jaz^2 = (4) (a+7) (a + 5)^2 =
4 ( a + 7) (a^2 + 10a + 25) =
(4a + 28) (a^2 + 10a + 25) =
4a^3 + 40a^2 + 100a
+ 28a^2 + 280a + 700
_________________________
4a^3 + 68a^2 + 380a + 700
Geometric Sum where r = 1.12
9 [ 1 - (1.12)^5] / [ 1 - 1.12 ] ≈ 57 miles
8 /125 * blank = 5/2 multiply both sides by 125 / 8
blank = (5/2) (125/8) = 625 / 16
The form is x^2 + bx + c
Sum of the roots = 11 = -b → b = -11
Product of the roots = c = 28
The quadratic is x^2 -11x + 28
Here : https://web2.0calc.com/questions/graphing-parabolas_8
sin A = 3/4 = BD / BA
3/4 = BD / 24
(3/4)(24) = BD = 18
sin C = 1/4 = BD / BC
4BD = BC
4 (18) = BC = 72
DC = sqrt [ 72^2 - 18^2 ] = sqrt [ 18^2 ( 4^2 - 1^2) ] = 18 sqrt (15)
.97777.... =
(97 - 9) / ( 90) = 88/90 = 44/45
a - b = 44 - 45 = -1
By a little inspection.....let x = 16 and y= 81
sqrt (16) + sqrt (81) =
4 + 9 = 13
And
4 (16) + 9(81) = 793
So....x = 16
132 , 198 , 264 , 330 , 396 , 462 , 528 , 594 , 660 , 726 , 792 , 858 , 924 , 990 , Total = 14 such integers.
3
18 mod 3 = 0
16 mod 3 = 1
****
The hour hand moves at (1/2)° every minute
The minute hand moves 12 times as fast = 6° every minute
From 12 Noon....the hour hand has moved (1/2)° (48) = 24°
The minute hand has moved (6°) (48) = 288°
The larger obtuse angle between them = (288 - 24)° = 264°
The smaller obtuse angle between them = (360 - 264)° = 96°
Lateral suface area = 2 * pi * r * h
3.5 = 2*pi * r * h → solve for h
(3.5) / ( 2 * pi * r) = h
Volume = pi * r^2 * h
5 = pi * r^2 * ( 3.5) / ( 2 *pi * r)
5 = 1.75 r
5 /1.75 = r = 20 / 7 in
sqrt (27) * sqrt (12) * sqrt (300) =
sqrt (9) * sqrt (3) * sqrt (4) * sqrt (3) * sqrt (3) * sqrt (100) =
3 * sqrt (3) * 2 * sqrt (3) * sqrt (3) * 10 =
3 * 2 * 10 * [sqrt (3) * sqrt (3)] * sqrt (3) =
3 * 2 * 10 * 3 * sqrt (3) =
180 sqrt (3)
sqrt (2) * sqrt (6) * sqrt (110) * sqrt (156) =
sqrt (2) * [ sqrt (2) * sqrt (3) ] * [ sqrt (11) * sqrt (5) * sqrt (2) ] * [sqrt (4) * sqrt (3) * sqrt (13) ] =
sqrt (2) * sqrt (2) * sqrt (2) * sqrt (4) * sqrt (3) * sqrt (3) * sqrt (11) * sqrt (13) * sqrt (5) =
2 * sqrt (2) * 2 * 3 * sqrt (11) * sqrt (13) * sqrt (5) =
12 * sqrt [ 2 * 11 * 13 * 5 ] =
12 sqrt [ 1430 ]
https://web2.0calc.com/questions/probability_75612
\(f(2) = {3 \over 2} = 1.5\)
\(f(3) = 3^3 = 27\)
\(f(4)=3^4=81\)
Now, finish it off..
For the first function the range is [-3, inf )
For the second function the range is [3 , inf)
So..taking the greater range → [ -3, inf)
Here's a very good article from Khan Academy that you can learn from: https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/variance-standard-deviation-population/a/calculating-standard-deviation-step-by-step
Rearrange as ... y = 8 - abs ( x -1)
This will form a triangle
The max height occurs when x = 1 and the height = 8
To find the x intercepts we have
8 - abs (x -1) = 0
8 = abs ( x -1)........this sets up two equations
8 = x - 1 - 8 = x -1
x = 9 x = -7
So the x intercepts are -7 and 9 and the base of the triangle = 9 - (- 7 ) = 16
So.....the area = (1/2) (16)(8) = 64
f(12) = 12/2 + 1 = 7
f(f(12)) = f(7) = 3(7) -1 = 20
f(f(f(12))) = f(20) = 20/2 + 1 = 11
f(f(f(f(12)))) = f (11) = 3(11) - 1 = 32
Very nice, Melody !!!!!
What is the range of the function?
Hello Guest!
\(f(x) = 3 - 2\cdot 51x\)
The range of this line is:
\(\color{blue}x\in \mathbb R\ |\)\(\color{blue}-\infty\) < x < \(\color{blue}\infty\)
!
Find all values of c
\(3^{2c+1} = 28\cdot 3^c\ |\ /\div 3^c \\ 3^{c+1}=28\\ lg\ 3\cdot (c+1)=lg\ 28\\ c=\dfrac{lg\ 28}{lg\ 3}-1\\ \color{blue}c=2.0331\)
123456 ==1 combination
12, 16, 24, 32, 36, 52, 56, 64==8 permutations
8 / [6 P 2] ==8 / 30 ==4/15
!
