(a) Given the position function
x(t) = (B m/s²) t² + 5 m
it's clear that the object accelerates at B m/s² (differentiate x(t) twice with respect to t), so that the force exerted on the object is
F(t) = (2 kg) (B m/s²) = 2B N
(b) Recall the work-energy theorem: the total work performed on an object is equal to the change in the object's kinetic energy. The object is displaced by
∆x = x(5 s) - x(0 s)
∆x = ((B m/s²) (5 s)² + 5 m) - ((B m/s²) (0 s)² + 5 m)
∆x = 25B m
Then the work W performed by F (provided there are no other forces acting in the direction of the object's motion) is
W = (2B N) (25B m) = 50B² J = 200 J
Solve for B :
50B² = 200
B² = 4
B = ± √4 = ± 2
Since the change in kinetic energy and hence work performed by F is positive, the sign of B must also be positive, so B = 2 and the object accelerates at 2 m/s².
(c) We found in part (b) that the object is displaced 25B m, and with B = 2 that comes out to ∆x = 50 m.
We are given : -3(4-6x) < x+5.
Solution: -3 is in front of Parenthesis.
We need to multiply -3 by (4-6x).
So, we need to applying distributive property.
On distributing, we get
-12+18x < x+5 (By distributive property)
The reverse operation of addition is subtraction. So we need to subtract x from both sides, we get
-12+18x-x < x-x+5 (By subtraction property of equality).
-12+17x < 5
Now, we need to get rid -12 from left side.
So, we need to apply addition property of equality, we need to add 12 on both sides, we get
-12+12+18x < x+5+12 (By addition property of equality)
17x < 17
We need to get rid 17 from left side. So we need to apply division property of equality.
On dividing both sides by 17, we get
17x/17 < 17/17 (By division property of equality)
x < 1.
Answer: The answer is 51 degrees
Step-by-step explanation:
<span>
f(x)=2^(x-2) = 2^(-4) = 1/2^4 = 1/16
answer
</span><span>A.
f(x)=2^(x-2)</span>
