The Sequence:
1 , 1+2 , 1+2+3 , 1+2+3+4, ...
here, every term is an AP. finding the general formula for the sum of the elements of each term is:
Sₙ = [tex]\frac{x}{2}(2a + (x-1)d)[/tex] [where x = number of term, a = first term and d = common difference]
here, the first term is always 1 and so is the common difference.
Sₙ = [tex]\frac{x}{2}(2 +x-1)[/tex]
Sₙ = [tex]\frac{x}{2}(1 +x)[/tex] = [tex]\frac{1}{2}(x + x^{2})[/tex]
which is the formula for a general term in our series
now, we need to find the sum of the first n terms of this series
[tex]\displaystyle\sum_{x=1}^{n} [\frac{1}{2}(x + x^{2})][/tex]
[tex]\displaystyle\frac{1}{2} [\sum_{x=1}^{n} (x) + \sum_{x=1}^{n}(x^{2})][/tex]
in this formula, for the first term, it's just an AP from x = 1 to x = n
for the second term, we have a general formula [tex]\frac{n(n+1)(2n+1)}{6}[/tex]
[tex]\frac{1}{2}[\frac{n}{2}(2a + (n-1)d)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
in this AP (first term), the first term and the common difference is 1 as well
[tex]\frac{1}{2}[\frac{n}{2}(2 + n-1)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
[tex]\frac{1}{2}[\frac{n}{2}(n+1)+ \frac{n(n+1)(2n+1)}{6} ][/tex]
[tex][\frac{n}{4}(n+1)+ \frac{n(n+1)(2n+1)}{12} ][/tex]
[tex]\frac{n}{4}(n+1) [1+\frac{(2n+1)}{3} ][/tex]
[tex]\frac{n}{4}(n+1) [\frac{(3+2n+1)}{3} ][/tex]
[tex]\frac{n}{4}(n+1) [\frac{(2n+4)}{3} ][/tex]
[tex]\frac{n}{2}(n+1) [\frac{(n+2)}{3} ][/tex]
[tex]\frac{n(n+1)(n+2)}{6}[/tex]
which is the sum of n terms of the given sequence
Help anyone can help me do this question,I will mark brainlest.
Answer:
Step-by-step explanation:
E ⊂ F ⊂ G
The Coal Utility Company is burning coal to produce electricity. The following cost function illustrates the cost in dollars (C) of removing t% of the hazardous toxins generated from burning coal. What happens to the cost as t approaches 100?
C= 55,000t/100-t for 0 ≤ t < 100
A The cost continues to increase.
B The cost continues to decrease.
C The cost approaches $0.
D The cost approaches $55,000.
Answer:
the cost continues to increase
Step-by-step explanation:
the cost (C) approaches infinity (or becomes very large) as t approaches 100%. Thus, the correct answer is: A. The cost continues to increase.
To determine what happens to the cost (C) as t approaches 100%, we can take the limit of the cost function as t approaches 100.
The cost function is given as: [tex]\[ C = \frac{55,000t}{100 - t} \][/tex]
Now, let's find the limit of C as t approaches 100:[tex]\[ \lim_{{t \to 100}} C = \lim_{{t \to 100}} \frac{55,000t}{100 - t} \][/tex]
To find this limit, we can use direct substitution:[tex]\[ \lim_{{t \to 100}} \frac{55,000 \times 100}{100 - 100} = \lim_{{t \to 100}} \frac{5,500,000}{0} \][/tex]
Since the denominator approaches 0 as t approaches 100, the limit is undefined (infinite).
Therefore, the cost (C) approaches infinity (or becomes very large) as t approaches 100%. Thus, the correct answer is: A. The cost continues to increase.
To know more about infinity:
https://brainly.com/question/31331496
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i need helpp !! ill mark brainliest !
393/1000. i think, sorry. :c
Explain how you can use absolute value to tell whether
the sum of two integers is positive or negative.
Answer:
Let the integers are p and q.
In case both integers are positive or negative, you add the numbers up and apply their sign to the sum.
Examples:
10 + 88 = 98-20 + (-15) = -35In case one of the integers is negative and one positive.
p < 0, q > 0Use absolute value in this case.
Subtract the numbers and apply the sign of the number with the greater absolute value.
Examples:
- 10 + 15 = |15 - 10| = |5| = 5- 15 + 10 = - |15 - 10| = - |5| = -5Step-by-step explanation:
Let the numbers be x and y
If both are of same signs then
|x + y| = x + y
-|x + y| = -(x + y) = -x - y
If one is negative and one is positive
-|x + (-y)| = -|x - y| = -x + y
-|y + (-x)| = -|y - x| = -y + x
help me please????????
Answer:
c
Step-by-step explanation:
Option c is correct. All points are equally spaced from the line x=1 as their images do. They are symmetric about the line x=1. For instance, point A and A' are both 3 units from the line x=1.
Option a and B are wrong as we cannot see and swapping of x and y coordinates to a point.
For option d, only point A is shifted 6 units to the left to A', but point B shifted 8 units to B'. Incorrect.
Rational numbers include whole numbers, integers, fractions, and some decimals?
Answer:
TRUE
Step-by-step explanation:
this is true.
rational= ratio
Is the relation a function? Explain
Set-builder notation?
Domain/range?
Answer:
doamin = set builder nation
Answer:
domain= set builder notation
Brooke spent 3/4 hours playing her flute each day for 7 days. How many hours did she play her flute in all
Answer:
5 and 1/4 hours or 5 hours and 15 minutes
Step-by-step explanation:
She played her flute 3/4 hours every day for 7 days, so to find the total number of hours we can multiply 3/4 by 7 to get 21/4. This is equal to 5 and 1/4 hours, or 5 hours and 15 minutes.
Answer: 5.25 hrs
Step-by-step explanation: 3/4 of an hour is 45 min. 45 min x 7 days is 315 min which is 5 hours and 15 min or 5.25 hrs
2 = 2.27 - m/4
I am so bad at math, lol! ^^ HELP ME PWEASE!
Answer:
m = 1.08
Step-by-step explanation:
Subtract 2.27 from both sides.2 - 2.27 = -m/4
Simplify 2 - 2.27 to -0.27.-0.27 = -m/4
Multiply both sides by 4-0.27 × 4 = -m
Simplify -0.27 × 4 to -1.08.-1.08 = -m
Multiply both sides by -1 (-m is also known as -1)1.08 =m
Answer:
m = 1.08
Step-by-step explanation:
Basically, we can start off by finding the difference between 2 and 2.27(which is 0.27). Then we can see that 0.27 is equal to m/4. Since 0.27*4=1.08, we can see that m=1.08.
-2x + 9x5 + 1 - 9x2
What’s the answer to this someone help plz
Answer:
factored = -2(x-14) Simplified= -2x+28
Step-by-step explanation:
Simplify the expression by combining like terms:
8x + 3y + 2x^2 + 6y^2 + 7 =
a
10x^2 + 9y^2 + 7
b
8x + 3y + 2x^2 + 6y^2 + 7
c
11xy + 8xy^2 + 7
Answer:
8x + 3y + 2x^2 + 6y^2 + 7 =
Step-by-step explanation:
8x + 3y + 2x^2 + 6y^2 + 7 =
Combine like terms
There are no like terms
8x + 3y + 2x^2 + 6y^2 + 7 =
Let's combine
8x+3y+2x²+6y²+7No like terms present
We may arrange in order of degrees.
2x²+6y²+8x+3y+7x² + 4x from 5x² + x
MARKING BRAINLIEST !! using the distance formula falculate the perimeter of the triangle below
a. 27.9 units
b. 24.3 units
c. 25.7 units
d. 28.2 units
Answer:
a
Step-by-step explanation:
i didn't use the distance formula, instead i used the pythagrean theorum. i counted the units for the legs, and made three smaller triangle and solved them to find the lengths of the hypotenuse and the added the three of those together to find the perimiter of the original triangle
Determine whether each relation is a function
Please help I dont wanna fail math this year
Thanks
(I am in Algebra 1 btw)
Find the coordinates of the image of J (−5, −1) after the translation (x, y) → (x − 2, y).
A. (−7, −3)
B. (−5, −3)
C. (−3, −1)
D. (−7, −1)
The coordinates of the image of J (−5, −1) after the translation (x, y) → (x − 2, y) will be (−7, −1). Then the correct option is D.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
The rule of the translation is given below.
(x, y) → (x − 2, y)
The coordinates of the image of J (−5, −1). Then the location of the point J after the translation will be
(x, y) → (x − 2, y)
(−5, −1) → (−5 −2, −1)
(−5, −1) → (−7, −1)
The coordinates of the image of J (−5, −1) after the translation (x, y) → (x − 2, y) will be (−7, −1). Then the correct option is D.
More about the transformation of a point link is given below.
https://brainly.com/question/27224339
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Describe a relationship between two sets that you can describe mathematically
Answer:
LOVE and CARING for each other
Step-by-step explanation:
can anyone help me solve this function please?
Answer:
f(-5) = 19
Step-by-step explanation:
f(t) = -3t+4
Let f(t) = 19
19 = -3t+4
Subtract 4 from each side
19 - 4 =-3t+4-4
15 = -3t
Divide each side by -3
15/-3 = -3t/-3
-5 = t
Answer:
the answer is -5
Step-by-step explanation:
F(t)=-3(t)+4
it told you that F(t) is equal to 19
so -3*-5=15+4=19
Which graph shows the function f(x) = x with an input of f(x – 3)?
Mrs. Eskew saved her money for 32 years and had $4,119,184 in the bank. She used her money to go a vacation for a month and spent $978,349. How much did she have left after her vacation?
Answer:
$3,140,835
Step-by-step explanation:
4,119,184-978,349=3,140,835
hope this helped!
What does the term "cube root" mean?
Simplify square root of -200
Answer:
14.1421356i
Step-by-step explanation:
hope it helps
What is one of the best ways to stop procrastinating and study More
Answer:
use the two minute rule. you tell yourself you will study for two minutes or ten minutes and then if you're in a flow you keep going. hope this helps :)
Given that
a
= 3 cm and
b
= 21 cm, work out
θ
rounded to 1 DP.
Answer:
I am sorry I not no
this question
Step-by-step explanation:
sorry dear friend
the number 126 is divisible by what numbers ? 2,3,4,5,6,9,10
Answer:
1,
Step-by-step explanation:
You may also be interested to know that all the numbers that 126 is divisible by are also known as the factors of 126. Not only that, but all the numbers that are divisible by 126 are the divisors of 126.
Xian and his cousin Kal both collect stamps. Xian has 52 stamps, and Kal has 68 stamps. The boys recently
joined different stamp-collecting dubs. Xian's club will send him 20 new stamps per month. Kai's club will
send him 16 new stamps per month. After how many months will Xlan and Kal have the same number of
stamps? How many stamps will each have?
Answer:
In 4 months, they will both have 132 stamps.
Step-by-step explanation:
Let x = # of months
52 + 20x = 68 + 16x
4x = 16
x = 4
Plug x value into both expressions and see if it checks out
52 + 20(4) = 68 + 16(4)
52 + 80 = 68 + 64
132 = 132
At a competition with 7 runners, medals are awarded for first, second, and
third places. Each of the 3 medals is different. How many ways are there to
award the medals?
Decide if this is a permutation or a combination, and find the number of ways
to award the medals.
Answer:
35 different combinations
Step-by-step explanation:
This would be a combination because the same person cannot get all three medals so permutation is not the correct way to calculate this. We use the formula C(n,r)=(nr)=n!(r!(n−r)!)=? where n is the number of total objects and r is the number of objects taken from the total.
brainliest pls . . . uwu
A goat is grazing outside of a rectangular barn that has dimensions 20 ft by 30 ft.
He's tied to a corner of the barn with a 12 ft rope. Find the grazing area of the goat.
Answer:
108π ft² or 339.29 ft²Step-by-step explanation:
Refer to attached picture.
The grazing area of the goat is 3/4 of area of circle with 12 ft radius:
A = 3/4(πr²) = 3/4(π*12²) = 108π or 339.29 ft²Tied to the corner
Means 1part among 4parts of circle or a quarter area
So grazing field
πr²-1/4πr²3/4πr²3/4(12)²π3/4(144)π108π339.3ft²Perform the indicated operations. Write the answer in standard form, a+bi.
5 - 3i / -2-9
[tex] \huge \boxed{\mathfrak{Answer} \downarrow}[/tex]
[tex] \large \bf\frac { 5 - 3 i } { - 2 - 9 } \\ [/tex]
Subtract 9 from -2 to get -11.
[tex] \large \bf \: Re(\frac{5-3i}{-11}) \\ [/tex]
Divide 5-3i by -11 to get [tex]\sf-\frac{5}{11}+\frac{3}{11}i \\ [/tex].
[tex] \large \bf \: Re(-\frac{5}{11}+\frac{3}{11}i) \\ [/tex]
The real part of [tex]\sf-\frac{5}{11}+\frac{3}{11}i \\ [/tex]is [tex]\sf-\frac{5}{11} \\ [/tex].
[tex] \large \boxed{\bf-\frac{5}{11} \approx -0.4545..} \\ [/tex]
Answer:
[tex] \frac{5 - 3i}{ - 2 - 9} \\ = \frac{ 5 - 3i}{ - 11} \\ = \frac{5}{ - 11} + \frac{3i}{11} \\ thank \: you[/tex]
one half of a number plus 7
Answer:
1/2n + 7
n = unkown number
Step-by-step explanation:
Answer:
1/2(x) + 7
Step-by-step explanation:
x= unknown number
Pls help how do I solve this?
Answer:
area is just multiplication of sides so..
(4.2x^2 - 3xy) (5)
= 21 x^2 - 15 xy
doneeeeee
