Answer:
The result is 2 > 1. Hence, the series diverges
Step-by-step explanation:
You have the following series:
[tex]2+\frac{4}{2^2}+\frac{8}{3^2}+\frac{16}{4^2}+...+\frac{2^n}{n^2}=\sum_{i=1}^{i=n}a_n[/tex] (1)
You use the ratio test to determine if the series is convergent or divergent. The ratios test is given by:
[tex]\lim_{n \to \infty} \frac{a_{n+1}}{a_n}[/tex] (2)
Then, you replace the series (1) in (2):
[tex]\lim_{n \to \infty} \frac{\frac{2^{n+1}}{(n+1)^2}}{\frac{2^n}{n^2}}= \lim_{n \to \infty} \frac{(2^n2)(n^2)}{2^n(n+1)^2}\\\\\lim_{n \to \infty} \frac{2n^2}{n^2+2n+1}= \lim_{n \to \infty} \frac{2n^2}{n^2[1+\frac{2}{n}+\frac{1}{n^2}]} \\\\\lim_{n \to \infty} \frac{2}{1+\frac{2}{n}+\frac{1}{n^2}}=\frac{2}{1+0+0}=2[/tex]
In the ratio test you have that if the limit is greater than 1, the series diverges.
The result is 2 > 1. Hence, the series diverges.
reflection hurry algebra two
Answer:
i think it is g(x) = 1/2-x (sorry if wrong)
Step-by-step explanation:
Answer:
Option 1
Step-by-step explanation:
After reflection over the y-axis
f(x) maps onto f(-x)
g(x) = f(-x)
g(x) = 1/(-x + 2)
g(x) = 1/(2 - x)
a rectangular field has side lengths that measure 9/10 mile and 1/2 mile what is the area of the field
Answer:
[tex]\frac{9}{20}miles^2=0.45miles^2[/tex]
Step-by-step explanation:
To find the area of a rectangle:
[tex]a=l*w[/tex]
where [tex]l[/tex] is the length and [tex]w[/tex] is the width.
In this case:
length: [tex]l=\frac{9}{10}miles[/tex]
width: [tex]w=\frac{1}{2} miles[/tex]
thus, we multiply this quantities to find the area:
[tex]a=(\frac{9}{10} miles)(\frac{1}{2}miles )\\\\a=\frac{9*1}{10*2}miles^2\\ \\a=\frac{9}{20}miles^2[/tex]
the area of this rectangle is 9/20 miles squared, or what is the same 0.45 miles squared
Solve the system of equations
Y=1-1/3x
X^2+y^2=1
Answer:A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Declan says that for any number n, the product 4x n is greater than 4. Which value of n shows why Declan is incorrect
Answer:
[tex]n > 1[/tex]
Step-by-step explanation:
Given
Statement: 4x n is greater than 4
Required
Value of n
First we need to rewrite the statement in algebraic form;
Product 4 * n is represented by 4n
greater than 4 is represented by > 4
Bringing these two together, it gives the following
[tex]4n > 4[/tex]
Divide through by 4
[tex]\frac{4n}{4} > \frac{4}{4}[/tex]
[tex]n > 1[/tex]
We've arrive at solution;
This means that n is greater than 1
So, the values of n must start from 2 to show that the condition is true
The value of n = 7/8 makes the inequality 4n > 4 false because 7/8 is less than 1.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
We have n as a number.
4n > 4
Plug n = 5
20 > 4 (true)
Plug n = 9/5
36/4 > 4
9 > 4 (true)
Plug n = 3
12 > 4 (true)
Plug n = 7/8
28/8 > 4
3.5 > 4 (false)
Thus, the value of n = 7/8 makes the inequality 4n > 4 false because 7/8 is less than 1.
Learn more about the inequality here:
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What is the quotient?
Answer:
4x10^12
Step-by-step explanation:
What is the missing leg length
Answer:
b = 16
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
12^2 + b^2 = 20^2
144+b^2 = 400
Subtract 144 from each side
b^2 = 400-144
b^2 = 256
Take the square root of each side
sqrt(b^2) = sqrt(256)
b = 16
Find each pair of similar solids, find the ratio of the volume of the first figure to the volume of the second
Step-by-step explanation:
Scale factor = 4/3. Therefore radius if larger cone = 4r/3 where r is the radius of the smaller cone and height of larger cone = 4h/3 where h is the height of the larger cone.
So ratio of volumes = r^2 * h/(4r/3)^2 * 4h/3) = 9/16 * 3/4 = 27/64
30 is a similar process except it's cylinders so find the scale factor and go on with that problem.
asap-worth 25% of overall
Answer:
ummm
Step-by-step explanation:
what is the question
PLEASE HELP ME ASAP I WILL GIVE YOU BRAINLIEST TO THE FIRST PERSON WHO ANSWERS CORRECTLY- find the value of Y
Answer:
Y=7
Step-by-step explanation:
PYTHAGOREAN THEOROM
A company is trying to calculate the amount of
concrete that will be needed to create one concrete
block that is in the form below.
The concrete block is a rectangular prism with two
cubes cut out. The cubes have a side length of 6
inches.
What is the total volume, cubic feet, of concrete
needed to make this block?
Answer:
[tex]0.19\,\,cubic\,\,feet[/tex]
Step-by-step explanation:
Given:
The concrete block is a rectangular prism with two cubes cut out. The cubes have a side length of 6 inches.
To find: total volume, cubic feet, of concrete needed to make this block
Solution:
Side of cube = 6 inches
Volume of cube = [tex](side)^3=6^3=216\,\,cubic\,\,inches[/tex]
So, volume of two cubes = 2(216) = 432 cubic inches
Length of rectangular prism = 12 inches
Breadth of rectangular prism = 8 inches
Height of rectangular prism = 8 inches
Volume of rectangular prism = length × breadth × height = [tex]12(8)(8)=768 \,\,cubic\,\, inches[/tex]
Total volume of concrete needed to make this block = Volume of rectangular prism - Volume of two cubes = 768 - 432 = 336 cubic inches = [tex]\frac{336}{1728} =0.19\,\,cubic\,\,feet[/tex]
( use 1 cubic inch = [tex]\frac{1}{1728} \,\,feet[/tex])
Patricia and John both used their credit cards to purchase $225.00 worth of gas and groceries for the month of July.
Patricia paid off her credit card transactions on the same day that she made them, while John did not. They both
received their credit card statements at the same time. Patricia's balance was zero, and she had only paid $225.00 to
the credit card company. However, John had a finance charge of $3.82 added to his balance of $225.00. Explain why
John had a finance charge and Patricia did not. Answer in complete sentences.
ever figure it out?
i have the same question
Answer:
John didnt pay off his card right away so there was a fee of $3.82
Step-by-step explanation:
Write the number 38 in base five.
Answer:
I believe since 38 is base 10 then in bas 5 it will be 123 I hope I helped
Step-by-step explanation:
Will give brainliest answer
Answer:
4
Step-by-step explanation:
diameter = 2r
r = radius
radius = 2
2 * 2 = 4
Answer:
4 units
Step-by-step explanation:
the radius of the circle is 2 units. and the radius if half the size of the diameter.
so if we did 2 units × 2, that would give you 4 units.
therefore the answer is
4 units
i hope this helps you! <3
100 points if you want it. Puppy b weighs 8 pounds, which is about 75% of its adult weight. what will be the adult weight of puppy B.
Answer:
10.(6) pouds
Step-by-step explanation:
8 pouds .......... 75%
x pouds ...........100%
x = 8×100/75 = 800/75 = 10.(6) pouds
Given: CD = I, and
matrix inverse
Find the elements of D.
a =
b =
c =
d =
e =
f =
g =
h =
i =
Answer:
Edge answers in order:
a= -9
b= 7
c= 12
d= -5
e= 4
f= 7
g= 3
h= -2
i= -4
Step-by-step explanation:
just did the activity on edge.
Answer:
a = -9
b = 7
c = 12
d = -5
e = 4
f = 7
g = 3
h = -2
i = -4
Step-by-step explanation:
Evaluate: 4+8= 2 x (6 - 3)
16
33
25
Answer:
I'm not so sure because there is no solution to that equation
Step-by-step explanation:
Always start by solving the parenthesis equation and multiply, divide, subtract, or add before you get into adding. Next you add those 2 numbers together and when you look at the answer on the left and on the right.. when they are different numbers, you know there is no solution. I'm not sure if this helped and if it didn't I'm sorry.. I tried.
Please help with this
Answer:
A
Step-by-step explanation:
Henry starts the day with $30. He and his sister go to the fair. He pays for his own admission of $10,but fails to notice that $15 falls out of his wallet while he is paying. His sister lends him $10 so that he can still enjoy the fair. Write the equation that illustrates his day’s financial events.
Answer:
30-10-15+10
Step-by-step explanation:
Answer:
15 is the awnser
Step-by-step explanation:
30-10-15+10=15
Three listening stations located at (3300, 0), (3300, 4400), and (-3300, 0) monitor an explosion. The last two stations detect the explosion 4 seconds and 4 seconds after the first, respectively. Determine the coordinates of the explosion. (Assume that the coordinate system is measured in feet and that sound travels at 1100 feet per second.)
Answer:
hang gang ok
i10 Njan malayalam verupikkal is my job
I need help finding the length of GH.
Answer:
length of arc=2r+teete ×2πr
360
2×13+155°×2×22×13
360. 7
26+155°×572
360. 7
26+88660
2520
88686
2520
35.404
Which function will have a y-intercept at –1 and an amplitude of 2?
f (x) = negative sine (X) minus 1
f (x) = negative 2 sine (x) minus 1
f (x) = negative cosine (x)
f (x) = negative 2 cosine (x) minus 1
Answer:
Options B and D.
Step-by-step explanation:
The general form of sine function
[tex]h(x)=A\sin (Bx+C)+D[/tex]
where, |A| is amplitude, [tex]\frac{2\pi}{B}[/tex] is period, [tex]\frac{-C}{B}[/tex] is phase shift and D is y-intercept.
The general form of cosine function
[tex]h(x)=A\cos (Bx+C)+D[/tex]
where, |A| is amplitude, [tex]\frac{2\pi}{B}[/tex] is period, [tex]\frac{-C}{B}[/tex] is phase shift and D is y-intercept.
In function, [tex]f(x)=-\sin x-1[/tex]
Amplitude : [tex]|A|=1[/tex]
y-intercept : -1
In function, [tex]f(x)=-2\sin x-1[/tex]
Amplitude : [tex]|A|=2[/tex]
y-intercept : -1
In function, [tex]f(x)=-\cos x[/tex]
Amplitude : [tex]|A|=1[/tex]
y-intercept : 0
In function, [tex]f(x)=-2\cos x-1[/tex]
Amplitude : [tex]|A|=2[/tex]
y-intercept : -1
Therefore, the correct options are B and D.
Answer:
B
Step-by-step explanation:
edge2020 quiz
PLEASE ASAP
graph
-1
Answer:
on a graph paper draw the coordinate plane and locate -1 and draw a horizontal line
Step-by-step explanation:
You open your first interest-bearing savings account with an initial deposit of
$2,500. Interest is compounded quarterly at a rate of 3.5%. Assuming you do not
deposit any more money into the account, how much money will you have in the
account after 5 years?
Answer:
$2,975.85
Step-by-step explanation:
Lets use the compound interest formula provided to solve this:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time
First, change 3.5% into a decimal:
3.5% -> [tex]\frac{3.5}{100}[/tex] -> 0.035
Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:
[tex]A=2,500(1+\frac{0.035}{4})^{4(5)}[/tex]
[tex]A=2,975.85[/tex]
After 5 years, the account will have $2,975.85
Which linear function has the same y-intercept as the one that is represented by the graph?
The function shown is y=-2x+10
If we want the same y-intercept all we need to fo is change the slope.
For example, these are valid asnwers,
y=-3x+10
y=0.5x+10
y=10x+10
Answer:
y = 2x+10
Step-by-step explanation:
Mr. Eichmann 's salary is $42,000. This year, he receives a raise of 7%. What will be his salary this year?
What is a reasonable estimate for the volume of a number cube:
8 cm3, 27 in?, or 1 ft??
Answer:
I think the 8 cm one :D
What are the coordinates of point K?
(-
)
()
Answer:5/8 and 1/4
Step-by-step explanation:
The coordinates of point K can be given by (-1/4, 5/8).
What are cartesian coordinates?Cartesian coordinates are the values on a graph that can be used to show the location of a point on the graph.
The coordinates of point K can be found as follows:There are 4 lines between 0 and -1 on the x-axis which divide it into 4 equal parts.
Point K lies on the first line. This means that the x-coordinate of the point is -1/4.
There are 8 lines between 0 and 1 on the y-axis which divide it into 8 equal parts.
Point K lies on the fifth line. This means that the y-coordinate of the point is 5/8.
From this, we can understand that the coordinates of the point K on the graph can be given by (-1/4, 5/8).
Therefore, the coordinates of point K can be given by (-1/4, 5/8).
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meg mixes 3 parts silver paint with 4 parts green paint to get a specific color. Is the ratio 5:6 equivalent to 3:4?
Yes, because both ratios show a pair of numbers that have a difference of 1.
Yes, because any combination of silver and green will work.
No, because the numbers in the given ratio must be multiplied by the same number.
No, because there cannot be more than 4 green parts.
Answer:
No, because the numbers in the given ratio must be multiplied by the same number.
Step-by-step explanation:
Essentially, ratio to be equal must be equal. E.g. 3:4 would be equal to 6:8 because you multiply both sides of the ratio by 2.
Answer:
answer is No, because the numbers in the given ratio must be multiplied by the same number. or c
Step-by-step explanation:
Theresa is comparing the graphs of y=2x and y=5x. Which statement is true?
The y-intercept of y=2x is (0, 2), and y-intercept of y=5x is (0, 5).
Both graphs have a y-intercept of (0, 1), and y=2x is steeper.
Both graphs have a y-intercept of (0, 1), and y=5x is steeper.
Neither graph has a y-intercept.
Answer:
Both graphs have a y-intercept at 0,1. The y=2^x is steeper than y=5^x
Step-by-step explanation:
If you graph these on a graphing calculator you will clearly see they have the same y-intercept (0,1) and that y=2^x is steeper.
The correct option is option B that is both graphs have a common y-intercept of (0, 1) and y = 2x is steeper.
What is the intercept of a line ?
The point where the line or curve crosses the axis of the graph is called intercept. If a point crosses the x-axis, then it is called the x-intercept.
Theresa is comparing graphs of y = 2x and y = 5x
The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x = 0.
Let's check
which is y = 2x.
For x = 0 , y = 0
for x = 1 , y = 2
So , here y-intercept will be (0,2)
So , for both the values y - intercept exists for first function which is y = 2x.
Similarly, for y = 5x , there will be a y -intercept of (0,5).
Both graphs have a common y-intercept of (0, 1).
We know that if the slope of the graph is steeper then we can say that the tangent of the angle made by it will be more and it will make more angle with the x axis.
Here , y = 2x is more steeper than y = 5x.
Therefore , the correct option is option B that is both graphs have a common y-intercept of (0, 1) and y = 2x is steeper.
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The population P of birds in an area is modeled by the exponential model
P(t) = 30e-95t where t represents time in years.
Is the population of birds increasing or decreasing?
a. Increasing
b. Decreasing
