If the length, height, and width of the volume are L, W, and H, respectively. Then the volume would be equal to V = L(W)(H) = LWH.
Given that the length and width have tripled, then the new length and width of the prism would be 3L and 3H. Thus, the volume of the new prism is V = (3L)(3H)(W) = 9LWH.
Comparing this to the original volume, we can clearly see that the volume has increased 9 times after the changes.
Answer: Volume becomes 9 times larger.
Answer:
0.2036
Step-by-step explanation:
u = arcsin(0.391) ≈ 23.016737°
tan(u/2) = tan(11.508368°)
tan(u/2) ≈ 0.2036
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You can also use the trig identity ...
tan(α/2) = sin(α)/(1+cos(α))
and you can find cos(u) as cos(arcsin(0.391)) ≈ 0.920391
or using the trig identity ...
cos(α) = √(1 -sin²(α)) = √(1 -.152881) = √.847119
Then ...
tan(u/2) = 0.391/(1 +√0.847119)
tan(u/2) ≈ 0.2036
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<em>Comment on the solution</em>
These problems are probably intended to have you think about and use the trig half-angle and double-angle formulas. Since you need a calculator anyway for the roots and the division, it makes a certain amount of sense to use it for inverse trig functions. Finding the angle and the appropriate function of it is a lot easier than messing with trig identities, IMO.
Answer:
c.
Step-by-step explanation:
Answer: 11 year
P(1) = 37,100
P(4) = 58,400
The linear equation (for x ≥ 1)
P(x) = 37,100 + a(x-1)
For x = 4
58,400 = 37,100 + a(4-1)
58,400 - 37,100 = 3a
21300 = 3a
a = 7100
So, the linear equation:
P(x) = 37100 + 7100*(x-1)
P(x) = 37100 + 7100x - 7,100
P(x) = 7100x + 30000
To find when the profit should reach 108100, we can substitute P(x) by 108100.
108100 = 7100x + 30000
108100 - 30000 = 7100x
78100 = 7100x
x = 78100/7100
x = 11
Answer: 11 year
