Answer:
The particle changes its direction 2 times within the time -3<t<3
Step-by-step explanation:
The particle is moving only in a single dimension (x-axis), and whenever the particle changes its direction it also means that it's velocity while changing the direction will be zero.
Hence,
v(t) = 0
but since we're not concerned with the actual values of t when v(t)=0, we'll only consider how many times does the particle changes its direction.
for that we'll simply plot the curve using half-steps from -3 to 3.
t, v(t)
-3, 115
-2.5, 23.9375
-2, -16
-1.5, -25.0625
-1, -19
-0.5, -9.0625
0, -2
0.5, -0.0625
1, -1
1.5, 1.9375
2, 20
2.5, 68.9375
3, 169
What we need to check is at what points does the sign of v(t) values change (because only between those points will v(t) cross the x-axis, hence it's value would've crossed 0)
so there are two points!
between the intervals t = [-2.5,2] and [1,1.5]
so there are two points where the particle changes its directions and those points lie somewhere between these two aforementioned intervals.
Answer:
3x - 3 = 20
Step-by-step explanation:
Times is a word that represents multiplication. A number can be represented by x.
3x - 3 = 20
Solving this:
3x - 3 = 20 1. Add 3 on both sides
3x = 23 2. Divide by 3 on both sides
x = 7 2/3
Answer:
The company needs to sell either 30 or 40 items.
Step-by-step explanation:
We are given that the cost for selling <em>x</em> items given by the function:
And the revenue for selling <em>x</em> items is given by:
The profit function is the cost function subtracted from the revenue function:
Substitute and simplify:
To find how many items must be sold in order to obtain a weekly profit of $300, we can let <em>P</em> equal 300 and solve for <em>x</em>. So:
Solve for <em>x</em>. Subtract 300 from both sides:
We can divide both sides by -0.4:
Factor:
Zero Product Property:
Solve for each case:
So, in order to obtain a weekly profit of $300, the company need to sell either 30 <em>or</em> 40 items.
