end{cases}[/tex]
cancel out y from the second equation:
[tex] \displaystyle \begin{cases} \displaystyle 2x - y= 3 \dots \dots i\\ x = 2y \dots \dots ii\end{cases}[/tex]
substitute the value of x to the first equation:
[tex] \displaystyle \begin{cases} \displaystyle 2.2y-y= 3 \\ x = 2y \end{cases}[/tex]
simplify:
[tex] \displaystyle \begin{cases} \displaystyle 3y= 3 \\ x = 2y \end{cases}[/tex]
divide both sides by 3:
[tex] \displaystyle \begin{cases} \displaystyle y= 1 \\ x = 2y \end{cases}[/tex]
substitute the value of y to the second equation which yields:
[tex] \displaystyle \begin{cases} \displaystyle y= 1 \\ x = 2 \end{cases}[/tex]
Question-3:by order pair we obtain;
[tex] \displaystyle \begin{cases} \displaystyle 2p + q = 2 \dots \dots i\\3q + 2p = 3 \dots \dots ii\end{cases}[/tex]
rearrange:
[tex] \displaystyle \begin{cases} \displaystyle 2p + q = 2 \\2p + 3q= 3 \end{cases}[/tex]
subtract and simplify
[tex] \displaystyle \begin{array}{ccc} \displaystyle 2p + q = 2 \\2p + 3q= 3 \\ \hline - 2q = - 1 \\ q = \dfrac{1}{2} \end{array}[/tex]
substitute the value of q to the first equation:
[tex] \displaystyle 2.p+ \frac{1}{2} = 2[/tex]
make q the subject of the equation:
[tex] \displaystyle p = \frac{3}{4} [/tex]
hence,
[tex] \displaystyle q = \frac{1}{2} \\ p = \frac{3}{4} [/tex]
Answer:
see above
............
Rewrite the quadratic equation in the form y= a(x - h)2 + k.
y = 5x2 – 30.3 + 95
Y= ?
Answers
Lmk if this was right or not.
Which choice represents the fraction below as a single exponential expression? (ap3x)
Answers
Answer:
d^5
Step-by-step explanation:
d^8 / d^3
We know that a^b / a^c = a^(b-c)
d^(8-3)
d^5
Option b
Find the surface area of the regular pyramid.
Answers
Answer:
D
Step-by-step explanation:
Base perimeter = side x 5 = 4 x 5 = 20 in
LA = (base perimeter x slant height)/2 = (20 x 8)/2 = 80 in^2
SA = base area + LA = 27.5 + 80 = 107.5 in^2
HELPP what is the area of this cylinder
Answers
Answer:
1,884
Step-by-step explanation:
The formula for solving the area of a right cylinder like this one is:
=2πrh+2πr2
Note:
Pls notify me if my answer is incorrect for the other users that will see this response. Thank you.
-kiniwih426
In triangle CAT, points DOG......
Answers
9514 1404 393
Answer:
46 units
Step-by-step explanation:
Each midline is half the length of the parallel side of ΔCAT. This tells us ...
TO = AO = DG = 10
AD = GO = 7
GT = DO = 9
The perimeter of the trapezoid is ...
TA +AD +DG +GT = (TO+OA) +AD +DG +GT
= (10 +10) +7 +10 +9 = 46
The perimeter of the trapezoid is 46 units.
explain how to write an equation of a line given the slope and one point on the line
Answers
I hope my explanations were clear lol cause I usually suck at explaining :D
Hope this helps シ
2
D
3
In the diagram above, Z1 = 2x+20 and
Z2 = 3x+10. Find the measure of 21.
Z1 = [ ? 10
Answers
9514 1404 393
Answer:
∠1 = 40°
Step-by-step explanation:
Angles 1 and 2 are "alternate interior" angles, so are congruent.
∠1 = ∠2
2x +20 = 3x +10
10 = x . . . . . . . . . . . subtract 2x+10 from both sides
The measure of ∠1 is ...
∠1 = 2x +10 = 2(10) +20 . . . . . degrees
∠1 = 40°
Solve the equation for all real solutions.
X^2 + 11z +9 = 5z
Someone help plz ):
Answers
Answer:
[tex]z = -3[/tex]
Step-by-step explanation:
Given
[tex]z^2 +11z+9 = 5z[/tex] --- the correct equation
Required
Solve
Equate to 0
[tex]z^2 +11z-5z+9 = 0[/tex]
[tex]z^2 +6z+9 = 0[/tex]
Expand
[tex]z^2 +3z+3z+9 = 0[/tex]
Factorize
[tex]z(z +3)+3(z+3) = 0[/tex]
Factor out z + 3
[tex](z +3)(z+3) = 0[/tex]
Split
[tex]z + 3 =0[/tex] --- twice
[tex]z = -3[/tex]
Pythagorean theorem..
Answers
[tex]{\huge{\underbrace{\bf{\pink{Answer}}}}}[/tex]
Length of missing leg = 12 km
Using Pythagoras theorem
a² = 15² - 9²
a = √ 225 - 49
a = √144
a = 12 km
HOPE IT HELPS..
(Hypotenuse)² = (Base)²+ (Perpendicular)²
Taking, Hypotenuse As H
Base As B
Perpendicular As P
_________________________
Solving The QuestionH²= B²+ P²
[tex]15 {}^{2} = 9 {}^{2} + p {}^{2} \\ \\ p {}^{2} = 15 {}^{2} + 9 {}^{2} \\ \\ p {}^{2} = 225 - 81 \\ \\p {}^{2} = 144 \\ \\ p = \sqrt{144} \\ \\ p = 12[/tex]
Hope This Helps You ❤️Nalani says the expression 3 - 8s cannot be factored using the GCF. Is she correct? Explain why or
why not.
Answers
Answer:
she is correct because there is not common factor of 3 and 8 so it cannot be factored
Step-by-step explanation:
hey yallll
so i need notes on a discussion about how a deaf persons opinions might vary your own, yes this is for asl. so please if you have the time, can yall have a discussion down below abt this topic?
tysm :)
Answers
Answer:
When someone is deaf they can’t hear, but they still have the ability to see. I believe the main part of living is being able to see, because even if you can’t hear at least you can see and remember the special moments that have occurred in your life. Of course, there are occasions in which it is necessary to hear, but being able to see is something truly valuable for someone because they are able to discover new things with their ability to see. Or maybe you can’t hear your partner tell you that they love you, but at least they can demonstrate it to you and actions speak louder than words in everything.
Step-by-step explanation:
I hope this helped you out
Solve for X - ln (2x-15) = - 3
Answers
Answer:
-In(2x-15)=-3
ln(2x-15)=3
2x-15=e^3
2x-15=20
2x=35
x=17.5
+12<16
Please with steps :)
Answers
Answer:
0,1,2,3
Step-by-step explanation:
PLEASE HELP ASAP PLS !!! WILL GIVE BRAINLIEST TO WHOEVER GETS IT RIGHT !!! you’ll get blessed with 10 years of good luck
Answers
Answer: Choice C
Perpendicular because the slopes are negative reciprocals of each other.
=======================================================
Explanation:
Use the slope formula to find the slope of line AB
m = (y2-y1)/(x2-x1)
m = (-1-(-2))/(4-8)
m = (-1+2)/(4-8)
m = 1/(-4)
m = -1/4
The slope of line AB is -1/4
Repeat those steps for line CD
m = (y2-y1)/(x2-x1)
m = (-9-11)/(-2-3)
m = (-20)/(-5)
m = 4
The slope of line CD is 4
---------
The slopes of AB and CD are -1/4 and 4 respectively.
We can see that the two slopes are negative reciprocals of each other. Meaning that one slope will have us flip the fraction and the sign to form the other slope, and vice versa. Therefore, the two lines are perpendicular.
One useful property is that perpendicular slopes like this multiply to -1
(-1/4)*(4) = -1
---------
Side note: If the slopes were equal, then the lines would be parallel (assuming the two lines have different y intercepts).
Answer:
perpendicular because the slopes are negative reciprocals of each other
Step-by-step explanation:
Vector AB (8-4, -2 - -1) = AB(4, -1)
Vector CD(3- -2, 11- -9) = CD(5, 20)
Dot product of AB.CD = (4,-1).(5,20) = 4*5+(-1)*20 = 20-20 = 0 => perpendicular
If the area of a rectangle is 36 ina and the length is 9 in, what is the width?
Answers
Answer:
4in
Step-by-step explanation:
The width of the rectangle is
36:9=4
If Length is 9,
9W=36
W=4
Find the size of the of angle x.
Answers
Total degrees in any triangle = 180
Angles given = 65 + 35 = 100
X = 180-100 = 80
Answer:
80 degrees
Step-by-step explanation:
Since a triangle is 180 degrees
you then add to 2 degrees given and subtract it from 180
65+35=100
180-100=80 degrees
What is the simplified form of √10,000x64 ?
Answers to choose from:
5000x^64
5000x^8
100x^8
100x^32
Answers
9514 1404 393
Answer:
(d) 100x^32
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)^c = a^(bc)
√a = a^(1/2)
__
Then ...
[tex]\displaystyle\sqrt{10000x^{64}}=(10^4\cdot x^{64})^{\frac{1}{2}}=10^{\frac{4}{2}}\cdot x^{\frac{64}{2}}=10^2\cdot x^{32}\\\\=\boxed{100x^{32}}[/tex]
Answer:
Step-by-step explanation:
5000x^8
which statement is true?
Answers
Answer:
Function A is less than the y value of Function B
Step-by-step explanation:
The y intercept of Function A is c = 3 [y = -3m + 3]
It's gradient will be m = 3 [ y = -9 + 3] to [y = -6]
Function B
answer for brainlest pls
Answers
[tex]{ \bf{ \underbrace{Given :}}}[/tex]
Radius of the circle = 7 in.
[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]
The area of the circle.
[tex]{ \bf{ \underbrace{Solution :}}}[/tex]
[tex]\sf\orange{The\:area \:of\:the\:circle\:is\:154\:in².}[/tex]
A. 154 inches squared. ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Area\:of\:a\:circle \:=\:πr²}[/tex]
[tex] = \frac{22}{7} \times 7 \times 7 \: {in}^{2} \\ \\ = 22 \times 7 \: {in}^{2} \\ \\ = 154 \: {in}^{2} [/tex]
[tex]\boxed{Therefore,\:the\:area\:of\:the\:circle\:is\:154\:in².}[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Need help on this one problem plz!
Answers
what is 2.8436 rounded to the nearest thousandth?
Answers
Answer:
2.844
Step-by-step explanation:
2.8436 is 2.844 when rounded to the nearest thousandth because the ten thousandth digit is 6, which means you round up for 3. Hope this helps!
Answer:
2.84
Step-by-step explanation:
2.8436 is rounded to the nearest thousands we get 2.84
the product of 2 numbers, p and q, decreased by 3 times their sum. (as an algebraic expression)
Answers
Answer:
3 - (p*q) im not sure lol
Step-by-step explanation:
The average horse requires 0.0333 Megacalories (Mcal) each day
for every kilogram (kg) it weighs. If your horse weights 665 kg,
and the food you are buying provides 950 kcal per pound of
food, how many pounds of food do you need each day for your
horse?
Answers
Answer:
23.31 pounds of food per day
Step-by-step explanation:
1 mcal = 1000 kcal
0.0333 mcal = x
0.0333 * 1000 = 33.3 kcal of food per kg
A horse which weighs 665 kg ; will this need :
(33.3 *665) = 22144.5 kcal of food per day
Kcal per pound of food purchased = 950 kcal
1 pound = 950 kcal
x pound = 22144.5 kcal
950x = 22144.5
x = 22144.5 / 950
x = 23.31 pounds of food
a rectangular field is 454 times as long as it is wide if the perimeter of the field is 540 yd what are the field dimensions
Answers
Answer:
WIDTH= 54yd, LENGTH= 216 yd
Step-by-step explanation:
Length can be denoted as L
Width can be denoted as W
From the question,
(L= 4W) ........... eqn(1)
But perimeter = [(2L + 2W)]........eqn(2)
Substitute eqn(1) into (2)
Perimeter= (8W + 2W) = 10W
From the question,
perimeter= 540 yd
540=10W
W=(540/10)= 54
W= 54 yd
Hence, WIDTH= 54yd
From equation (1) substitute W= 54 yd
(L= 4W)
L= (4×54)
L= 216 yd
Hence, LENGTH= 216 yd
The dimensions are WIDTH= 54yd, LENGTH= 216 yd
5. The Jones family orders four pizzas to eat. Each pizza is sliced into four parts. How many pizza slices do they get in total?
Answers
Answer:
16 slices
Step-by-step explanation:
Given :
Number of pizzas ordered = 4
Number of slices per pizza = 4
If 4 pizzas are each sliced into 4 parts ; the we have :
Pizza 1 = 4 slices
Pizza 2 = 4 slices
Pizza 3 = 4 slices
Pizza 4 = 4 slices
Total slices = (4 +4 +4 +4) = 16 slices
can someone answer this please? I'll give brainlest for correct answer
Answers
Answer:
xoy = 40º
toy = 140º
zox = 110º
toz = 70º
zoy = 70º
Step-by-step explanation:
There are 18 spaces so each is 180 / 18 = 10º
xoy = 40º
toy = 140º
zox = 110º
toz = 70º
zoy = 70º
Answer:
xoy = 40 degree angle
toy = 140 degree angle
zox = 110 degree angle
toz = 70 degree angle
zoy = 70 degree angle
Step-by-step explanation:
Use protractor to measure. Each mark is equal to 10 degrees.