The series Σ (from n = 1 to infinity) [(8n) / (7n - 5)] diverges.
The series provided is:
Σ (from n = 1 to infinity) [(8n) / (7n - 5)]
To determine its convergence or divergence, we can use the Limit Comparison Test. Let's compare it with the series 1/n:
a_n = (8n) / (7n - 5)
b_n = 1/n
Now, we find the limit as n approaches infinity:
lim (n → ∞) (a_n / b_n) = lim (n → ∞) [(8n) / (7n - 5)] / [1/n]
Simplify the expression:
lim (n → ∞) [(8n^2) / (7n - 5)] = lim (n → ∞) [8n / 7]
As n approaches infinity, the limit is 8/7, which is a positive finite number.
According to the Limit Comparison Test, since the limit is a positive finite number, the given series has the same convergence behavior as the series 1/n. The series 1/n is a harmonic series, which is known to diverge. Therefore, the given series also diverges.
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if the measure of angle 1 = 17x - 30 and the measure of angle 2 = 7x + 18, what is the value of x?
Answer:
do you know the answer
The value of x is 4.8.
Given that,
The measure of angle 1 = 17x - 30 and the measure of angle 2 = 7x + 18.Based on the above information, the calculation is as follows:
Angle 1 = ANgle 2
17x - 30 = 7x + 18
17x - 7x = 18 + 30
10x = 48
x = 4.8
Therefore we can conclude that the value of x is 4.8.
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A nesting box for a falcon is put on top of a 96 ft pole. There are 3 ft in 1 yd.
Answer:
32 yards
Step-by-step explanation:
find the value of x
Answer:
Is that 12
12+x+3
x = 12-3
x = 9
How many square feet of outdoor carpet will we need
8 square feet will be needed. 3x2= 6 + 2x1= 2= 8 square feet
In ΔIJK, i = 74 inches, j = 23 inches and ∠K=20°. Find the area of ΔIJK, to the nearest square inch.
Answer:
291in^2
Step-by-step explanation:
Using the formula
Area of the triangle = 1/2absin theta
A = 1/2ijsin<K
Given
i = 74in
j = 23in
<K = 20 degrees
Area = 1/2 * 74*23sin20
Area = 37*23sin20
Area = 852sin20
Area = 291.059in^2
Hence the area of the triangle to nearest square inch is 291in^2
Which situations can be represented by an exponential function?
Select each correct answer.
Every year, the number of online video subscriptions increases by 3 times what is was the previous year.
In a structure made of bricks, each row has 10 more bricks than the previous row.
The value of a vehicle decreases by 11% each year.
A dentist's office accepts 15 new patients each month.
9514 1404 393
Answer:
(a) subscriptions
(c) vehicle value
Step-by-step explanation:
Exponential functions are used to describe situations where the amount of change is proportional to the amount.
If the amount of change is a constant, then the function is linear.
A. video subscribers change by an amount proportional to their number, so is an exponential function.
B. the change in number of bricks in a row is a constant, so the function is a linear function.
C. The amount of change is proportional to the value, so the function is an exponential function.
D. The change in patient count is a constant, so the function is a linear function.
Jared made 12 3 fourhs cups of snack mix for a party his guests ate two thirds of the mix how much snack mix did his guests eat
Answer: Jared guests ate = 8 1/2 cups of the snack mix.
Step-by-step explanation:
Total snack mix made by Jared = 12 3/4 CUPS
Amount eaten by guests = 2/3 of Total snack mix
which means they ate = 2/ 3 x12 3/4
= 2/3 x 51/ 4
=17/2 = 8 1/2 cups of snack mix.
Jared guests ate 8 1/2 cups of the snack mix.
I need to write a word problem for this equation and I don't know how to get started. Help!!!! N + (n + 8) + 2n = 364
Answer:
n = 89
Step-by-step explanation:
Ok so,
n + (n+8) + 2n =364
n+n+8+2n = 364
4n + 8 = 364
4n = 356
n = 89
I checked it...its right
if you have any questions please ask me
hope this helps. have a good day :)!!
ILL GIVE BRAINLIEST AND 10 POINTS
A rectangular prism has a length of 9 in., a width of 4 in., and a height of 112 in.
The prism is filled with cubes that have edge lengths of 12 in.
How many cubes are needed to fill the rectangular prism?
Answer:
432
Step-by-step explanation:
Rectangles Volume / Cubes Volume
9.4.3/2/1/2.1/2.1/2
54/1/8
54.8
432
ans of this question
4 (3c+4d)
Answer: 12c+16d
Step-by-step explanation: 4(3c+4d)
(4)(3c+4d)
(4)(3c)+(4)(4d)
12c+16d
Answer:
Întâi faci paranteza și după de ie faci cu 4
help me pls kinda stuck lol
Answer:
see explanation
Step-by-step explanation:
(a)
To find the x- intercepts , let y = 0 , that is
6x - x² = 0 ← factor out x from each term
x(6 - x) = 0
Equate each factor to zero and solve for x
x = 0
6 - x = 0 ⇒ x = 6
Coordinates of P (6, 0 )
(b)
The axis of symmetry is a vertical line, positioned at the midpoint of the zeros
x = [tex]\frac{0+6}{2}[/tex] = [tex]\frac{6}{2}[/tex] = 3
Equation of axis of symmetry is x = 3
(c)
Given a parabola in standard form y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = 6x - x² = - x² + 6x ← is in standard form
with a = - 1, b = 6 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{6}{-2}[/tex] = 3
Substitute x = 3 into y = 6x - x² for y- coordinate
y = 6(3) - 3² = 18 - 9 = 9
coordinates of maximum point = (3, 9 )
A motorcyclist traveled at a rate of 60 miles per hour for 3 hours, then took a break for lunch for 45 minutes. She then traveled for another amount of time at 60 miles per hour before reaching her destination. If she traveled a total of 270 miles, and left at 9:30 a.m., at what time did she arrive at her destination?
Please help:( need this ASP
Answer:
2:45 p.m.
Step-by-step explanation:
60 miles per hour for 3 hours
time: 12:30
miles driven: 180
45 minutes for lunch
time: 1:15
miles driven: 180
60 miles an hour till she hits 270
270-180=90
90 miles = 1.5 hours of driving
1.5 hours plus 1:15 = 2:45
Danielle makes $5,000 per week as a surgeon. Soon she will receive a 15% raise. How much money will she make per week after this raise? $750 54.250 55.150 55.750 $7,500
Answer:
50000
Step-by-step explanation:
Answer:
$50,000 would be the answer
Step-by-step explanation:
In which quadrant is point G located?
III
I
II
IV
help help help help help help ill give brainiest
Answer:
wowee,,, i hope these are right :,)
Step-by-step explanation:
5/3-x+1/3 : -3/2+2+1/2x
3/5-13/5 = 6.9+4.9
3x+0 = 3x
2x-3 = x-3+x
2x-6 = -6+2x
Concept Check: Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable.
75°
174°
300°
-61°
-90°
Step-by-step explanation:
...............
......
2.
2.3*-1-3*
3*- 3x-1
Answer:
i got 27x-3.3 by simplifying
Step-by-step explanation:
if a function f(x)=x^3 has the domain {-3,0,2,4} what is it's range
Step-by-step explanation:
Range is y-values
= {-27,0,8,64}
please help.......................
Answer:
FD = 8
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{FD}{BA}[/tex] = [tex]\frac{FE}{BC}[/tex] , substitute values
[tex]\frac{x+3}{2x+2}[/tex] = [tex]\frac{16}{24}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )
2(2x + 2) = 3(x + 3) ← distribute parenthesis on both sides
4x + 4 = 3x + 9 ( subtract 3x from both sides )
x + 4 = 9 ( subtract 4 from both sides )
x = 5
Thus
FD = x + 3 = 5 + 3 = 8
Evaluate the expression. 6(3+5)/4
Answer:
12
Step-by-step explanation:
6(3+5)/4 add number inside parentheses
6(8)/4 multiply 6 and 8
48/4 divide
12
Hope this helped you!
-10x+y=-22 -8x+y=-18 solve by elimination
Answer:
x=2, y= -2
Step-by-step explanation:
Answer:
-10x+y=-22---------equation 1
-8x+y=-18----------equation 2
subtract eqn 1 and 2
-10x+y=-22
-8x+y=-18
(+) (-) (+)
__________
-2x=-4
or, x=2
put the value of x in equation 1 we get
-10×2+y=-22
y=-22+20
or, y = -2
therefore x=2 and y=-2 ans.
help plz i’ll give extra points
Answer:
A
Step-by-step explanation:
What is the area of the composite figure? 65 cm2
40 cm2
52.5 cm2
60 cm2
Area of the composite figure will be 52.5 cm².
Area of the composite figure,Divide the figure into small parts of different shapes.Add the areas of the divided figures.
Given composite figure is divided into two parts (1) triangle ABC (2) Rectangle DEFG
Area of ΔABC = [tex]\frac{1}{2}(AB)(BC)[/tex]
= [tex]\frac{1}{2}(5)[8-(1+2)][/tex]
= [tex]\frac{1}{2}(5)(5)[/tex]
= 12.5 cm²
Area of rectangle DEFG = Length × Width
= 8 × 5
= 40 cm²
Area of the composite figure = Area of triangle ABC + Area of DEFG
= 12.5 + 40
= 52.5 cm²
Therefore, area of the composite figure will be 52.5 cm².
Learn more about the area of the composite figure,
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gradient of line 6x+2y+9=0
Answer:
gradient = - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c( m is the slope (gradient) and c the y- intercept )
Given
6x + 2y + 9 = 0 ( subtract 6x + 9 from both sides )
2y = - 6x - 9 ( divide the 3 terms by 2 )
y = - 3x - [tex]\frac{9}{2}[/tex] ← in slope- intercept form
with gradient m = - 3
Find the sum by first finding the equivalent fractions so both of the fractions have common
denominators.
Answer:
3x3/8x2 = 9/16
9/16+7/16 = 16/16
=1
find the binomial which is a common factor of:-
plz ans it fast...
Step-by-step explanation:
step 1. why are you in a hurry?
step 2. a binomial that is a common factor of 121 - 25x^2 and 25x^2 + 55x + 121.
step 3. the factors. of 121 - 25x^2 are (11 - 5x)(11 + 5x).
step 4. the factors of 25x^2 + 55x + 121 are (5x + 11)(5x + 11).
step 5. the common factor is 5x + 11.
-6 x (-8) =
What is this answer I am stuck on it?
Answer:
It is 48
Step-by-step explanation:
Since the negative signs cancel out it is positive and 6 times 8 is 48.
HOPE THIS HELPS!
1.125+1 2/3-2 5/6×(-8/27)=
Find the slope and initial value of the graph below. Then write the equation of the line. Write the equation of the line.
Answer:
y= x + 2
Hope this helps.
Help with math angles please
Answer:
1. 70
2. 22
3. 56
4. 16
5. 38
6. 15
7. 260
8. 7