rainboworld3994
11.03.2020 •
Mathematics
Which exponential functions represent exponential decay?
Select all that apply.
f(x)=0.25(1.5)3x
f(x)=(0.85)x
f(x)=(1.01)x
f(x)=1.8(0.6)x
f(x)=(0.95)2x-*
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Ответ:
The function representing exponential decay are:
b)
d)
e)
Step-by-step explanation:
The exponential function is given as:
where , , and .
If and then the function represents exponential decay.
If and then the function represents exponential growth.
Thus, we can check each function given.
a)
For the given function and . So, it represents exponential growth.
b)
For the given function and . So, it represents exponential decay.
c)
For the given function and . So, it represents exponential growth.
d)
For the given function and . . So, it represents exponential decay.
e)
For the given function and . . So, it represents exponential decay.
Ответ:
∠ABC = 76°
BC = 20.1
CA = 28.0
Step-by-step explanation:Solving the triangle means finding all unknown angles and sides of the triangle.
(i) Two of the angles (∠BCA = 60° and ∠CAB = 44°) are given. To find the third angle (∠ABC), use one of the theorems stating that the sum of angles of a triangle is equal to 180°.
Therefore, the sum of angles of the triangle ABC is 180°. i.e
∠ABC + ∠BCA + ∠CAB = 180°
=> ∠ABC + 60° + 44° = 180°
=> ∠ABC + 104° = 180°
=> ∠ABC = 180° - 104°
=> ∠ABC = 76°
(ii) One side (BA) of the triangle is given. To get the other sides, we use the sine rule as follows;
=>
=>
Substitute the necessary values
---------------------(ii)
(a) To get side BC, use the first two terms of equation (ii)
Cross multiply
BC x sin 60 = 25 x sin 44
BC x 0.8660 = 25 x 0.6947
0.8660 x BC = 17.3675
BC =
BC = 20.05
=> BC = 20.1 to the nearest tenth
(b) To get CA, use any two terms of equation (ii). Using the first and third terms, we have;
Cross multiply
CA x sin 60 = 25 x sin 76
CA x 0.8660 = 25 x 0.9703
0.8660 x CA = 24.2575
CA =
CA = 28.01
=> CA = 28.0 to the nearest tenth