Answer:
A(t) = 300 -260e^(-t/50)
Step-by-step explanation:
The rate of change of A(t) is ...
A'(t) = 6 -6/300·A(t)
Rewriting, we have ...
A'(t) +(1/50)A(t) = 6
This has solution ...
A(t) = p + qe^-(t/50)
We need to find the values of p and q. Using the differential equation, we ahve ...
A'(t) = -q/50e^-(t/50) = 6 - (p +qe^-(t/50))/50
0 = 6 -p/50
p = 300
From the initial condition, ...
A(0) = 300 +q = 40
q = -260
So, the complete solution is ...
A(t) = 300 -260e^(-t/50)
___
The salt in the tank increases in exponentially decaying fashion from 40 grams to 300 grams with a time constant of 50 minutes.
If a 12 oz bottle of shampoo lasted for 16 weeks, we have a ratio of 12:16 which can be shortened to 3:4.
Now if we have 18 oz bottle we know that it's 1/2 more than 12 oz bottle, so the ratio will be also 1/2 more. So if it was 12:16, the new ratio will be:
12 + (1/2 * 12) : 16 + (1/2 * 16)
12 + 6 : 16 + 8
18 : 24
It means that 18 oz bottle should last for 24 weeks. Of course the ratio has to stay the same in its lowest form in both situations and as 18:24 can be shortened to 3:4, it proves it's correct :)
Answer:
the answer is c
Step-by-step explanation:
Becuase he is given 100 dollars and he uses 20 dollars a day, so you put x with 20 to calculate how many days that he can spend $20 on
<u><em>Answer:</em></u>
y + 2 = 1 (x+3) ............> y + 2 = x + 3
<u><em>Explanation:</em></u>
<u>The general form of the equation of a line in point-slope form is:</u>
y - y₁ = m (x - x₁)
<u>where:</u>
m is the slope of the line
(x₁ , y₁) is a point that belongs to the line
<u>The general form of the equation of a line in slope-intercept form is:</u>
y = mx + c
<u>where:</u>
m is the slope
c is the y-intercept
<u>1- Getting the point:</u>
We are already given the point (-3 , -2) so we'll directly use it
<u>2- Getting the slope</u>
<u>We are given that our line is parallel to the line:</u>
y = 1x - 7
We know that parallel lines have equal slopes
<u>This means that:</u>
slope of the line we want = 1
<u>3- Getting the equation:</u>
Substitute with the point and slope in the above form to get the equation
<u>This is done as follows:</u>
y - y₁ = m (x - x₁)
y - (-2) = 1 (x - (-3))
y + 2 = 1 (x + 3)
y + 2 = x + 3
Hope this helps :)
Answer:
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