This is a refreshing question!
We are given that
f(r)=ar+b, and
Sum f(r) =125 for r=1 to 5
Sum f(r) = 475 for r=1 to 10.
and we know, using Gauss's method, that
G(n)=sum (1,2,3.....n) = n(n+1)/2 or
G(n)=n(n+1)/2
Sum f(r) =125 for r=1 to 5
=>
sum=a(sum of 1 to 5) + 5b => G(5)a+5b=125 [G(5)=15]
15a+5b=125 ...................................................(1)
Similarly, Sum f(r) = 475 for r=1 to 10 => G(10)a+5b=475 [G(10)=55]
=>
55a+10b=475.................................................(2)
Solve system of equations (1) and (2)
(2)-2(1)
55-2(15)a=475-2(125) => 25a=225 =>
a=9
Substitute a=9 in 1 => 15(9)+5b=125 => 5b=-10
b=-2
Substitute a and b into f(r),
f(r)=9r-2
check: sum f(r), r=1,5 = (9-2)+(18-2)+(27-2)+(36-2)+(45-2)=135-10=125 [good]
We define the sum of f(r) for r=1 to n as
S(n)=sum f(r) for r=1 to n = 9(sum 1,2,3....n)-2n = 9n(n+1)/2-2n = 9G(n)-2n
S(n)=9n(n+1)/2-2n
checks:
S(5)=9(15)-2(5)=135-10=125 [good]
S(10)=9(55)-2(10)=495-20=475 [good]
Hence
(a)
S(n)=sum f(r) for r=1,n
= 9(sum i=1,n)+n(-2)
= 9(n(n+1)/2 -2n
=(9(n^2+n)/2) -2n
(b) sum f(r) for i=8,18
=sum f(r) for i=1,18 - sum f(r) for i=1,7
=S(18)-S(7)
=(9(18^2-18)/2-2(18))-(9(7^2-7)/2-2(7))
=1503-238
=1265
$1000×10%=$100 six mouth=two quarterly. So, the answer should be $200.($100×2)
56 - 12 = 44 comics left after giving 12 to his brother.
44 + 14 = 58 comics after borrowing 14 from his friend.
Ray now has a total of 58 comics.
Hello!
I don't exactly understand your question. If you mean to be asking whether or not 1002 is geater than 100, it is.
If you mean to be asking to add it: 102 + 900 + 100 = 1102
Answer:
The missing height is approximately 78.8011 feet.
Step-by-step explanation:
To solve for the height of the kite, you need to use a trigonometry function called sine. Sine - or sin when used to calculate - is most commonly used for right triangles, and the sine of a right triangle angle is equivalent to the side opposite (or the only side of the right triangle that does not help create that angle) of the angle divided by the hypotenuse of the right triangle. So you can now create the following function to solve the height: sin(52°) = where x represents the unknown height of the kite. From there, you can get that 52°, which equals approximately 78.8011 feet. Since there isn't a specific decimal place to round to, I rounded the answer to four decimals. If your teacher asks you to round to a specific place value, use 78.8011 to get your simplified answer.