Consider the function graphed below.
1 answer:
Answer:
B. (see attached)
Step-by-step explanation:
All the answers agree that the function is x² for x < 1. Where they disagree is in the slope and y-intercept of the linear portion for x > 1.
The line has a slope that is less than 1 unit of rise for 1 unit of run, so will not be selections A or C, which have slopes of 3.
The y-intercept is clearly positive if we extend the line to the left until it reaches the y-axis. This eliminates selection D from consideration, leaving only selection B.
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#1) A
#2) E
#3) C
#4) 0.5840
#5) 0.6945
#6) 0.4911
#7) D
#8) G
#9) 0.4375
#10) 0.5203
The formula we use for this is
,
where
is the speed of sound, f is the frequency (or pitch) of the note, and λ is the wavelength.
#1) 0.77955f = 343
Divide both sides by 0.77955:
0.77955f/0.77955 = 343/0.77955
f = 439.997 ≈ 440. This is the pitch for A.
#2) 0.52028f = 343
Divide both sides by 0.52028, and we get f = 659.260. This is the pitch for E.
#3) 0.65552f = 343
Divide both sides by 0.65552, and we get f = 523.25. This is the pitch for C.
#4) 587.33λ = 343
Divide both sides by 587.33 and we get λ = 0.583999 ≈ 0.5840.
#5) 493.88λ = 343
Divide both sides by 493.88, and we get λ = 0.6945.
#6) 698.46λ = 343
Divide both sides by 698.46 and we get λ = 0.49108 ≈ 0.4911.
#7) 0.5840f = 343
Divide both sides by 0.5840 and we get f = 587.3288 ≈ 587.33. This is the pitch for D.
#8) 0.4375f = 343
Divide both sides by 0.4375 and we get f = 784. This is the pitch for G.
#9) 783.99λ = 343
Divide both sides by 783.99 and we get λ = 0.4375.
#10) 659.26λ = 343
Divide both sides by 659.26 and we get λ = 0.52028 ≈ 0.5203.
#2) E
#3) C
#4) 0.5840
#5) 0.6945
#6) 0.4911
#7) D
#8) G
#9) 0.4375
#10) 0.5203
The formula we use for this is
where
#1) 0.77955f = 343
Divide both sides by 0.77955:
0.77955f/0.77955 = 343/0.77955
f = 439.997 ≈ 440. This is the pitch for A.
#2) 0.52028f = 343
Divide both sides by 0.52028, and we get f = 659.260. This is the pitch for E.
#3) 0.65552f = 343
Divide both sides by 0.65552, and we get f = 523.25. This is the pitch for C.
#4) 587.33λ = 343
Divide both sides by 587.33 and we get λ = 0.583999 ≈ 0.5840.
#5) 493.88λ = 343
Divide both sides by 493.88, and we get λ = 0.6945.
#6) 698.46λ = 343
Divide both sides by 698.46 and we get λ = 0.49108 ≈ 0.4911.
#7) 0.5840f = 343
Divide both sides by 0.5840 and we get f = 587.3288 ≈ 587.33. This is the pitch for D.
#8) 0.4375f = 343
Divide both sides by 0.4375 and we get f = 784. This is the pitch for G.
#9) 783.99λ = 343
Divide both sides by 783.99 and we get λ = 0.4375.
#10) 659.26λ = 343
Divide both sides by 659.26 and we get λ = 0.52028 ≈ 0.5203.