Answer:
Step-by-step explanation:
An exponential function is of the form
where a is the initial value and b is the growth/decay rate. Our initial value is 64. That's easy to plug in. It goes in for a. So the first choice is out. Considering b now...
If the rate is decreasing at .5% per week, this means it still retains a rate of
100% - .5% = 99.5%
which is .995 in decimal form.
b is a rate of decay when it is greater than 0 but less than 1; b is a growth rate when it is greater than 1. .995 is less than 1 so it is a rate of decay. The exponential function is, in terms of t,
16 percent of 32 million is 5.12 million
7) Rectangular pyramid:
Length = 8m ; width = 4.6m ; Volume = 88m³
Volume of a rectangular pyramid = (Length * Width * Height)/3
88m³ = (8m * 4.6m * height)/3
88m³ * 3 = 36.8m² * height
264m³ = 36.8m² * height
264m³ / 36.8m² = height
7.2 m = height
8) Cone:
r = 5 in ; volume = 487 in³
Volume of a cone = π r² h/3
487 in³ = 3.14 * (5in)² * h/3
487 in³ * 3 = 3.14 * 25in² * h
1,461 in³ = 78.5 in² * h
1,461 in³ / 78.5 in² = height
18.6 in = height
The only way to have two numbers that are the same and add up to be 15
is if they're both 7.5 , but those don't multiply to be 36. So I guess there's
no answer that satisfies all the conditions of this question.
Answer:
2) 162°, 72°, 108°
3) 144°, 54°, 126°
Step-by-step explanation:
1) Multiply the equation by 2sin(θ) to get an equation that looks like ...
sin(θ) = <some numerical expression>
Use your knowledge of the sines of special angles to find two angles that have this sine value. (The attached table along with the relations discussed below will get you there.)
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2, 3) You need to review the meaning of "supplement".
It is true that ...
sin(θ) = sin(θ+360°),
but it is also true that ...
sin(θ) = sin(180°-θ) . . . . the supplement of the angle
This latter relation is the one applicable to this question.
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Similarly, it is true that ...
cos(θ) = -cos(θ+180°),
but it is also true that ...
cos(θ) = -cos(180°-θ) . . . . the supplement of the angle
As above, it is this latter relation that applies to problems 2 and 3.
