Answer:
Here, 
, hence the quadratic equation has two distinct real roots.
Step-by-step explanation:
Given quadratic equation is 
.
Let, the quadratic equation is 
[where, 
are the constants]
The Discriminant 
Case 
: 
, if the discriminant is greater than 
, it means the quadratic equation has two real distinct roots.
Case 
: 
, if the discriminant is less than , it means the quadratic equation has no real roots.
Case 
: 
, if the discriminants is equal to , it means the quadratic equation has two real identical roots.
Now,
we have , where 
∴
Here, , hence the quadratic equation has two distinct real roots.
The solution for this problem is:
dV/dt = r/(t + 1)², V(0) = $500000, V(1) = $500000 - $200000 = $300000
∫dV = r∫ 1/(t + 1)² dt
V(t) = -r/(t + 1) + C
500000 = -r/(0 + 1) + C
400000 = -r/(1 + 1) + C
C = 300000, r = -100000
V(t) = 100000/(t + 1) + 300000
V(6) = 100000/(6+ 1) + 300000
V(6) = 14285.7143 + 300000
V(6) = $314285.71
Step-by-step explanation:
a. lim(x→2) [g(x) + h(x)]
Use additive property of limits.
= lim(x→2) g(x) + lim(x→2) h(x)
= 0 + 5
= 5
b. lim(x→2) [3 h(x)]
Use multiplication property of limits.
= [lim(x→2) 3] [lim(x→2) h(x)]
= 3 lim(x→2) h(x)
= 3 (5)
= 15
c. lim(x→2) [g(x) h(x)]
Use multiplication property of limits.
= [lim(x→2) g(x)] [lim(x→2) h(x)]
= (0) (5)
= 0
Answer:
f(x) = -7x + 1
Step-by-step explanation:
Slope intercept form is
y = mx + b
m is slope
b is y-intercept
--------------------------
y decreases by 7 for each increase of 1 in x
slope = -7
to find "b" plug in one of the points and m = -7
using point (3, -20)
y = mx + b
-20 = -7(3) + b
-20 = -21 + b
b = 1
The equation is
f(x) = -7x + 1
Answer:
A circle which has the exact same radius no matter what direction you measure in
Step-by-step explanation:
Probably
