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Nataly [62]
3 years ago
11

A rectangle has a length that is 8 less than its width, w. The perimeter is 52. Which equation can be used to determine its widt

h?
Mathematics
1 answer:
ankoles [38]3 years ago
8 0
52= 2(w-8) + 2x
X is the unknown length because the question is only telling us one side of the rectangle
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algol13
When you see questions of this nature, test the individual inequalities and look out for their intersection.

For
y < \frac{2}{3} x
Choose a point in the lower or upper half plane created by the line
y = \frac{2}{3} x
The above line is the one which goes through the origin.

Now testing (1,0) yields,

0 < \frac{2}{3} (1)
That is,

0 < \frac{2}{3}
This statement is true. So we shade the lower half of
y = \frac{2}{3} x

For
y \geqslant - x + 2
We test for the origin because, it is not passing through the origin.

0 \geqslant - (0) + 2
This yields
0 \geqslant 2
This statement is false so we shade the upper half.

The intersection is the region shaded in B. The top right graph
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Step-by-step explanation:

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Suppose that a large mixing tank initially holds 100 gallons of water in which 50 pounds of salt have been dissolved. Another br
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Answer:

dA/dt = 12 - 2A/(100 + t)

Step-by-step explanation:

The differential equation of this problem is;

dA/dt = R_in - R_out

Where;

R_in is the rate at which salt enters

R_out is the rate at which salt exits

R_in = (concentration of salt in inflow) × (input rate of brine)

We are given;

Concentration of salt in inflow = 4 lb/gal

Input rate of brine = 3 gal/min

Thus;

R_in = 4 × 3 = 12 lb/min

Due to the fact that solution is pumped out at a slower rate, thus it is accumulating at the rate of (3 - 2)gal/min = 1 gal/min

So, after t minutes, there will be (100 + t) gallons in the tank

Therefore;

R_out = (concentration of salt in outflow) × (output rate of brine)

R_out = [A(t)/(100 + t)]lb/gal × 2 gal/min

R_out = 2A(t)/(100 + t) lb/min

So, we substitute the values of R_in and R_out into the Differential equation to get;

dA/dt = 12 - 2A(t)/(100 + t)

Since we are to use A foe A(t), thus the Differential equation is now;

dA/dt = 12 - 2A/(100 + t)

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