I think the first one is
x<3
And the second one is
x<2
Answer: IX - 4I ≤ 4
Step-by-step explanation:
In the numer line we can see that our possible values of x are in the range:
0 ≤ x ≤ 8
And we want to find an absolute value equation such that this set is the set of possible solutions.
An example can be:
IX - 4I ≤ 4
To construct this, we first find the midpoint M of our set, in this case is 4.
Then we write:
Ix - MI ≤ IMI
Notice that i am using the minor and equal sign, this is because the black dots means that the values x = 0 and x = 8 are included, if the dots were empty dots, it would be an open set and we should use the < > signs.
Answer:
Total volume of all the bins = xS + yL
Step-by-step explanation:
Given: x cubic inches represent the volume of the smaller bin and y cubic inches represents the volume of the larger bin. The store has S smaller bins and L larger bins.
To find: an expression that represents the total volume of all the bins
Solution:
The volume of the smaller bin = x cubic inches
The volume of the larger bin = y cubic inches
Also, the store has S smaller bins and L larger bins
So,
Total volume of all the bins = xS + yL
As usual, draw a diagram. You can easily see that if you are x away from the wall,
<span>the angle of elevation of the bottom of the screen (A) is </span>
<span>cotA = x/3 </span>
<span>A = arccot(x/3) </span>
<span>angle B to the top is </span>
<span>cotB = x/10 </span>
<span>B = arccot(x/10) </span>
<span>So, since θ = B-A </span>
<span>dθ/dt = dB/dt - dA/dt </span>
<span>= -3/(x^2+9) + 10/(x^2+100) </span>
<span>= 7(x^2-30)/((x^2+9)(x^2+100)) </span>
<span>so, at x=30 </span>
<span>dθ/dt = 203/30300</span>
