AF = AC / 2 ∠BAC = 45º ∠DFA = 60º
Use the law of sines to calculate side DF
8x - 31 = 6x + 3 solve for x
(5y + 35) + (6x + 3) = 180 solve for y
Write 5 = 3 + 2, and expand using the Binomial Theorem. Then appy the Reduction Lemma to finish.
The sum of the constant terms is 14.
height = sqrt(102 - 62)
diagonal = sqrt(162 + 82)
https://web2.0calc.com/questions/help_98205#r3
First philosophical question?
Sum = F / [1 - r]
40 = F / [1 - (- 1/5)]
40 = F / [6 / 5]
F =40 x [6/5]
F =240 / 5
F = 48 - First term
Just to expand on the above and your observation that: 3^n /[4^n*5^n] =2^n. The answer is NOT 2^n but 2*n. So: We can write your expression as follows: 3^2016 / [4 * 4^2016 * 5^2 * 5^2016] =2 * 2016 + 2=4034 digits after the decimal point, which is correct indeed! There are 1663 zeros to the right of the decimal point + 2371 other digits = 4034 digits after the decimal point. I had this confirmed by writing a short computer code in C++, which printed ALL 4034 decimal digits. I hope that helps you.
nine
Multiplying the polynomial by a constant (integer) does nothing to change the degree
A ball is dropped straight down from a height of 20 feet. If it bounces back each time to a height one-half the height from which it last fell, how far will the ball have traveled when it hits the floor for the sixth time?
Distance up 10 up 5 up 2.5 up 1.25 up 0.625
down 20 down 10 down 5 down 2.5 down 1.25 down 0.625
Hit the floor 1st 2nd 3rd 4th 5th 6th
Add up the
distances 20 + 20 + 10 + 5 + 2.5 + 1.25 = 58.75 unless I messed up somewhere.
.
The sum of all possible values of d is 8.
The probability is 5/8.
an = 27 - 4(n-1)
a6 = 27 - 4(6-1)
a6 = 7
Sum6 = n (a1 + a6 )/2
= 6 (27+7)/2 = 102 boxes
Similar triangles
100 ft is to x as x is to 36 ft where x is the height of the scond pole (and the length of shadow1 )
100/x = x/36
x^2 = 3600
x = 60 ft
1 - a_n = 31 - 4 n
a(6) =31 - 4*6
a(6) =31 - 24
a(6) = 7 boxes in the top row
2 - Sum =6/2 *[2*7 + 4*(6 - 1)] Use AP Formula for summing them up.
= 3 * [14 + 20]
= 3 * 34
= 102 Cereal boxes on display.
3 - Check: 27, 23, 19, 15, 11, 7 = 102 Cereal boxes on display.
Write each square root as an infinite periodic decimal. Then multiply. :)
Read this:
https://web2.0calc.com/questions/let-q-x-x-2-bx-c-where-b-and-c-are-integers-if-q
Nearly same problem. Maybe if you read the solution, it will help you understand how to do this question.
https://web2.0calc.com/questions/let-f-x-x-3-bx-c-where-b-and-c-are-integers-if-f
Maybe CPhil's solution will help. :)
Hint: Try using the Shoelace Formula
a=1;b=0;c=0;p=0; cycle:d=a*100+b*10+c;if(c > b, goto loop, goto next); loop:printd," ",;p=p+1; next:c++;if(c<10, goto cycle, 0);c=0;b++;if(b<10, goto cycle, 0);c=0;b=0;a++;if(a<10, goto cycle,0);print"Total = ",p
OUTPUT = 405 such numbers.
You're welcome , Spaggehity !
(3^2016) / (4^2017 * 5^2018) =9999499344264..........43212890625 =2371 digits excluding extraneous zeros to the right of the decimal point.
Oh, silly me. I didn't even begin to think about the time it took him to set up! Thank you so much!
