Step-by-step explanation:
From the statement:
M: is total to be memorized
A(t): the amount memorized.
The key issue is translate this statement as equation "rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized"
memorizing rate is
.
the amount that is left to be memorized can be expressed as the total minus the amount memorized, that is
.
So we can write

And that would be the differential equation for A(t).
Divide each by 100. You get the ratio
765 : 1000
Now divide by 5
153 : 200
You can use this or
0.765 : 1
9514 1404 393
Explanation:
<u>Given</u>:
- The attached figure showing circle O, chord BC, central angle BOC and inscribed angle BAC
- angle BAC = α + β
<u>Prove</u>:
<u>Proof</u>:
∠BOA +∠BOC +∠AOC = 360° . . . . . sum of arcs of a circle is 360°
2α +∠BOA = 180°, 2β +∠AOC = 180° . . . . . sum of triangle angles is 180°
∠BOA = 180° -2α, ∠AOC = 180° -2β . . . . solve statement 2 for central angles
(180° -2α) +∠BOC +(180° -2β) = 360° . . . . . substitute into statement 1
∠BOC = 2(α +β) . . . . . add 2α+2β-360° to both sides
∠BOC = 2×∠BAC . . . . . substitute given for α+β; the desired conclusion
We are given a data set and we are asked to write the model that fits the data. We notice that for each step of "x" the values of "y" increase by the same amount. That means that the data follow a linear model, therefore, we will use:

Where:

To determine the slope "m" we will use the following formula:

Where:

Are data points. From the table we choose the following points:

Now, we substitute in the equation for the slope:

Solving the operations:

Therefore, the slope is -7. Substituting in the equation of the line we get:

Now, we substitute one of the points to get the value of "b". We will substitute the value x = -8, y = 47, we get:

Solving the product:

Now we subtract 56 from both sides:

Now, we substitute the value of "b" in the equation of the line:

And thus we get the line equation.
Both of them are 32. 96/3 is simplified 2 equal 32/1 which is 32 and 160/5 also equals 32/1 which is also 32.