Determine the missing measures. 38, a=
1 answer:
Answer:
a = 6 units
Step-by-step explanation:
Given:
Let Labelled the diagram first
Δ ABC right angle at ∠ C = 90°
∠ B = 45 °
AB = c
BC = a
AC = 6
To Find:
a =?
c =?
Solution:
In Δ ABC
∠ A + ∠ B + ∠ C = 180°.....{Angle Sum Property of a Triangle}
∴ ∠ A + 45 + 90 = 180°
∴ ∠ A = 180 - 135
∴ ∠ A = 45°
Now ∠ A = ∠ B = 45° in Δ ABC
∴ Δ ABC is an Isosceles Triangle.
∴ Two sides are equal of an Isosceles Triangle.
∴ AC = BC = a = 6 units
Now for c we use Pythagoras theorem
Substituting the given values we get
c² = a² + 6²
c² = 6² + 6²
c² = 36 + 36
c² = 72
∴ c = ±√72
as c cannot be negative
∴
a = 6 units
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Explanation:
It is given that the coordinates of the graph are (0,200), (1,300) and (2, 450)
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From the graph, we can see that the line meets y = 200 when x = 0
Thus, the coordinates are (0,200)
Hence, the number of bacteria at time x is 0 when y = 200.
Option b: Now, we shall determine the exponential function of the population.
The general formula for exponential function is
Where a is the starting point and
b is the common difference.
To determine the common difference, let us divide,
Also,
Hence, the common difference is
Thus, substituting the values and
in the formula
,
we have,
Hence, An exponential function that represents the population is
Option c: To determine the population after 10 minutes, let us substitute in
, since the x represents the population of the bacteria in minutes.
Thus, we have,
Hence, the population after 10 minutes is 11534(app)