Answer:
-45
Step-by-step explanation:
The question is asking for the sum of the sequence. Therefore, there is no such thing as a "radians" answer.
When you evaluate the sum, you should get -45 as your answer. To find so, you simply plug in 1 as n and other numbers then add the result.
The sum telescopes. Consider the N-th partial sum of the series,
[tex]S_N=\displaystyle\sum_{n=1}^N\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)[/tex]
[tex]S_N=\bigg(\tan^{-1}\sqrt1-\tan^{-1}\sqrt2\bigg)+\bigg(\tan^{-1}\sqrt2-\tan^{-1}\sqrt3\bigg)+\bigg(\tan^{-1}\sqrt3-\tan^{-1}\sqrt4\bigg)+\cdots+\bigg(\tan^{-1}\sqrt N-\tan^{-1}\sqrt{N+1}\bigg)[/tex]
Notice how [tex]\tan^{-1}\sqrt2[/tex] is added, then immediately subtracted. The same goes for [tex]\tan^{-1}\sqrt3[/tex], then [tex]\tan^{-1}\sqrt4[/tex], and so on, up to [tex]\tan^{-1}\sqrt N[/tex]. This leaves us with
[tex]S_N=\tan^{-1}\sqrt1-\tan^{-1}\sqrt{N+1}[/tex]
The value of the given sum is obtained as [tex]N\to\infty[/tex]. We get
[tex]\displaystyle\sum_{n=1}^\infty\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)=\lim_{N\to\infty}S_N=\tan^{-1}1-\lim_{N\to\infty}\tan^{-1}\sqrt{N+1}[/tex]
To compute the limit, recall that [tex]\tan^{-1}x[/tex] has a range of [tex]\left(-\frac\pi2,\frac\pi2\right)[/tex]; in particular, [tex]\tan^{-1}x\to\frac\pi2[/tex] as [tex]x\to\infty[/tex]. So we have
[tex]\displaystyle\sum_{n=1}^\infty\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)=\frac\pi4-\frac\pi2=\boxed{-\frac\pi4}[/tex]
The average price of gasoline in Paris, France, is 1.91 euros per liter. If there are 3.785 liters in one gallon, and the exchange rate is 1.203 euros for one dollar, what is the price of gas in dollars per gallon for gasoline in Paris?
The price of gasoline in Paris is $.61/gallon
The price of gasoline in Paris is $2.38/gallon
The price of gasoline in Paris is $6.00/gallon
Answer:
The price of gasoline in Paris is $6.00/gallon
Step-by-step explanation:
We are asked to find the price of gas in dollars per gallon for gasoline in Paris.
Step 1
We are told in the question that: the average price of gasoline in Paris, France, is 1.91 euros per liter.
Also we are told that, the exchange rate is 1.203 euros for one dollar
We convert the Euros to dollars
If, 1.203 euros = 1 dollar
1.91 euros = x dollars
We Cross Multiply
1.203 euros × x dollars = 1.91 euros × 1 dollar
x dollars = 1.91 euros × 1 dollar/ 1.203 euros
x dollars = 1.5876974231 dollars
Therefore, 1.203 euros = Approximately 1.59 dollars.
Hence, the price of gasoline in Paris, France is 1.59 dollars per liter.
Step 2
We convert the from liter to gallon
In the question, we are told that:
If there are 3.785 liters in one gallon
Therefore, if
1 liter of gasoline = 1.59 dollars
3.785 liters of gasoline =
Cross Multiply
= 3.785 liters × 1.59
= 6.01815 dollars.
Approximately to the nearest whole number = 6.00 dollars.
Since 3.785 liters of gasoline = 1 gallon of gasoline, therefore, the price of gas in dollars per gallon for gasoline in Paris is $6.00/gallon
is the square root of 5 between 2 and 3
Answer: Yes, it’s 2.23607
5 divided by 2/5
5 divided by 2/5
Answer:
Hey there!
5 divided by 2/5 is equal to 25/2, or 12.5
Hope this helps :)
Answer:
[tex] \boxed{ \bold{ \huge {\boxed{ \sf{ \frac{25}{2} }}}}}[/tex]
Step-by-step explanation:
[tex] \sf{5 \div \frac{2}{5} }[/tex]
When any number of fraction is divided by a fraction , we multiply the dividend by reciprocal of the divisor.
We can obtain the reciprocal of any fraction by interchanging the position of numerator and denominator.
⇒[tex] \sf{5 \times \frac{5}{2} }[/tex]
To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator.
⇒[tex] \sf{ \frac{5 \times 5}{2} }[/tex]
Multiply the numbers : 5 and 5
⇒[tex] \sf{ \frac{25}{2} }[/tex]
Hope I helped!
Best regards! :D
A math club has 25 members, of which 11 are males and the rest are females. What is the ratio of females to all club members?
Answer:
The answer is 14/25
Step-by-step explanation:
If there are a total of 25 club member, and 11 of them are male, that would make the other 14 female. So it would be 14/25.
The population of algae in an
experiment has been increasing by 40% each day. If there were 20 algae at the beginning of the experiment, predict the number of algae in 7 days.
First, complete the equation:
Future Amount = [?](1+[]0
The equation is y = 20(1.40)^x
where x is the number of days and y is the future amount after x days go by
The 1.40 is from the fact that 1+r = 1+0.40 = 1.40, where r is the decimal form of 40%, so r = 0.40
-----------------------------
Plug in x = 7 to get
y = 20(1.40)^x
y = 20(1.40)^7
y = 210.827008
y = 211
We round to the nearest whole number since it doesn't make much sense to have a fractional portion of an algae. After 7 days, there are about 211 algae.
Which square root is between 4 and 5?
O 10
O 014
0 24
V32
Answer:
C. 25
Step-by-step explanation:
4*4=16
5*5=25
24 is found in the middle of 16 and 25.
Hope this helps ;) ❤❤❤
cual es el resultado de (7.006×10⁴¹)×(5.09×10²²)
Answer:
El resultado de (7.006×10⁴¹)×(5.09×10²²)=3.566054*10⁶⁴
Step-by-step explanation:
La notación científica es una manera rápida de representar un número utilizando potencias de base diez.
Los números se escriben como:
a*10ⁿ
donde:
a es un número real mayor o igual que 1 y menor que 10.n es un número entero, que recibe el nombre de exponente u orden de magnitud. Representa el número de veces que se desplaza la coma. Siempre es un número entero, positivo si se desplaza a la izquierda, negativo si se desplaza a la derecha.Para realizar la multiplicación con notación científica, debes multiplicar las magnitudes afectadas por las potencias de 10 y, por separado, multiplicar las potencias de 10, recordando la propiedad:
Si dos bases son iguales (el mismo número o variable), y son los factores de una multiplicación, ambas bases quedan en una sola y sus exponentes son sumados: xᵃ*xᵇ= xᵃ⁺ᵇEn este caso:
(7.006×10⁴¹)×(5.09×10²²)=(7.006*5.09)*(10⁴¹*10²²)=35.66054*10⁴¹⁺²²= 35.66054*10⁶³
Siguiendo el formato a*10ⁿ, debes ajustar el valor de la base a de manera que sea un número real mayor que 1 y menor que 10. Entonces, se mueve la coma decimal hacia la izquierda tantos espacios hasta llegar a la derecha del primer dígito. Y se escribe la base 10, al cual el exponente se suma la cantidad de espacios que se mueve la coma, que es un número positivo porque la coma se desplaza a la izquierda.
Entonces 35.66054*10⁶³= 3.566054*10⁶⁴
El resultado de (7.006×10⁴¹)×(5.09×10²²)=3.566054*10⁶⁴
Which property is not a characteristic of a parallelogram?
O A. Opposite sides are congruent.
B. All angles are congruent.
O C. Opposite sides are parallel.
D. Opposite angles are congruent.
Answer:
B
Step-by-step explanation:
I don't get this at all can you pls help me?
Answer: -13.85
Step-by-step explanation:
Simplify.
4.6−7.28−11.17
=−13.85
Answer:
[tex]\huge \boxed{\mathrm{-13.85}}[/tex]
Step-by-step explanation:
[tex]4.6+(-7.28)-11.17[/tex]
Removing brackets.
[tex]\Rightarrow 4.6-7.28-11.17[/tex]
Combining.
[tex]\Rightarrow -2.68-11.17[/tex]
[tex]\Rightarrow -13.85[/tex]
Select all the ways the rectangle could have been rotated to get from Frame 1 to Frame 2. 40 degrees clockwise 40 degrees counterclockwise 90 degrees clockwise 90 degrees counterclockwise 140 degrees clockwise 140 degrees counterclockwise Lesson 3
Answer:
40 degrees clockwise
140 degrees counterclockwise
Step-by-step explanation:
The rectangle is rotated in Figure B. The angle of rotation is 40 degrees. If we rotate a rectangle at an angle of 40 degrees clockwise then wit will be at the position as shown in figure B. The 90 degrees angle is perpendicular angle. Rectangle will not reach the desired position. If we rotate the rectangle at 140 degrees counterclockwise this will be the figure B representation. The rotation to 90 degree counterclockwise is either not suitable for the desired rectangle position.
what is the standard deviation for 54, 36, 30, 28, 27
Answer:
11.18
Step-by-step explanation:
Step 1: average : (54+36+30+28+27) / 5 = 35
Step 2: variance:
sum of the squares of (each number - average value) divided by (n-1)
[ (54-35)^2 + (36-35)^2 + (30-35)^2 + (28-35)^2 + (27-35)^2 ] / (5-1) = 125
Step 3: standard deviation = √(variance) = √125 = 5√5 (about 11.18)
In a certain county, the number of charter schools is 6 less than twice the number of alternative schools. We know that there are 52 charter schools in the county. How many alternative schools are in the county?
Answer:
29
Step-by-step explanation:
Answer:
29
Step-by-step explanation:
So, 52 charter schools and the number is 6 less than the alternative schools doubled. In order to find the number of alternative schools, we need to reverse the equation. 52+6=58. That means 58 is twice the amount of alternative schools. 58/2 equals 29, therefore the answer is 29
What is the domain of the function represented by the graph?
U
2
2
all real numbers
-43x4
0-3
Oy <0
Answer:
I believe its ALL REAL NUMBERS
Step-by-step explanation:
im not sure because they didnt put in a picture of the graph
A store sells three varieties of cheese cheddar, Gouda, and Swiss. Each variety of cheese is available in two different styles shredded or sliced. How many possible outcomes for the variety and style of cheese are there?
Answer:
6 possible outcomes
Step-by-step explanation:
To solve this problem, we have to make use of the Fundamental Counting Principle formula.
The formula counting principle states that when we are given two or more distinct events, in order to get the total number of possible outcomes, we multiply such events together.
In the above question, we are given two events.
Event 1
3 varieties of cheese: Cheddar, Gouda, and Swiss.
Event 2
2 styles of cheese: Shredded and Sliced
The possible outcomes for the variety and style of cheese = Event 1 × Event 2
= 3 × 2
6 possible outcomes.
These 6 Possible outcomes are listed below:
1) Cheddar cheese , Shredded
2) Cheddar cheese , Sliced
3) Gouda cheese , Shredded
4) Gouda cheese , Sliced
5) Swiss cheese , Shredded
6) Swiss cheese , Sliced
need this answer quick due soon help
Answer:
2/9
Step-by-step explanation:
Let 0.2222..... be x
10x = 2.2222222......
=> 10x - x = 2.22222..... - 0.22222....
=> 9x = 2
=> x = 2/9
3 + (5 + 7) = (3 + 5) + 7
Answer:
true
Step-by-step explanation:
3 + (5 + 7) = (3 + 5) + 7
3 + (12) = (8) + 7
15 = 15
Is ......... a rational number ?
Answer:
The third one.
Step-by-step explanation:
Growth and decay question
Answer:
Decay
Step-by-step explanation:
Staring at 3000 every y = half of the previous one.
the presence of a segment bisected will result in what type of segments?
A: noncoplanar segments
B. parallel segments
C. congruent segments
D. perpendicular segments
first person to get it right will get brainliest
Answer:
Option C → Congruent segments
Step-by-step explanation:
The meaning of segment bisector is a segment which divides another segment into two equal parts.It is not necessary that the segement which is bisecting the another segment are perpendicular with one another.
So, when a segment is bisected the two segments are equal.
Equal means the two segments are congruent.
Most appropriate statement
Answer:
Congruent.
Step-by-step explanation:
Bisecting will give 2 segments of equal length.
3 + 3w < -9
.........
Answer:
w < - 4
Step-by-step explanation:
Given
3 + 3w < - 9 ( subtract 3 from both sides )
3w < - 12 ( divide both sides by 3 )
w < - 4
Mitch wants to buy a poster to put on the wall between his bathroom door and closet door. There is exactly 22.25 inches of space between the doors. What could be the width of the poster?
Answer:
22.25 inches
Step-by-step explanation:
Since in the question it is mentioned that the mitch wants to buy a poster and wants to put on a wall that is between his door of the bathroom and the closet door
Also the space between these two doors is 22.25 inches
So based on the above information, the width of the poster should be equivalent to the given space i.e. 22.25 inches and the same is to be considered
Answer:
Mitch wants to buy a poster to put on the wall between his bathroom door and closet door. There is exactly 22.25 inches of space between the doors. What could be the width of the poster? (The poster needs to fit on the wall, so it needs to be smaller or equal to the width between the doors
Step-by-step explanation:
Let n represent the number of tablets the vet should prescribe. Which expressions will correctly solve the problem? Select all that apply. response - correct 25n =2×25 25n=252 n=2×2525 n=2×25. Solve How many tablets should the vet prescribe per day? Enter the value in the box tablets per day.
Answer:
Step-by-step explanation:
uu89yhuhiojsijdoyjtdoyitpoyirtudyjfjfj
Answer:
here this will help
Step-by-step explanation:
Help a girl out pls! Lmkkk!
divide 10kg in the ratio of 13 : 7
Answer:
6.5 : 3.5
Step-by-step explanation:
So to do this sum;
First, add both 13 and 7 which is 20
Then, 13/20 *10 = 6.5
and 7/20 *10 = 3.5
In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3). Equal quotients correspond to equal ratios.
A restaurant chef made 1 1/4 pints of mushroom soup. Each bowl of soup holds 5/8 of a pint.
How many bowls of soup will the chef be able to fill?
Answer:
2 bowls of soup
Step-by-step explanation:
1. Make 1 1/4 an improper fraction
1 1/4 = 5/4
2. Then divide 5/4 by 5/8 (KCF - Keep the 5/4 - Change the division sign to multiplication - 'Flip' 5/8 to 8/5)
5/4 x 8/5 = 40/20
3. Simplify the fraction (divide the numerator and denominator by 20)
40/20 = 2
4. Final answer:
2 (bowls of soup)
Where would you place root 8 on the Venn diagram? A) integers B) natural numbers C) rational numbers D) irrational numbers
Answer:
Option (D)
Step-by-step explanation:
All rational and irrational numbers are real numbers.
{-2, -1, -1.8, 0, 1, 2.......}
Numbers written in the form of [tex]\frac{p}{q}[/tex] are rational numbers. They are the part of irrational numbers.
{-2.5, -2, -1, 0, 1, 2.....}
Whole numbers with negative or positive notation are integers.
{-3, -2, -1, 0, 1, 2, 3, 4......}
Positive integers are the whole numbers (including zero).
{0, 1, 2, 3, 4, .......}
All whole numbers excluding zero are the natural numbers.
{1, 2, 3, 4,........}
Irrational numbers are the part of real numbers written in the form of [tex]\frac{p}{q}[/tex].
{[tex]\sqrt{2},\sqrt{5},\pi, \sqrt{10}[/tex]}
Therefore, [tex]\sqrt{8}[/tex] comes under Irrational numbers.
Option (D) is the answer.
Will give brainliest who can answer this simple algebra 2 question
Answer:
it reflected over y axis
the answer is the top left
Step-by-step explanation:
economic factors in decision making fall under
Answer:
external factors...
Step-by-step explanation:
...
Taking the square root of a number is the *blank * Of squaring a number
Answer:
Opposite
Step-by-step explanation:
They are complete opposites:
When you take the square root of a number, you are taking the number to the 1/2 power. For example, the square root of 9 is 3.
When you square a number, you multiply it by itself. For example, 3 squared is 9.
So, these are opposites because when doing these operations to the same number, the products will be "opposites" of each other, like the examples above.
consider the following expression
-10x^2 + 5x +3
2x^2 + 4
select the true statements
the numerator has 3 terms
the denominator includes a coefficient of 4
the denominator includes a coefficient of 2
the numerator has 2 terms
the numerator includes a coefficient of 3
Answer:
Statements 1 and 3 are correct
Step-by-step explanation: