Answers
Answer:
B
Step-by-step explanation:
This is a ratio of polynomials. As n approaches infinity, an approaches 4n / n⁸ = 4 / n⁷, which is a convergent p-series.
Using Limit Comparison Test:
an = (2 + 4n) / (1 + n²)⁴
bn = 4 / n⁷
lim(n→∞) an / bn = 1
The limit is greater than 0, and bn converges, so an also converges.
Related Questions
What are the slopes of the perpendicular lines?
1: y=-5/2x-8
2: y=5x
3: y=3x-8
Answers
Answer:
1. 2/5
2. -1/5
3. -1/3
Step-by-step explanation:
the parpendicular slope is found by taking the original slope and finding the opposite reciprocal. so just flip the slope and make it the opposite sign
-5/2 ---> 2/5
+5/1 ---> -1/5
+3/1 ---> -1/3
1. 2/5
2. -1/5
3. -1/3
Explanation:
There are two key concepts that we have to understand in order to answer this question:
1) The given equations are organized in slope-intercept form: y=mx+b. Here’s what the variables mean:
Y= the y coordinate
M=the slope
X= the coordinate
B= the y intercept
From the given equations we can now identify the slopes as -5/2, 5 and 3.
2) Perpendicular lines have slopes that are NEGATIVE RECIPROCALS of each other.
Example: Line A has the slope 8. A line that is perpendicular to line A would have a slope of -1/8.
Example #2: Line B has the slope -2/3. A line that is perpendicular to line B would have a slope of 3/2 (two negatives make a positive).
Now that we understand these two concepts, we need to look at the slopes of the given lines and determine their negative reciprocals to find the slopes of their perpendicular lines.
1. y=-5/2x-8
We can see that -5/2 is in the place of “m” in y=mx+b. The negative reciprocal of -5/2 is 2/5, so therefore, the slope of the line perpendicular to y=-5/2x-8 is 2/5.
2. y=5x
There is no “b” value in this equation, but we can still identify 5 as “m”. The negative reciprocal of 5 is -1/5, so therefore, the slope of the line perpendicular to y=5c is -1/5.
3. y=3x-8
The negative reciprocal of 3 is -1/3, so therefore, the slope of the line perpendicular to line y=3x-8 is -1/3.
I hope this helps! Please comment if you have any questions.
Find the slope of the line passing through the points (8,-4) and (-6,-3).
Anybody know this ?
Answers
Answer:
= -1/14
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -3 - -4)/( -6 -8)
= ( -3+4)/( -6-8)
1/-14
= -1/14
Find the surface area of a right cone with a diameter of 6 inches and a slant height of 5 inches.
Answers
Answer:
about 172.82
Step-by-step explanation:
Answer:
83.23
Step-by-step explanation:
to work out surface area of a right cone u
A=πr(r+h2+r2)
hope this helps
im not sure if its right tho
1. You are eating on a Tootsie Roll Lollipop that is in the shape of a sphere. It is giving up volume at a steady rate of 0.25 in3 /min. How fast will the radius be decreasing when the Tootsie Roll Pop is .75 inches across?
Answers
Answer:
Step-by-step explanation:
Since the Tootsie Roll lollipop is a sphere
volume of sphere= [tex]\frac{4}{3}piR^3[/tex] = -0.25 [tex]in^3/min[/tex]
the negative sign indicates that the volume is decreasing
upon differentiating
as the diameter given is =0.75 so radius will be = 0.375
[tex]dV/dt = 4piR^2*dR/dt[/tex]
so [tex]dR/dt = 0.25/4*3.14 *(0.375)^2[/tex]
So the radius is decreasing at the rate of dR/dt= 0.142in/min
How much mixed spice will she need for 6 spice
Answers
Answer:
who
Step-by-step explanation:
4 1/8÷2 3/4 convert the mixed numbers to improper fractions
Answers
Answer:
Check picture
Step-by-step explanation:
9514 1404 393
Answer:
1 1/2
Step-by-step explanation:
[tex]\dfrac{4\dfrac{1}{8}}{2\dfrac{3}{4}}=\dfrac{\left(\dfrac{4\cdot8+1}{8}\right)}{\left(\dfrac{2\cdot4+3}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{11}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{22}{8}\right)}=\dfrac{33}{22}=\dfrac{3}{2}[/tex]
Then the improper fraction 3/2 can be written as the mixed number 1 1/2.
(4 1/8) / (2 3/4) = 1 1/2
_____
Comment on division of fractions
Fractions can be divided several ways. Two ways that are commonly taught are "invert and multiply", or "match denominators". Here, we have used the second of these methods.
If we were to "invert and multiply", the computation would be ...
(33/8)(4/11) = (33/11)(4/8) = 3(1/2) = 3/2
Instead, we multiplied 11/4 by 2/2 to make it be 22/8, so having a denominator of 8 matching that of the numerator. Then the value of the compound fraction is the ratio of the numerators:
(33/8)/(22/8) = 33/22 = (3/2)(11/11) = 3/2
I NEED HELP PLEASE AND SHOW THE WORK PLEASE
Answers
Answer:
6. x = 28 degrees
7. z = 1.6 cm
Step-by-step explanation:
6.
Notice that you can use the property that tells us that the addition of all internal angles of a triangle must give 180 degrees, then you write the following equation:
50 + 69 + (2 x +5) = 180
combine like terms:
119 + 2 x + 5 = 180
124 + 2 x = 180
subtract 124 from both sides:
2 x = 56
divide by 2 both sides:
x = 56 / 2
x = 28 degrees
Problem 7.
If the two triangles are congruent, then the side MN must equal side RS.
Since MN measure 1,8 cm, then RS must also measure 1.8 cm
and we can write the equation:
1.8 = 3 z - 3
adding 3 to both sides:
1.8 + 3 = 3 z
4.8 = 3 z
dividing both sides by 3:
z = 4.8 / 3
z = 1.6 cm
There is a box with an area of 112 sq inches and a height of 3.5 inches. What is the width of the box?
Answers
Answer:
32 inches
Step-by-step explanation:
Because height times width equals area,
we can divide 112 by 3.5 to get the width
So it is 32 inches
A regular hexagon is rotated about its center. By which angle could the hexagon be rotated so that it is mapped onto itself?
30°
45°
600
90°
Previous
Answers
Answer: 60
Step-by-step explanation:
twice a number is three more than nine
Answers
Answer:
6
Step-by-step explanation:
Let that number be x.
[tex]2x = 9 + 3[/tex]
[tex]2x = 12[/tex]
[tex]x = 6[/tex]
What is 5 8/100
as a decimal?
O
A. 5.008
0
B. 5.08
O
C. 5.8
0 D. 58
Answers
Answer:
5.08
Step-by-step explanation:
5 8/100
Since there are 2 zero's in 100, we need two numbers in the top
Replace 8 with 08 which is the same number
5 08/100
Now write as a decimal
5.08
Answer:
B. 5.08
Step-by-step explanation:
[tex]5\frac{8}{100} = \frac{508}{100}[/tex] 508 ÷ 100 = 5.08I hope this helps!
8x - 9 = - 2x + 11
Answers
Answer:
10/3
3.333333
3 1/3
Step-by-step explanation:
hope this helps
· At what point does the value of f(x) exceed the value of g(x) if
f(x)=200(1.194) and g(x) = 8x + 225? Justify your answer with a graph.
Someone help I’m dying
Answers
Step-by-step explanation:
hope this helps, good Luck xD.
Write a positive or negative integer that represents the situation.
An elevator goes down 8 floors.
Answers
this is the last question i need help on! i will mark brainlessttt :)thanks
Answers
Answer:
A.3
Step-by-step explanation:
Since the lines are parallel that angle is 90 same as the other. So you plug in all your answers to see with one gives you 90 that being 3 because 30(3)=90.
f(x) = x^3- 9x
What is the average rate of change of f over the interval [1, 6]
Answers
Answer:
Step-by-step explanation:
[tex]\frac{f(b)-f(a)}{b-a}[/tex] This is the formula for the average rate of change
over the interval (a, b)
a and b are x values
f(a) ad f(b) think of them as y values
Start calculating f(a) and f(b) a=1 b=6
replace all x's in formula with a, (1)
f(1)=1³-9(1) = 1-9= -8 f(1) = -8
Now do : b (6)
f(6) = 6³ - 9 (6) = 216-54=162 f(6) = 162
now plug everything into your equation
[tex]\frac{f(6)-f(1)}{6-1} =\frac{162- (-8)}{5} =\frac{170}{5} =34[/tex] average rate of change.
notice the 162 - (-8) In math there is no subtraction, and you would change it to + and when you do that you much change the sign of the next value making -8 a +8.
Hope this helps. Good luck!
Write an inequality representing the following phrase:
One-tenth of a number h is less than or equal to ten
Answers
Answer:
[tex]\frac{1}{10} h\leq 10[/tex]
Step-by-step explanation:
Basically, we are just translating the phrase into an algebraic expression.
324 soldiers queued up such that the number of queues is equal to the number of soldiers in each queue. find the number of queues
Answers
Hi Guys
Please answer this question. I will choose Brainliest.
Also please do a step by step method.
Worth 10 points and it is a Maths question.
Cheers,
Jake
Answers
Answer:
In simplifying this is simple.
2-4 x + 3x-12.2x+9x2-x-12solve the quadratic equation 3x^2-5x-7=0
Answers
Step-by-step explanation:
[tex]3x^{2} -5x -7 = 0 \\ 3x^{2} -5x = 7 \\ x^{2} -\frac{5}{3}x = \frac{7}{3} \\ x^{2} -\frac{5}{3}x +\frac{25}{36} = \frac{7}{3} +\frac{25}{36} \\ (x -\frac{5}{6})^{2} = \frac{84 +25}{36} \\ (x -\frac{5}{6})^{2} = \frac{109}{36} \\ x -\frac{5}{6} = ±\sqrt{\frac{109}{36}} \\ x -\frac{5}{6} = ±\frac{\sqrt{109}}{6} \\ x = ±\frac{\sqrt{109}}{6} +\frac{5}{6}[/tex]
Equation from the positive root:
[tex]x = \frac{\sqrt{109}}{6} +\frac{5}{6} \\ x = \frac{\sqrt{109} +5}{6}[/tex]
Equation from the negative root:
[tex]x = -\frac{\sqrt{109}}{6} +\frac{5}{6} \\ x = \frac{-\sqrt{109} +5}{6}[/tex]
Answer:[tex]x = \frac{\sqrt{109} +5}{6}\\[/tex] and [tex]x = \frac{-\sqrt{109} +5}{6}\\[/tex] satisfy your quadratic equation.
Given : A quadratic equation is given to us . The equation is 3x² - 5x - 7 = 0 .
To Find : The roots of the equation .
Solution : Given quadratic equation is 3x²-5x-7=0. So , let's factorise it to get the zeroes of the equation .
⇒ 3x² -5x - 7 = 0.
Here now , use Quadratic formula , of the quadratic equation in standard form of ax² + bx + c = 0.
[tex]\boxed{\red{\bf x\:\:=\:\:\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}}[/tex]
On substituting respective values ,
⇒ x = -(-5) ± √ (-5)² - 4×3×(-7) / 2 × 3.
⇒x = 5 ± √ [ 25 + 84 ]/ 6 .
⇒ x = 5 ± √ 109 / 6 .
⇒ x = 5 + √109 / 6 , 5 - √109 / 6.
[tex]\purple{\underbrace{\underline{\boxed{\red{\tt \purple{\longmapsto} x = \dfrac{5+\sqrt{109}}{6}, \dfrac{5-\sqrt{109}}{6}}}}}}[/tex]
A person with a height of 2 meters stand near a tree. The tree casts a shadow that is 30 meters long and the person has a shadow that is 3
meters long. What is the height of tree
Answers
9514 1404 393
Answer:
20 m
Step-by-step explanation:
The 30 m shadow of the tree is 10 times the 3 m length of the person's shadow. We expect the tree to be 10 times as tall as the person:
10(2 m) = 20 m . . . height of the tree
name the type of triangle of a b is equal to BC BC is equals to see a is equals to 6 CM
Answers
Given ,
AB = BC
BC = CA
CA = 6 cm
This is an equilateral triangle as the first side is equal to the second side and the third side is equal to the second side which is equal to the first side . As all the sides are equal to 6 cm , this triangle is said to be an equilateral triangle .
∴ Triangle ABC is an equilateral triangle , where :- AB = BC = CA = 6 cm .
Al changes saved
4. Ten students in your class put their names on slips of paper inside a box. Out of the ten students, four
are girls, and six are boys. Five names are chosen.
What is the probability that three girls and two boys are chosen?
O 7.14%
350%
O 1.90%
O 23.81%
Answers
Answer:
1.90 percent
Step-by-step explanation:
Helpppppp!!! PLEASE
:((
Answers
Answer:
Using the vertical line test, the functions are b, c, d, and f
Step-by-step explanation:
a and e both fail the vertical line test, therefore, it's not a functions.
What’re these two problems simplified?
Answers
Step-by-step explanation:
-2(3x-12)+4-13
=-6x+24+4-13=-7x-15
=6x-15
4(5x-1)+8x-20=20x-4+8x-20
=28x-24
So this is ur solution.
But if u wnt to solve these eq. together thn it will be:-
6x-15=28x-24
6x-28x=-24+15
-22x=-9
x=22/9=2.44
Hope u like it.
Answer:
-8+9 is problem one
Step-by-st-ep explanation:
A juice box has a length of 2 inches, a width of 1 inch, and a height of 4 inches. What is the volume of the juice box?
Answers
Answer:
8 in
Step-by-step explanation:
L × W × H = V2 × 1 × 4 = 8 inI hope this helps!
Rectangle ABCD has a perimeter represented by the expression 9x + 3. Rectangle PQRS has a
perimeter represented by the expression 6x + 2. Write the expression that represents the
difference in the perimeters of Rectangle ABCD and Rectangle PQRS. Write the steps and
solution.
Answers
Answer:
D. [tex] 3x + 1 [/tex]
Step-by-step explanation:
Perimeter of Rectangle ABCD = [tex] 9x + 3 [/tex]
Perimeter of Rectangle PQRS = [tex] 6x + 2 [/tex]
Difference between perimeter of Rectangle ABCD and Perimeter of Rectangle PQRS:
[tex] (9x + 3) - (6x + 2) [/tex]
Open Parentheses
[tex] 9x + 3 - 6x - 2 [/tex]
Collect like terms
[tex] 9x - 6x + 3 - 2 [/tex]
[tex] 3x + 1 [/tex]
if m<2 = 115 degrees what is m<1 ? (There you go)
Answers
Answer:
65
Step-by-step explanation:
180 - 115 = 65
This is the easiest way to think about and do it but your teacher might want you to do it a different way.
Answer:
65
Step-by-step explanation:
find the value of x.
The answer is 13, but I need to show my work
Thank you guys
Answers
Answer:
Know the properties of vertical angles.
Step-by-step explanation:
Vertical angles are equal to each other, so we must make them equal to each other in an equation:
6x+2=80
6x=78
x=13
If a, b and c are positive integers for which (a,b,c) is the only
ordered triple such that 6a +9b + 20c = 61, then what is
a+b+c?
Answers
If a, b, and c are all positive integers and 6a + 9b + 20c = 61, then right away you know c < 3, because if c = 3, then 20c = 60, and there are no solutions for a and b.
So consider two cases:
• If c = 2, then we're left with 6a + 9b = 21.
• If c = 1, then 6a + 9b = 41.
We have gcd(6, 9) = 3, but 41 is prime and 3 does not divide 41. So we throw out the second case.
This leaves us with 6a + 9b = 21. Notice that if a = b = 1, then 6a + 9b = 15. Add 6 to both sides to get 21. So a = 2, b = 1, and c = 2, and hence a + b + c = 5.