Answer:
The sequence converges to 1.
Step-by-step explanation:
Sequence 2/4, 3/5, 4/6, 5/7
This sequence can be summarized as:
[tex]\sum_{n=0}^{\infty} \frac{n+2}{n+4}[/tex]
To test if it converges, we can calculate the limite of [tex]\frac{n+2}{n+4}[/tex] as n goes to infinite.
Limit:
[tex]\lim_{n \rightarrow \infty} \frac{n+2}{n+4}[/tex]
Considering only the terms with the highest exponent in the numerator and the denominator:
[tex]\lim_{n \rightarrow \infty} \frac{n+2}{n+4} = \lim_{n \rightarrow \infty} \frac{n}{n} = \lim_{n \rightarrow \infty} 1 = 1[/tex]
Thus, the sequences converges to 1.
Is anyone free to help me? It's a picture .
Answer:
1. 8 units downwards and 2 units left
2.7 units right and 4 units upwards
3. 5 units right and 4 units downwards
Step-by-step explanation:
That how it goes
Work out the sum of 1/4 1/6 and 1/3
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4} +\frac{1}{6} +\frac{1}{3}[/tex]
4 = 2 × 2 × 1
6 = 2 × 3 × 1
3 = 3 × 1
GCF = 1
4 × 6 × 3 = 72
[tex]\frac{18}{72} +\frac{12}{72} +\frac{24}{72}[/tex]
[tex]\frac{18+12+24}{72}[/tex]
[tex]\frac{54}{72}[/tex]
54 = 2 × 3 × 3 × 3
72 = 2 × 2 × 2 × 3 × 3
GCF = 2 × 3 × 3
GCF = 18
[tex]\frac{\frac{54}{18} }{\frac{72}{18} }=\frac{3}{4}[/tex]
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{Looking for your LCD (Least Common Denominator) of each fraction}\downarrow\\\\\\\mathsf{\dfrac{1}{4}=\dfrac{3}{12}}\\\\\\\mathsf{\dfrac{1}{6}=\dfrac{2}{12}}\\\\\\\mathsf{\dfrac{1}{3}=\dfrac{4}{12}}\\\\\\\\\\\large\textsf{The LCD is \underline{12}}[/tex]
[tex]\mathsf{\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{3}}[/tex]
[tex]\mathsf{= \ \dfrac{1\times3}{4\times3}+\dfrac{1\times2}{6\times2}+\dfrac{1\times4}{3\times4}}[/tex]
[tex]\large\textsf{Solving for the numerators (TOP numbers)}\downarrow\\\\\mathsf{1\times3=\boxed{\bf 3}}\\\\\mathsf{1\times2=\boxed{\bf 2}}\\\\\mathsf{1\times4=\boxed{\bf 4}}[/tex]
[tex]\large\textsf{Solving for the denominators (BOTTOM numbers)}\downarrow\\\\\mathsf{4\times3=\boxed{\bf 12}}\\\\\mathsf{6\times2=\boxed{\bf 12}}\\\\\mathsf{3\times4=\boxed{\bf 12}}[/tex]
[tex]\mathsf{=\ \dfrac{3+2+4}{12}}[/tex]
[tex]\large\textsf{Solving for your numerator (TOP number) }\downarrow\\\\\\\mathsf{3+2+4}\\\\\mathsf{= 5+4}\\\\\mathsf{= \boxed{\large\textsf{\bf 9}}}[/tex]
[tex]\mathsf{=\ \dfrac{9}{12}}[/tex]
[tex]\mathsf{\dfrac{9\div3}{12\div3}}\\\\\\\\\mathsf{9\div3= \boxed{\large\textsf{\bf 3}}}\\\\\mathsf{12\div3=\boxed{\large\textsf{\bf 4}}}[/tex]
[tex]\mathsf{= \dfrac{3}{4}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: }\boxed{\mathsf{\bold{ \dfrac{9}{12}\ or\ \dfrac{3}{4}}\ either\ of\ those\ fractions\ should\ work\ because}}}}\\\boxed{\boxed{\large\textsf{they are equal to each other!}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A regular decagon has a radius of 8 cm.
What is the approximate area of the decagon? Recall that a decagon is a polygon with 10 sides.
188 cm2
198 cm2
304 cm2
375 cm2
Answer:
188cm^2
Step-by-step explanation:
A regular decagon has ten sides. Therefore, a decagon with radius of 8 cm has an approximate area of 188 cm²
What is a decagon?A decagon is a polygon with 10 sides.
Therefore, the approximate area of a decagon can be found as follows:
area of decagon = r²sin(360/n) / 2 × 10
where
r = radius
n = number of sides
Therefore,
r = 8 cm
area of decagon = 8² sin (360/ 10) / 2 (10)
area of decagon = 64 sin 36 / 2 × 10
area of decagon = 64 × 0.58778525229 / 2 × 10
area of decagon = 37.6182561467 / 2 × 10
area of decagon = 18.8091280734 × 10
area of decagon = 188 cm²
learn more on decagon here: https://brainly.com/question/27314677
x³+y³=(x+y)(x² - xy +y²)
Answer:
__________________________________
➡️x3+y3 = (x+y)(x^2-xy+y^2)
--------------------
R.H.S
(x+y)(x^2-xy+y2)
=>x3-x^2y+xy^2+x^2y-y^2x+y3
NOW after cancelling we get :
=> x3+y3
-------------------
L.H.S
=> x3+y3
L.H.S. = R.H.S
Hence VERIFIED✔✔
_______________________________
Step-by-step explanation:
How can -6/4x = 12 be solved in one step?
Answer:
Multiply each side by -4/6 to isolate x
Step-by-step explanation:
-6/4x = 12
Multiply each side by -4/6 to isolate x
-4/6 *(-6/4x) = 12*(-4/6)
x =-8
Answer:
12 divided by -6/4
Step-by-step explanation:
you need to isolate the x, since -6/4 is being multiplied to x, you gotta divide it to move -6/4 to the other side x=12 divided by -6/4
How many mLs are in 1300mG
Answer:
1.3 mL
Step-by-step explanation:
1 mg = 0.001 mL
1300 mg * 0.001 mL/mg = 1.3 mL
Need help with this
PLZZ HELPPPPPP!!!!!!!!
Answer:
$1043.33
$494.47(1 +1)(1 + .055)
Step-by-step explanation:
Please fill the blanks
Answer:
First box
8pi-(7pi/4)= pi/4
Second Box:
Tan 7pi/4= 0.09625006863
Step-by-step explanation:
find the product write your question in exponential form 7 ^-1 x 7 ^-7
Answer:
[tex] {7}^{ - 8} [/tex]
Step-by-step explanation:
[tex] {7}^{ - 1} \times {7}^{ - 7} \\ {7}^{ - 1 + - 7} \\ {7}^{ - 8} [/tex]
Hope this helps you.
The measures of the exterior angles of a hexagon are x°, 2x°, 4x°, 6x°, 7x°, and 10x°. Find the measure of the smallest exterior angle.
Answer
x is the smallest angle so 12 is the answer.
Step-by-step explanation:
x + 2x + 4x + 6x + 7x + 10x = 360 degree (sum of exterior angles of a hexagon)
30x = 360
x = 360/30
x = 12
the smallest exterior angle of hexagon is 12 degree.
The measure of the smallest exterior angle is 12 degrees.
What is Polygon?Polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
A hexagon is a six-sided polygon or 6-gon creating the outline of a cube.
The measures of the exterior angles of a hexagon are x°, 2x°, 4x°, 6x°, 7x°, and 10x°.
We need to find the smallest exterior angle which is x.
we know that the sum of the exterior angles of any polygon is always equal to 360.
x° + 2x° + 4x° + 6x° + 7x° + 10x° = 360
30x=360
Divide both sides by 30
x=360/30
x=12
Hence, the measure of the smallest exterior angle is 12 degrees.
\
To learn more on Polygons click:
https://brainly.com/question/28276384
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Un microempresario realiza una inversión donde le pagan una rentabilidad del 5,36% mensual simple, él desea que esa inversión se triplique ¿Cuánto tiempo deberá esperar para que esto ocurra?
Answer:
Deberá esperar 37.31 años para que esto ocurra.
Step-by-step explanation:
Este es un problema de interés simple.
La fórmula del interés simple viene dada por:
[tex]E = P*I*t[/tex]
En el que E es la cantidad de interés ganado, P es el principal (la cantidad inicial de dinero), I es la tasa de interés (anual, como decimal) y t es el tiempo.
Después de t años, la cantidad total de dinero es:
[tex]T = E + P[/tex]
5,36% mensual simple
Esto implica que [tex]I = 0.0536[/tex]
Inversión se triplique ¿Cuánto tiempo deberá esperar para que esto ocurra?
Tiempo t para que la cantidad de interés sea lo doble de la cantidad inicial, o sea, [tex]E = 2P[/tex].
[tex]E = P*I*t[/tex]
[tex]2P = P*I*t[/tex]
[tex]It = 2[/tex]
[tex]0.0536t = 2[/tex]
[tex]t = \frac{2}{0.0536}[/tex]
[tex]t = 37.31[/tex]
Deberá esperar 37.31 años para que esto ocurra.
verify that :- 2/7 x (-3/5 +4/10)=2/7x-3/5 +2/7 x 4/10
please help me fast please
Answer:
hope it helps you............
Answer:
-2/35.....................
If f(x) = 3x - 1 and g(x) = x + 2, find (f- g)(x).
PLZZ HELPPP
This the answer
If f(x) = 3x - 1 and g(x) = x + 2, find (f- g)(x).
PLZZ HELPPP
2x-3
please help!!! i’ll give brainliest.
no links
do not comment random things
i need asap!!
ill give as many points as i can
Answer:
a,d,e
Step-by-step explanation:
75+a1 = 180
so a1=105
a1=x-15
105=x-15
x=120
then using rules of parallel lines with commone intersecting line gives the others.
Select the correct answer.
What is the solution for x in the equation?
-x + 3/7 = 2x - 25/7
Answer:
= 4/ 3
Step-by-step explanation:
-x+3/7=2x-25/7
We move all terms to the left:
-x+3/7-(2x-25/7)=0
We add all the numbers together, and all the variables
-x-(+2x-25/7)+3/7=0
We add all the numbers together, and all the variables
-1x-(+2x-25/7)+3/7=0
We get rid of parentheses
-1x-2x+25/7+3/7=0
We multiply all the terms by the denominator
-1x*7-2x*7+25+3=0
We add all the numbers together, and all the variables
-1x*7-2x*7+28=0
Wy multiply elements
-7x-14x+28=0
We add all the numbers together, and all the variables
-21x+28=0
We move all terms containing x to the left, all other terms to the right
-21x=-28
x=-28/-21
x=1+1/3
Answer:
x = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Given
- x + [tex]\frac{3}{7}[/tex] = 2x - [tex]\frac{25}{7}[/tex] ( multiply through by 7 to clear the fractions )
- 7x + 3 = 14x - 25 ( subtract 14x from both sides )
- 21x + 3 = - 25 ( subtract 3 from both sides )
- 21x = - 28 ( divide both sides by - 21 )
x = [tex]\frac{-28}{-21}[/tex] = [tex]\frac{4}{3}[/tex]
For the following system, use the second equation to make a substitution for x in the first equation.
3x + 2y = 7
x - y + 3 = 0
What is the resulting equation?
Step-by-step explanation:
x value is 0.2
y value is 3.2
A can of soup is 8 centimeters in diameter and 10 centimeters high. What is the volume of the can in terms of ?
Answer:
volume= 502.4cm
Step-by-step explanation:
see attachment for detailed solution
Answer:
Step-by-step explanation:
Formulae for Volume = Pi x r2 x h
Pi = 3.14 or 314/100 because the radius is not a product of 7
Radius = 4 cm
Height = 10 cm
314/100 x 4 x 4 x 10 = 512.4 cm2
= 512.4 cm2
An apartment has 90 square meters of carpeting. How much is this in square feet? Use the following conversion: 1 square meter is 10.8 square feet.
An explanation on how to do it would also be amazing!
Answer:
Area = 972 square feet
Step-by-step explanation:
Let 90 square meter be = x square feet
Given :
square meter square feet
1 10.8
90 x
[tex]\frac{1}{90} = \frac{10.8}{x}\\\\1 \times x =10.8 \times 90 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ cross \ multiply \ ]\\\\x = 972[/tex]
Therefore , 90 square meter = 972 square feet
The sum of three numbers is 86. The third number is 4 times the first. The first number is 10 more than the second. What are the numbers?
Answer:
The first number is 16
The second number is 6
The third number is 64
Step-by-step explanation:
The information from the word problem are;
The count of the numbers in the sum = 3 numbers
The value of the sum of the three numbers = 86
The value of the third number = 4 × The value of the first number
The value of the first number = 10 + The value of the second
Let 'x' represent the first number, let 'y' represent the second number and let 'z' represent the third number, we have;
x + y + z = 86...(1)
z = 4 × x...(2)
x = y + 10...(3)
From equation (3), we get;
x = y + 10
∴ y = x - 10...(4)
Substituting the value of z from equation (2) and the value of y from equation (4) in equation (1) gives;
x + y + z = 86
z = 4 × x = 4·x
y = x - 10
∴ x + y + z = x + (x - 10) + 4·x = 86
x + (x - 10) + 4·x = x + x - 10 + 4·x = 6·x - 10 = 86
6·x = 86 + 10 = 96
∴ x = 96/6 = 16
x = 16
From equation (2), we get;
z = 4 × x
∴ z = 4 × 16 = 64
z = 64
From equation (4), we get
y = x - 10
∴ y = 16 - 10 = 6
y = 6
Therefore; x = 16, y = 6, and z = 64
The numbers are 16, 6, and 64
what fraction of 3 hours is 30 minutes?
Answer:
7/2
Step-by-step explanation:
I need help with this! Quick ASAP?
Answer:
a) F
b) B, E, D
Step-by-step explanation:
a) The segment with the greatest gradient has the largest change in y-values per unit change in x-values
From the given option, the rate of change of the y to the x-values of B = the gradient = (4 units)/(2 units) = 2
The gradient of F = (-3units)/(1 unit) = -3
The gradient of A = 4/4 = 1
The gradient of C = -2/5
The gradient of D = 2/6 = 1/3
The gradient of E = 3/4
The segment with the greatest gradient is F
b) The steepest segment has the higher gradient
From their calculated we have;
The gradient of segment B = 2 therefore, B is steeper than E that has a gradient of 3/4, and E is steeper than D, as the gradient of D = 1/3
Therefore, we have;
B, E, D.
Find an equation in point-slope form for the line having the slope m =1/3 and containing the point (-3,- 6).
math:John is buying new shoes. He finds the shoes he wants on sale for 30%, and the original price is $88. How much will he pay for the shoes?
Answer:
26.4
Step-by-step explanation:
hd hd hd hd hd hd hd hd hd hd hd hd
Answer:$61.6
Step-by-step explanation: The sale is 30% so we have to look for 70% of $88 because that's what we're paying for. So, that would be 88 times 70/100 which ends with 61.6.
Ryan draws a trend line through the following data
points. Did he draw the line correctly?
Answer: C, You can tell the trend line is incorrect since all of the points are below it. A trend line should be in-between all of the points to give the best estimate.
Step-by-step explanation:
Given d= 4t+1 can you determine the value of the y-
intercept?
HELP!! asap!
helppppppppppppppppp
Answer:
Click the third one.
Answer:
3rd one
Step-by-step explanation:
Mark me brainliest pls
Hope this helps!
Which of the following is the maximum value of the function y = −2x2 + 5?
5
−2
25
0
Answer:
The answer is 0 because the minimum is 5
Step-by-step explanation:
Use the formula
x = − b /2 a
to find the maximum and minimum.
( 0 , 5 )
What is the following values of:
XZ:
XY:
Find the sum of the series
{1875 + 750 + 300+...
+3.072}
Answer:
Find the indicated sum for each geometric series.
{1875+750+300+⋯+3.072}
Answer: 3122.952
Step-by-step explanation:
{1875+750+300+⋯+3.072}
r=0.4 3.072=1875(0.4)n−1
0.0016384=(0.4)n−1
7=n−1→n=8
Sn=1875(1−(0.4)8)1−0.4=3122.952
I think is like this.