Answers
Answer:
L = 7/6 , and the correct option is B, the series diverges.
Step-by-step explanation:
Here we have that:
[tex]an = \frac{(3n + 3)*7^n}{6^{n+4}}[/tex]
Now we want to see the quotient test, then we need to do find the value of the quotient as n tends to infinity. Then we first need to find the quotient:
[tex]a(n + 1)/a(n) = \frac{(3(n + 1) + 3)*7^{n + 1}}{6^{n + 1 + 4}}*\frac{6^{n + 4}}{(3*(n) + 3)*7^{n}}[/tex]
We can simplify the right part to get:
[tex]\frac{(3(n + 1) + 3)*7^{n + 1}}{6^{n + 1 + 4}}*\frac{6^{n + 4}}{(3*(n) + 3)*7^{n}}= \frac{(3n + 3 + 3)*7^{n + 1}}{6^{n + 5}}*\frac{6^{n + 4}}{(3*n + 3)*7^{n}}[/tex]
[tex]\frac{(3n + 3 + 3)*7^{n + 1}}{6^{n + 5}}*\frac{6^{n + 4}}{(3*n + 3)*7^{n}}= \frac{(3n + 3 + 3)*7}{(3*n + 3)*6}[/tex]
Now we want to find the limit of this as n goes to infinity, we can see that both parts will tend to infinity, then we need to use the Lhopital rule and find the limit of the quotient of the first derivatives.
The first derivatives are:
For the denominator: (3*6)
For the numerator: (3*7)
Then we need to find the limit as n goes to infinity to:
[tex]\frac{3*7}{3*6} = \frac{7}{6}[/tex]
But this does not depend on the value of n, then the limit is just 6/7.
L = 7/6
And 7/6 > 1.
Then we can conclude that our series diverges.
Related Questions
Bro I am so bad at math and I need help ;-;
Answers
Answer:
1. M > -7
2. y < -1
3. m < -12
4. k > -2
5. c > -9
Please let me know if you need me to explain these answers! :)
The difference of two positive integers is 5 and the sum of their squares is 433. Find their integers.
Answers
Answer:
12, 17
Step-by-step explanation:
Let the two positive integers be x and (5 + x).
According to the given description:
[tex] {x}^{2} + {(x + 5)}^{2} = 433 \\ {x}^{2} + {x}^{2} + 10x + 25 = 433 \\ \\ 2 {x}^{2} + 10x + 25 - 433 = 0 \\ \\ 2 {x}^{2} + 10x - 408 = 0 \\ \\ 2( {x}^{2} + 5x - 204) = 0 \\ \\ {x}^{2} + 5x - 204 = 0 \\ \\ {x}^{2} + 17x - 12x - 204 = 0 \\ \\ x(x + 17) - 12(x + 17) = 0 \\ \\ (x + 17)(x - 12) = 0 \\ \\ x + 17 = 0 \: or \: x - 12 = 0 \\ \\ x = - 17 \: or \: x = 12 \\ \\ \because \: x \: is \: a \: + ve \: integer \\ \\ \implies x \neq - 17 \\ \\ \therefore \: x = 12 \\ \\ 5 + x = 5 + 12 = 17 \\ [/tex]
Thus, the two positive integers are 12 and 17.
Answer:
12 and 17
Step-by-step explanation:
17 - 12 = 5, and 17^2 (289) + 12^2 (144) = 433
Hope this helps :D
Find the equation of the line specified.
The slope is -4, and it passes through (5,8).
a. y = 4x + 8
b. y = -4x + 28
c. y = -4x - 12
d. y = -8x + 28
Answers
Answer:
B) y=-4x+28
Step-by-step explanation:
y-y1=m(x-x1)
y-8=-4(x-5)
y=-4x+20+8
y=-4x+28
Answer the eqation
6h=-24
Answers
Answer:
h=-4
Step-by-step explanation:
6 times -4 is -24
helloo
============================
Answer:
-4
Step-by-step explanation:
6h= -24
h = -24/6
h = -4
hope this helps
please mark it as a brainiest
Susan's math teacher assigned x homework problems on Monday. On Tuesday, she assigned 15 more problems. Over the two
days, a total of 24 homework problems were assigned. Which equation could be used to find x, the number of problems assigned on
Monday?
A. 15x=24
B.24+x=15
C. x+15=24
D.x-15=24
Answers
Answer:
C
Step-by-step explanation:
We know that there were 24 questions in the 2 days
And we know that tuesday had 15 more question.
That means Monday had "x questions" + the 15 on tuesday to get 24 in total.
Which number line shows the solution of -3x+6>12?
Answers
Answer:
when I solve the equation of -3×+6>12
-3×>12-6...........subtract 6 from both side
-3×>6................simplify
-3×/-3 <6/-3......when we divide or multiple by negative number the sign will be in opposite direction
×<-2 ...........× is solved
s.s( solution set ) ={x<-2 like -3,-4,-5 infinity }
Step-by-step explanation:
i hope it is help full
Please help this is the last problem I need
Answers
Answer:
[tex]sin 54 = \frac{x}{14}[/tex]
Step-by-step explanation:
[tex]sine = \frac{opposite}{hypotenuse}[/tex]
Side z is the adjacent, since it is next to the angle you are solving for.
Side x is the opposite, since it is opposite the angle you are solving for.
The side measuring 14 is the hypotenuse, since it is across from the right angle.
[tex]sin 54 = \frac{x}{14}[/tex]
Two airplanes leave an airport at the same time on different runways. One flies on a bearing of N 66°W at 325 miles per hour. The other airplane flies on a bearing of S 26°W at 300 miles per hour. How far apart will the airplanes be after two hours
Answers
If correct, can you mark as brainliest?
After solving the equations, the distance between two airplanes after two hours will be equal to 861.21 miles.
What is Speed?The speed of an entity, which is a scalar quantity in regular usage and kinematics, can be defined as the size of the change in direction per unit of time or the size of the change in position over time for an object. The initial speed is the upper limit of maximum pace as the duration of a time interval gets closer to zero.
Assume that both the planes are on similar point A at the start.
Assume that x is the 325 mph flying object.
Consequently, it would have traveled a distance of after two hours of 325 × 2 = 650 miles.
Let B represent the location of the plane two hours later.
That means AB = 650 miles
Assume that y is the 300 mph flying object.
It would have traveled a distance of two hours = 300×2=600 miles.
After two hours, let C represent the location of the second plane.
This means AC=600 miles
After two hours, BC separates the two aircraft.
So, the angle between their paths is 87°.
Cos A = (AC² + AB² - AC²)/(2(AC)(AB))
cos 87 = (600² - 650² - AC²)/(2 × 600 × 500)
40822.04 = 782500 - AC²
AC² = 782500 - 4082204
AC = 861.21 miles.
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If you wanted to figure
out how much air is in
a basketball, would
you use plane
geometry or solid
geometry?
Answers
Answer:
solid gemontery
Step-by-step explanation: Plane geomentry is flat and soild is balls sqaures and other types of shapes.
please help asap((((:
Answers
Answer:
Angle 3 is 95, angle 1 is 30.
Step-by-step explanation:
I already answered a lot of your other angle questions so I will make this one QUICK...
Angle 4 is 85, so to find angle 3, simply subtract: 180 - 85 = 95
So angle 3 is 95
We know two out of the three angles in a triangle and they are: 95 and 55, so 95 + 55 = 150. The sum of the angles in a triangle is 180 so we have: 180-150 = 30, which is the answer for angle 1.
So angle 1 is 30
I need help with math trigonometry and law of sines
Answers
Answer:
Step-by-step explanation:
sinx/6=sin90/19
sinx=6sin90/19
x=arcsin(6sin90/19
x=18 degrees
Need help
Value of n2(m+r)if m=3,n=2,r=4
Answers
Graph y + 2 = -1(x + 3).
Answers
you should use desmos
Answer: y= -10x - 10
Step by step explanation: All you need to do is distrubute then solve for y and then graph, and that is all you need to do, you can do this on Desmos
4+3 (x+2) simplify the expression
Answers
Answer:
4+3x+6
10+3x
this is the answer
Answer: 3x+10
Step-by-step explanation:
Distribute:
=4+(3)(x)+(3)(2)
=4+3x+6
Combine Like Terms:
=4+3x+6
=(3x)+(4+6)
=3x+10
Josie bought a soda and 2 candy bars. The soda costs $1.10. Her total bill was $2.40. How much was each candy bar
Answers
Answer:
$0.65
Step-by-step explanation:
2.40-1.10=1.3
1.3/2=.65
In this question use
1 cubic foot = 6.23 gallons
1 cubic foot = 0.028 cubic metres
Convert 3738 gallons into cubic metres.
Answers
Answer:
16.8 cubic metres
Step-by-step explanation:
Given: 1 cubic foot = 6.23 gallons
1 cubic foot = 0.028 cubic metres
Let the conversion into cubic metres be represented by x.
Thus we can say that;
6.23 gallons = 0.028 cubic metres
and
3738 gallons = x cubic metres
So that,
x = [tex]\frac{3738*0.028}{6.23}[/tex]
= 16.8
x = 16.8 cubic metres
The conversion of 3738 gallons into cubic metres is 16.8 cubic metres.
which fraction is equivalent to -3/2?
3/-2
-(3/-2)
-3/-2
-(-3/2)
Answers
What does -2 - 10 equal to?
Answers
The absolute value of 7
−12
is
Answers
Answer:
7
Step-by-step explanation:
Answer:
Step-by-step explanation:
Do you mean 7-12, or 7/(-12)?
7-12 = -5, so the absolute value of 7-12 is 5.
The absolute value of 7/(-12) is 7/12.
In the figure, BC is a support for the roof
of a garage. What is the length of BC?
Answers
Answer:
Bc = √63 ft
Step-by-step explanation:
Here, we want to get the length of BC
As we can see, there is a right angled triangle ABC, with 12ft being the hypotenuse and 9 ft the other side
So we want to get the third leg which is BC
we can use the Pythagoras’ theorem here
And that states that the square of the hypotenuse equals the sum of the squares of the two other sides
let the missing length be x
12^2 = x^2 + 9^2
144 = x^2 + 81
x^2 = 144-81
x^2 = 63
x = √63 ft
What is the scale factor?
please help!
Answers
Answers:
Scale factor = 5/3 (which is approximately equal to 1.67)x = 10========================================
Work Shown:
To find the scale factor, we divide a side of triangle MNO over a corresponding side of triangle FGH. We can only pick the horizontal bottom sides since we don't know what x is yet.
scale factor = ON/HG = 15/9 = (5*3)/(3*3) = 5/3
In decimal form, this is approximately 5/3 = 1.67; however, I find it's better to stick with the fraction since it's exact.
---------------
Let's solve for x
One way to do so is to follow these steps
(FG)/(MN) = (HG)/(ON)
6/x = 9/15
6*15 = x*9 ..... cross multiply
90 = 9x
9x = 90
x = 90/9
x = 10
Or we could solve like this
(FG)/(HG) = (MN)/(ON)
6/9 = x/15
6*15 = 9x
90 = 9x
9x = 90
x = 90/9
x = 10
We end up with the same result because we got to 90 = 9x after cross multiplying, which was found in the previous set of steps as well. There are other ways to solve using a proportion. But they should all lead to x = 10.
Note how,
MN/FG = 10/6 = (5*2)/(3*2) = 5/3
which was the scale factor we found earlier
5/3 is going to be your answer.
Help me in number 10 please 6 points!!!!
Answers
Answer:
answer is 8.5
Step-by-step explanation:
$12 per pizza how many pizzas can i get for $400
Answers
Answer:
$388
Step-by-step explanation:
subtract 400 and 12
(sorry if its wrong)
If a triangle ABC is classified as a right triangle, which statement is true?
Answers
Answer:
Two slopes of triangle ABC are opposite reciprocals
Step-by-step explanation:
Hope This Helps!!!
Brainliest PLZ???
Answer:
Two slopes of triangle ABC are opposite reciprocals
Step-by-step explanation:
took the test
Solve for the roots in simplest form using the quadratic formula:
x2 – 14x = -33
Answers
Answer:
i think its x = 11 , 3
Step-by-step explanation:
I will give brainliest. Please help fast! (Solve for number 5)
Answers
Answer:
the area of the parallelogram is 120 units
4 times 12 divided by 16
Answers
Answer:
3
Step-by-step explanation:
4x12=48
48/16=3
=3
Answer:
the awnser is 60
Step-by-step explanation:
please help this is due today
Answers
Required
1
20 cm
R
What is the area of the shaded region? * 15
(100 Points)
20 cm
6 cm
w
8 cm
Enter your answer
Answers
Answer:
I think it is 116
Step-by-step explanation:
400 - 120 - 140 - 24 = 116
The volume of a cube is 413cm3.
Work out the length of its side rounded to 1 DP.
Answers
Answer:
Write the full question please
The length of the side of the cube, rounded to 1 decimal place, is approximately 7.6 cm .
To find the length of the side of a cube given its volume, we need to find the cube root of the volume .
Given that the volume of the cube is 413 cm³, we can calculate the length of its side as follows:
side length = ∛( volume )
side length = ∛( 413 cm³)
side length ≈ 7.6 cm (rounded to 1 decimal place)
Therefore, the length of the side of the cube, rounded to 1 decimal place, is approximately 7.6 cm .
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