What's the mean of 35, 16, 23, 42 90
1 answer:
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Answer:
A) The expression for the number of bacteria is .
B) After 5 hours there will be 19593 bacteria.
C) After 5.55 hours the population of bacteria will reach 30000.
Step-by-step explanation:
A) Here we have a problem with differential equations. Recall that we can interpret the rate of change of a magnitude as its derivative. So, as the rate change proportionally to the size of the population, we have
where stands for the population of bacteria.
Writing as
, we get
.
Notice that this is a separable equation, so
.
Then, integrating in both sides of the equality:
.
We have,
.
Now, taking exponential
.
The next step is to find the value for the constant . We do this using the initial condition
. Recall that this is the initial population of bacteria. So,
.
Hence, the expression becomes
.
Now, we find the value for . We are going to use that
. Notice that
.
Then,
.
Taking logarithm
, so
.
So, , and approximating to the fourth decimal place we can take
. Hence,
.
B) To find the number of bacteria after 5 hours, we only need to evaluate the expression we have obtained in the previous exercise:
.
C) In this case we want to do the reverse operation: we want to find the value of t such that
.
This expression is equivalent to
.
Now, taking logarithm we have
.
Finally,
.
So, after 5.55 hours the population of bacteria will reach 30000.
Answer:
The area of the parallelogram is;
32 square units
Step-by-step explanation:
The given parameters are;
The coordinates of the parallelogram RSTU = R(-4, 4), S(2, 6), T(6, 2), and U(0, 0)
We note that the area of a parallelogram = Base length × Height
From the drawing of the parallelogram RSTU, we have;
The base length = The length of = The length of
= √((2 - (-4))² + (6 - 4)²) = 2·√10
The height of a parallelogram is perpendicular to its base length = The line
∴ Where, the slope of the base length = m, the slope of the height = -1/m
The slope, 'm' of = (6 - 4)/(2 - (-4)) = 1/3
Therefore, the slope of the height = -1/(1/3) = -3
We note that a point on the height is the point 'T', therefore, the equation of the line in point and slope form is therefore;
y - 0 = -3·(x - 0)
∴ y = -3·x
Therefore, the coordinates of the point 'V' is given by the simultaneous solution of the equations of and
The equation of the line in point and slope form from the point 'R' and the slope 'm = 1/3' is given as follows;
y - 4 = (1/3) × (x - (-4)) = (1/3) × (x + 4)
y = x/3 + 4/3 + 4 = x/3 + 16/3
y = x/3 + 16/3
We then have the coordinate at the point 'V' (x, y) is given as follows;
-3·x = x/3 + 16/3
-9·x = x + 16
-10·x = 16
x = -16/10 = -1.6
x = -1.6
∴ y = -3·x = -3 × -1.6 = -4.8
y = 4.8
The coordinate at the point, V = (-1.6, 4.8)
The length of the line = The height of the parallelogram = √((-1.6 - 0)² + (4.8 - 0)²) = 8/5·√10
The height of the parallelogram = 8/5·√10
The area of the parallelogram, A = Base length × Height
∴ A = 2·√(10) × 8/5·√(10) = (16/5) × 10 = 32
The area of the parallelogram, A = 32 square units.
