Answer:
First, we must calculate the slope
m=Y2-Y1/X2-X1
= 9 - (-6) / 12 - (-8)
= 15/20
= 3/4
Therefore, the equation with the slope of 3/4 is Y=3/4x
To determine the rates at which the inlet and outlet pipes fill and empty the reservoir, we remember that work done equals rate multiplied by time. Let’s denote the inlet rate as i and for the outlet pipe as 0. Therefore,
i(24) = 1
o(28) = 1
In this context, the '1' represents the total number of reservoirs, since the problem states the time needed for each pipe to either fill or empty a singular reservoir. Solving for rates yields:
i = 1/24 reservoirs/hour
o = 1/28 reservoirs/hour
Over the first six hours, the inlet pipe fills (1/24)(6) = 1/4 reservoirs and during the same period, the outlet pipe empties (1/28)(6) = 3/14 reservoirs. To calculate the net volume of the reservoir filled, we subtract the emptying total from the filling total:
1/4 - 3/14 = 1/28 reservoirs (note that if emptying exceeds filling, a negative value results. In such cases, treat that negative value as zero, indicating that the outlet rate surpasses the inlet rate, leading to an empty reservoir).
Now we need to find out how long it will take to fill up one reservoir since we’ve already partially filled 1/28 of it, after closing the outlet pipe. In simpler terms, we need to determine the time required for the inlet pipe to finish filling the remaining 27/28 of the reservoir. Fortunately, we have already established the filling rate for the inlet pipe, leading to the equation:
(1/24)t = 27/28
Solving for t gives us 23.14 hours. Remember to add the initial 6 hours to this result since the question seeks the total time. Thus, the final total is 29.14 hours.
Please ask me any questions you may have!
Avoid repeating the question as it can be perplexing.
Given 100 cookies and 20 brownies,
What is the highest number you can divide them equally by?
To find the greatest common factor,
Factor them:
100 = 2*2*5*5
20 = 2*2*5
Thus, the greatest common factor, which is shared between them, is 2*2*5 or 20.
Calculating further, 100/20=5
20/20=1
This means there are 20 groups, each containing 5 cookies and 1 brownie.
20 groups
The salt enters at a rate of (5 g/L)*(3 L/min) = 15 g/min.
The salt exits at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.
Thus, the total rate of salt flow, represented by 
in grams, is defined by the differential equation,
which is linear. Shift the 
term to the right side, then multiply both sides by 
:
Next, integrate both sides and solve for :
Initially, the tank contains 5 g of salt at time 
, so we have
The duration required for the tank to contain 20 g of salt is 
, such that
Answer:
A. △ABC ~ △DEC
B. ∠B ≅ ∠E
D. 3DE = 2AB
Step-by-step explanation:
Transformation includes modifying the shape or size of a figure, using techniques such as reflection, dilation, rotation, and translation.
In this scenario, triangle ABC undergoes reflection and dilation to create triangle DEC. Each side of triangle DEC measures two-thirds the length of its corresponding side in triangle ABC. Thus, the following statements about the triangles are true:
i. △ABC ~ △DEC
ii. ∠B ≅ ∠E
iii. 3DE = 2AB
