Answer:
Step-by-step explanation:
Question 1: Assumption: This is a 30-60-90 triangle.
Remember that the sides of a 30-60-90 triangle are in the ratio 1:√3:2
The side opposite the 90° angle is 16, so the side opposite the 30° angle is 16/2 = 8
x = 8 units.
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Question 2: Assumption: This is an isosceles triangle.
Draw the altitude to the vertex angle and you get a 30-60-90 triangle.
The side opposite the 90° angle has length 22, so the side opposite the 30° angle has length 11.
x/2 = 11
x = 22 units
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Question 3: Assumption: This is a 45-45-90 triangle.
The sides of a 45-45-90 triangle are in the ratio 1:1:√2
The sides opposite the 45° angles are 19 and x.
x = 19
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Question 4: Assumption: This is an isosceles triangle.
x = 13 units
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Question 5: Assumption: This is a right triangle.
sin(54°) = x/45
x = 45sin(54°) ≅ 36.4 units
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Question 6: Assumption: This is a right triangle.
sin(35°) = z/23
z = 23sin(35°) ≅ 13.2 units
Differentiating the function
... g(x) = 5^(1+x)
we get
... g'(x) = ln(5)·5^(1+x)
Then the linear approximation near x=0 is
... y = g'(0)(x - 0) + g(0)
... y = 5·ln(5)·x + 5
With numbers filled in, this is
... y ≈ 8.047x + 5 . . . . . linear approximation to g(x)
Using this to find approximate values for 5^0.95 and 5^1.1, we can fill in x=-0.05 and x=0.1 to get
... 5^0.95 ≈ 8.047·(-0.05) +5 ≈ 4.598 . . . . approximation to 5^0.95
... 5^1.1 ≈ 8.047·0.1 +5 ≈ 5.805 . . . . approximation to 5^1.1
Answer:
Step-by-step explanation:
Answer:
0,1,-1
Step-by-step explanation:
A.
B