Answer: Part A - C, Part B - 12 pieces
Step-by-step explanation:
<u>Part A:</u>
We know that 1/4 of Meredith's sub is bigger than 1/4 of Jim's sub, so we can set up an inequality.
Let Meredith's sub size = m; Jim's = j
Therefore, 1/4*m > 1/4*j
We can multiply both sides by 4:
m > j
Thus, the correct answer is C
<u>Part B:</u>
Since he had 1/4 of it left, that means he at 1 - 1/4 of it = 3/4 of his sub.
We can calculate the value of 3/4 * 16 = 12 pieces
In order to have infinitely many solutions with linear equations/functions, the two equations have to be the same;
In accordance, we can say:
(2p + 7q)x = 4x [1]
(p + 8q)y = 5y [2]
2q - p + 1 = 2 [3]
All we have to do is choose two equations and solve them simultaneously (The simplest ones for what I'm doing and hence the ones I'm going to use are [3] and [2]):
Rearrange in terms of p:
p + 8q = 5 [2]
p = 5 - 8q [2]
p + 2 = 2q + 1 [3]
p = 2q - 1 [3]
Now equate rearranged [2] and [3] and solve for q:
5 - 8q = 2q - 1
10q = 6
q = 6/10 = 3/5 = 0.6
Now, substitute q-value into rearranges equations [2] or [3] to get p:
p = 2(3/5) - 1
p = 6/5 - 1
p = 1/5 = 0.2
Answer:
2160 cm³/hour
Step-by-step explanation:
By default, we know that the volume of a cube is given as s³
Thus, the Volume function, V = s³
When we differentiate with respect to time we have
dV/dt = 3s² (ds/dt), where ds/dt = 0.2
Then we go ahead and substitute all the given parameters
dV/dt = 3 x 60 x 60 x 0.2
dV/dt = 10800 * 0.2
dV/dt = 2160 cm³/hour
This means that the volume decreases by a rate of 2160 cm³/hour at the instant its edge is 60 cm
