25th term = 9th term + d (25 - 9) = -6 + (5/4) ( 16) = -6 + 20 = 14
Vpyramid = area of base * height / 3
Area of base = sqrt (3) / 4 * 14^2 = 49sqrt (3)
Volume = 49 sqrt (3) * 30 / 3 = 490 sqrt (3) units^3 ≈ 848.7 units^3
Excellent, EP !!!
2x^3 - 5x^2 + x - 2
x + 7 [ 2x^4 + 9x^3 - 34x^2 + 5x - 14 ]
2x^4 + 14x^3
____________________________________
- 5x^3 - 34x^2
- 5x^3 - 35 x^2
________________________
x^2 + 5x
x^2 + 7x
___________________
-2x -14
-2x - 14
____________
Let A be the arc length
A = R1 ( pi/3) → A / (pi/3) = R1
A = R2 ( pi/4) → A / (pi / 4) = R2
R1 / R2 = [A / ( pi/3) ] / [ A /(pi/4) ] = [ 3/pi ] / [ 4/pi ] = 3 / 4
Ratio of areas = (3/4)^2 = 9/16
64^(x - 2) = 256^(2x) get the bases the same
(2^6)^(x - 2) = (2^8)^(2x) [ a^b)^c = a^(b * c) ]
2^( 6x - 12) = 2^(16x)
We have the bases the same.....solve for the exponents
6x - 12 = 16x
-12 = 16x - 6x
-12 = 10x
x = -12/10 = - 6 / 5
a)
f(-1) = (-1)^3 + 5 = 4
So g ( f(-1) ) = g (4) = 3(4) = 12
b) f-1(x)
y = x^3 + 5
y - 5 = x^3 take the cube root
∛ ( y - 5) = x "swap" x and y
∛ ( x - 5 ) = y = f-1(x) = the inverse
-150 = 360 -150 = 210°
cos (210°) = -cos (30°) = -sqrt ( 3) / 2
25x^2 - 4 (5x - 2) ( 5x + 2) 5x + 2
__________ = ________________ = _________
5x^3 - 2x^2 x^2 ( 5x - 2) x^2
Note that minor arc DE = 360 - 238 = 122
We have this
DCE = (1/2) ( measure of major arc DE - measure of minor arc DE)
DCE = (1/2) ( 238 - 122)
DCE = (1/2) ( 116)
DCE = 58°
