the ratio of the length and width = 3:2
Step-by-step explanation:
let the length be =x
width be = 
area of a rectangle = length X width
so, x X = 384
or, 
X 2/3 = 384
or, = (384 X 3)/2
= 576
or, x = 24 ( taking square root)
hence, length is 24
width is = 24 X (2/3)
=16
so the ratio of length and width = 24 : 16
= 3:2
2ty'=4y
Replacing y'=dy/dt in the equation:
2t(dy/dt)=4y
Grouping terms:
dy/y=4dt/(2t)
dy/y=2dt/t
Integrating both sides:
ln(y)=2ln(t)+ln(c), where c is a constant
Using property logarithm: b ln(a) = ln(a^b), with b=2 and a=t
ln(y)=ln(t^2)+ln(c)
Using property of logarithm: ln(a)+ln(b) = ln(ab), with a=t^2 and b=c
ln(y)=ln(ct^2)
Then:
y=ct^2
Using the initial condition: y(2)=-8
t=2→y=-8→c(2)^2=-8→c(4)=-8
Solving for c:
c=-8/4
c=-2
Then the solution is y=-2t^2
Comparing with the solution: y=ct^r
c=-2, r=2
Answer: T<span>he value of the constant c is -2 (c=-2) and the exponent r is 2 (r=2)</span>
B) 200.96 because the area of a circle is 2*Pi* your radius which is 8 so you do 2 times 3.14 times 8 and you get 200.96 hope i helped!!
Answer:
3x < 4x < 3x + 8 < 4x + 3 < x² < x² + 6
Step-by-step explanation:
This is because as x → ∞
3x → 3∞ ,
Also, as x → ∞
4x → 4∞ ,
Also, as x → ∞
3x + 8 → 3∞ + 8,
Also, as x → ∞
4x + 3 → 4∞ + 3
,
Also, as x → ∞
x² → ∞²,
Also, as x → ∞
x² + 6 → ∞² + 6
and 3∞ < 4∞ < 3∞ + 8 < 4∞ + 3 < ∞² < ∞² + 6
Thus as x → ∞
3x < 4x < 3x + 8 < 4x + 3 < x² < x² + 6 in ascending order
Answer:
-22
Step-by-step explanation:
-4 + (5 - 2)(-6)
-4 + (3)(-6)
-4 + (-18)
-4 - 18
-22
Best of Luck!
