Answer:
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{100})[/tex]
Step-by-step explanation:
Given
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right)[/tex]
Required
The sum
Using the laws of logarithm, we have:
[tex]\log(a) + \log(b) = \log(ab)[/tex]
Take the first two terms of the series
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{2} * \frac{2}{3})[/tex]
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{3})[/tex]
Include the third term
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{3} * \frac{3}{4})[/tex]
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{4})[/tex]
Include the fourth term
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{4} *\frac{4}{5})[/tex]
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{5})[/tex]
Notice the following pattern
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3}) = \log(\frac{1}{3})[/tex] ---------------- n =2
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) = \log(\frac{1}{4})[/tex] -------------- n = 3
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ \log(\frac{3}{4}) + \log(\frac{4}{5}) = \log(\frac{1}{5})[/tex] ----------- n = 4
So the sum of n series is:
[tex]\log(\frac{1}{2}) + \log(\frac{2}{3})+ ............ + \log(\frac{n}{n+1}) = \log(\frac{1}{n+1})[/tex]
So, the sum of the series is:
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right)[/tex]
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{99+1})[/tex]
[tex]\log\left(\frac{1}{2}\right)+\log\left(\frac{2}{3}\right)+\log\left(\frac{3}{4}\right)+\log\left(\frac{4}{5}\right)+...+\log\left(\frac{98}{99}\right) +\log\left(\frac{99}{100}\right) = \log(\frac{1}{100})[/tex]
Which is NOT a type of federal student aid?
A. Scholarship
B. Student loans
C. Work study
D. Grants
2kg 300g - 375g help
Answer:1925g=1kg 925g
Step-by-step explanation:
1kg=1000g
2kg=2000g
2kg 300g=2300g
2300-375=1925g=1kg 925g
CAN ANYONE HELP ME PLS I NEED HELP PLS AND THANK YOU
Answer:
Here, BRX and NJY are two triangles in which,
Step-by-step explanation:
Someone help me please
Answer:
[tex] \sqrt{193} [/tex]
For what value of k, do the equations 2x – 3y + 10 = 0 and 3x + ky + 15 = 0 represent coincident lines
(a) -9/2
(b) 9/2
(c) 2/9
(d) -2/9
Answer:
b
Step-by-step explanation:
Solve the equation 3u+6=22
Step-by-step explanation:
3u+6=22
3u=16
u=16/3
!!!!!!!!!!!
0.03249 in standard form to 4 significant figures is
Answer:
3.349 • 10²
I moved the decimal over 2 spots to the left.
Which point is the center of the circle
Answer:
Do You Have Picture
Step-by-step explanation:
Mostly likely the focus of the circle, when solving circumference the radius is half of the circle, to the point of the center the circle.
Which of the following pairs of functions are inverses of each other?
Answer:
do you have a picture or something So I can answer your question?
Step-by-step explanation:
Option-A is accurate because f(x) = 9(x/2)-8 and g(x) = 2(x+8)/9 are the values we get when solving the function.
What is inverse function?A function receives values, performs certain operations on them, and outputs a result. After acting and concurring with the result, the inverse function switches back to the original function.
The inverse function, which also returns the initial value, returns the result of a function.
this selection. Option-A is the proper choice, so
f(x)=9(x/2)-8
consider the f(x)=y
y=9(x/2)-8
y+8=9(x/2)
(y+8)/9=x/2
2(y+8)/9=x
g(x)=2(x+8)/9
As a result, Option-A, which states that when the function is solved, the output is the inverse function, is correct. Its values are f(x) = 9(x/2)-8 and g(x) = 2(x+8)/9.
To know more about inverse function check:
https://brainly.com/question/2541698
#SPJ7
Find the median of the following data 20,14,6,25,18,13,19,10,9,12
Step-by-step explanation:
arrangement in ascending order
6,9,10,12,13,14,18,19,20,25
n = 10
median = 10 + 1 )/2 = 5.5 item =( 13 + 14 )/2 = 13.5
Raffle tickets cost $6 for 5 tickets. What is the price of 1 ticket? How many tickets can you get for $90
Answer:
1 ticket is worth 1.2$
90$ gets you 75 tickets
Step-by-step explanation:
t=ticket(s)
6=5t
6/5=t
90/(1.2)=75
Answer:
1 ticket = $1.2
Step-by-step explanation:
In \triangle JKL,△JKL, \overline{KL}\cong \overline{JK} KL ≅ JK and \text{m}\angle J = 17^{\circ}.M∠J=17 ∘ . Find \text{m}\angle K.M∠K.
Answer:
m<K = [tex]146^{o}[/tex]
Step-by-step explanation:
With the given conditions in the question, it would be observed that ΔJKL is an isosceles, since KL ≅ JK. So that JL is the base of the triangle:
m<J ≅ m<L = [tex]17^{o}[/tex] (base angle of an isosceles triangle are equal)
Then;
m<J + m<K + m<L = [tex]180^{o}[/tex] (sum of angles in a triangle)
[tex]17^{o}[/tex] + m<K + [tex]17^{o}[/tex] = [tex]180^{o}[/tex]
m<K + 34 = [tex]180^{o}[/tex]
m<K = [tex]180^{o}[/tex] - 34
m<K = [tex]146^{o}[/tex]
Thus, with respect to the given question, the measure of angle K is [tex]146^{o}[/tex]. Which is an obtuse angle of the triangle JKL.
I will give BRAINLIEST to the correct answer
Find the measure of
Answer: SOLN,
let,<FHC be x
<GHC+<FHC( sum of angle of triangle=180 degree
x+6m+55+8m+55=180
x+ 14m+110=180
x+14m=180-110
x+14m=70
x=70 divied by 14m
x=5m
therefore,the value of <FHC is 5m.
Point A(-6,-14) is translated left 12 units which of the following represents the coordinates of A'
Answer:
A' coordinate : ( - 18 , - 14 )
Step-by-step explanation:
since it is translated left, we will minus it from the x coordinate
-6 - 12 = -18
If this helps you, please mark brainliest!
Have a nice day!
Answer:
A(-18,-14)
Step-by-step explanation:
Movement 12 units left means add negative 12 to x-coordinate
-6 +(-12) = -18.
pls solve them all pls
Answer:
Step-by-step explanation:
Hope this helps u !!
Given ΔUTS with coordinates U(-4,-3), T(-2,1), S(0,-2), rotate the figure 90° Counterclockwise about the origin
Question 8 options:
U'(-2,1) T'(-4,-2) S'(0,0)
U'(4,3) T'(2,-1) S'(0,2)
U'(3,-4) T'(-1,-2) S'(2,0)
U'(-2,-2) T'(0,2) S'(2,-1)
Answer:
U'(3,-4) T'(-1,-2) S'(2,0)
Step-by-step explanation:
Firstly, we need the general rotation method
We have this as;
(x,y) to (-y,x)
So;
U (-4,-3) becomes U’ (3,-4)
T(-2,1) becomes T’(-1,-2)
S(0,-2) becomes S’ (2,0)
the sum of 3x^2 -8x -2 and 4x -2 is?
Answer:
3x^2−4x−4
Step-by-step explanation:
3x^2−8x−2+4x−2
=3x^2+−8x+−2+4x+−2
3x^2+−8x+−2+4x+−2
=(3x^2)+(−8x+4x)+(−2+−2)
=3x^2+−4x+−4
Answer:
3x^2 + 4x - 4
Step-by-step explanation:
3x^2 - 8x - 2
+ 4x - 2
––––––––––––
3x^2 + 4x - 4
make y the subject of these equations.
by² = d
Jay = 6
ay - cy = d.
cy - b) = y
Answer:
See all the answers below.
Step-by-step explanation:
by² = d
Jay = 6
ay - cy = d.
cy - b) = y
Option A
by² = d
divide both side by b
y² = d/b
square both sides
y=√d/b
Option B
Jay = 6
Divide both sides by Ja
y= 6/Ja
Option C
ay - cy = d
y(a-c)=d
divide both sides by (a-c)
y= d/(a-c)
Option D
(cy - b) = y
y-cy=-b
y(1-c)=-b
y= -b/(1-c)
what is this app and why are you reading this
4 x − 3 x + 2 y (simplify)
[tex]\huge\text{Hey there!}\\\\\large\text{4x - 3x + 2y}\\\\\large\text{\underline{\underline{COMBINE the LIKE TERMS}}}\\\\\large\text{(4x - 3x) + 2y}\\\\\large\text{4x - 3x = \bf 1x }\large\text{(or you could simply say \underline{x} because a variable by itself}\\\large\text{is understood as an invisible 1)}\\\\\large\text{\bf x + 2y}\\\\\\\boxed{\boxed{\huge\text{Therefore your answer is: x + 2y}}}\huge\checkmark\\\\\large\text{Good luck on your assignment and enjoy your day!}\\\\\\\\\frak{Amphitrite1040:)}[/tex]
The figure shows the letter W and four of its transformed images—A, B, C, and D:
Which of the four images was formed by a reflection of the letter W?
1. A
2. B
3. C
4. D
£100 is deposited in a bank paying 2.25% simple interest per annum. How much interest will have been paid after 5 years
Answer:
£11.25
Step-by-step explanation:
I = P * R * T
Where,
I = simple interest
P = principal = £100
R = interest rate = 2.25%
T = Time = 5 years
I = P * R * T
= 100 * 2.25% * 5
= 100 * 2.25/100 * 5
= (100 * 2.25 * 5) / 100
= 1,125/100
= 11.25
I = £11.25
Write the equation of the line that passes through the points (-8,-1) and (−2,9). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
not sure if understood you; slope: (-1-9)/(-8+2)=-10/-6=5/3, y-int: -1-(-40/3)=37/3; y=5/3x+37/3
Find the remainder when 8\10^18 + 1^18 is divided by 9.
Solve c =(a² + 3b)/4 for b.
Bruv take all my points I literally blow at math :'(
Answer:
[tex]b=\frac{4c-a^{2} }{3}[/tex]
Step-by-step explanation:
First: multiply both sides by 4. 4 times c is 4c and the other sides cancels out as you are doing the inverse operation of division
Then, you have [tex]4c=a^{2} +3b[/tex]
Subtract both sides by a squared
DO NOT TAKE THE SQUARE ROOT! This is because it is a squared plus 3b so you have to do the inverse of addition
From that you get [tex]4c-a^{2} =3b[/tex]
Finally, divide both sides by 3.
You get [tex]b=\frac{4c-a^{2} }{3}[/tex]
A regular octagon has a radius of 6 ft and a side length of 4.6 ft.
A regular octagon has a radius of 6 feet and side lengths of 4.6 feet.
What is the approximate area of the octagon?
71 ft2
101 ft2
110 ft2
202 ft2
Answer:
Area of regular octagon is 102.16 ft².
Step-by-step explanation:
Using Formula
Area of regular octagon = 2 a ² ( 1 + √2 )
substitute the values
Area of regular octagon = 2 ( 4.6 ft ) ²( 1 + √2 )
Evaluate the exponent
Area of regular octagon = 2 × 21.16 ft ²( 1 + √2 )
Using distributive property
Area of regular octagon = 42.32 × 1 + 42.32 × √2
multiply, we get
Area of regular octagon = 42.32 + 59.84
Add
Area of regular octagon = aaprox. 102.16 ft ²
Therefore, area of regular octagon is 102.16 ft².
Answer:
B - 101
Step-by-step explanation:
Trust the process
edge 2021
Keisha runs 3 miles in 25 minutes. At the same rate, how many miles would she run in 20 minutes?
Answer:
2.4 miles
Step-by-step explanation:
Which solution finds the value of x in the triangle below?
Answer: B
Step-by-step explanation:
WILL MARK BRAINILIEST
are the angles corresponding, alternate interior, alternate exterior, or constructive interior
Answer:
1) corresponding
3)corresponding,
5)alternate interior
Step-by-step explanation:
The perimeter of a rectangle is 84 cm. If the length is 29 cm write an equation you can use to answer this question
Answer:
Width = 13
Equation: 2 × 29 + 2W = 84
Step-by-step explanation:
Ace here!
I'm going to assume that we have to find the width. In a rectangle, there are 4 sides and opposite sides are congruent.
Let L represent the length and W represent the width.
Since there are 4 sides, we know that to find the of a rectangle perimeter, we have to do:
L+L+W+W=Perimeter
Let's first simplify this equation by combining like terms:
2L+2W = Perimeter
Now, let's plug in known values:
2(29) + 2W = 84
Divide everything by 2:
29+W=42
Isolate W:
W=42-29
W=13
Keep in mind, I didn't have to divide by 2 at the step that I had. I could've also done this:
2(29) + 2W = 84
Simplify:
58+2W=84
Bring everything to one side:
2W=26
Isolate W by dividing 2:
W=13
Two different slightly approaches, same answer.
I hope that helped, let me know if you have any questions.
