Answer:
k can either be
12
or
−
12
.
Step-by-step explanation:
Consider the equation
0=x2+4x+4
. We can solve this by factoring as a perfect square trinomial, so
0=(x+2)2→x=−2 and−2
. Hence, there will be two identical solutions.
The discriminant of the quadratic equation (b2−4ac) can be used to determine the number and the type of solutions. Since a quadratic equations roots are in fact its x intercepts, and a perfect square trinomial will have
2 equal, or 1
distinct solution, the vertex lies on the x axis. We can set the discriminant to 0 and solve:
k2−(4×1×36)=0
k2−144=0
(k+12)(k−12)=0
k=±12
Answer:
y = -3x + 6
Step-by-step explanation:
Slope-intercept form:
y = mx + b
m (slope) = 
or -3
b (y-intercept, or where the line crosses the y-axis) = 6
y = -3x + 6
If y = cos(kt), then its first two derivatives are
y' = -k sin(kt)
y'' = -k² cos(kt)
Substituting y and y'' into 49y'' = -16y gives
-49k² cos(kt) = -15 cos(kt)
⇒ 49k² = 15
⇒ k² = 15/49
⇒ k = ±√15/7
Note that both values of k give the same solution y = cos(√15/7 t) since cosine is even.
Answer: C 75
Step-by-step explanation: time to distance is ratio 4:5 = 60:X
In 1min He walks 5/4
in 60mins He walks 5/4 ×60
Answer:
625b^6
Step-by-step explanation:
= 5^3 * 5b^6
= 5^3 * 5
= 625
