Answer:
f
(
x
)
=
2
, means, whatever be the value of
x
, f(x)=2#.
∴
f
(
−
4
)
=
2
.
2y^3 – 2y – 10y + 10 + y^2 – 1 < 0 [the terms are simply reorganized again]
factor 2y from the first two terms, -10 from the second two terms
2y (y^2 -1) – 10 (y-1) + y^2 – 1 < 0
2y (y+1)(y–1) – 10 (y-1) + (y+1)(y–1) < 0 [ because y^2 – 1 = (y+1)(y–1) ]
factor out (y-1) from all the terms
(y-1) [2y(y+1)-10+ y+1] < 0
(y-1) [(y+1) (2y+1) - 10] < 0
Let us simplify (y+1) (2y+1) - 10 < 0 now
(y-1) (2y^2+y+2y+1-10) < 0
(y-1) (2y^2 +3y -9 < 0
(y-1) (2y^2 +6y -3y - 9) < 0 [ because 3y = 6y -3y] j
Answer:
a. 3⁄10 + 6⁄10 = 9/10
b. 1⁄3 + 1⁄4 + 1⁄6 = 3/4
c. 5⁄6 – 3⁄6 = 1/3
d. 2⁄3 – 6⁄10 = 1/15
e. 4⁄10 × 3⁄7 = 6/35
f. 1⁄6 × 6⁄15 = 1/15
g. 1⁄8 ÷ 4⁄9 = 9/32
h. 1⁄5 ÷ 3⁄4 = 4/15
Step-by-step explanation:
a. 3⁄10 + 6⁄10
= 3*1 + 6*1 / 10
= 3+6/10
= 9/10
b. 1⁄3 + 1⁄4 + 1⁄6
since denominators are different we take LCM of 3,4,6 which is 12
= 1*4 + 1*3 + 1*2 / 12
= 4+3+2/12
= 9 ÷ 3 / 12 ÷ 3
= 3 / 4
c. 5⁄6 – 3⁄6
= 5 - 3 / 6
= 2 ÷ 2 / 6 ÷ 2 = 1/3
d. 2⁄3 – 6⁄10
LCM of 3 and 10 is 30
= 2 * 10 - 6 * 3 / 30
= 20 - 18 / 30
= 2 ÷ 2 / 30 ÷ 2 = 1/15
e. 4⁄10 × 3⁄7
= 12 ÷ 2 / 70 ÷ 2 = 6/35
f. 1⁄6 × 6⁄15
= 6 ÷ 6/90 ÷ 6 = 1/15
g. 1⁄8 ÷ 4⁄9
= 1/ 8 * 9/4
=9/32
h. 1⁄5 ÷ 3⁄4
=1/5 * 4/3
= 4/15
A is the first value of the sequence, then you increase or decrease by d each time
volume of a cone = (1/3)*pi*r^2*h
180 = pi(r^2)h
180/pi(r*2) = h
