The scale of a model train is 1 inch to 13.5 feet. One of the cars of the model train is 5 inches long. What is the length, in f
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The figure that this question is referring to is attached. We must use the Law of Sines to solve this question, which is as follows:
a/sinA = b/sinB = c/sinC
This applies to any triangle. We are told that ∠ABD = 120º. We are asked to solve for ∠ADC. We know that ∠ADC + ∠ADB = 180º. If we assign ∠ADC = x, then ∠ADB = 180<span>º - x. We can now apply the law of sines to this data.
35/sin120 = 30/sin(180-x)
sin(180-x) = (30/35)(sin120)
sin(180-x) = 0.742
sin-1(sin(180-x)) = sin-1(0.742)
180 - x = 48</span><span>º
x = 132</span><span>º
</span>
We have already assigned x = ∠ADC; therefore, ∠ADC = 132<span>º.</span>
a/sinA = b/sinB = c/sinC
This applies to any triangle. We are told that ∠ABD = 120º. We are asked to solve for ∠ADC. We know that ∠ADC + ∠ADB = 180º. If we assign ∠ADC = x, then ∠ADB = 180<span>º - x. We can now apply the law of sines to this data.
35/sin120 = 30/sin(180-x)
sin(180-x) = (30/35)(sin120)
sin(180-x) = 0.742
sin-1(sin(180-x)) = sin-1(0.742)
180 - x = 48</span><span>º
x = 132</span><span>º
</span>
We have already assigned x = ∠ADC; therefore, ∠ADC = 132<span>º.</span>
2 normal types of sequences:
1. arythmetic sequences: each term is the same distance to the next term, example, 2,4,6,8, distance is 2
2. geometric sequences: the ratio of consecutive terms is the same, example: 2,4,8,16, ratio is 4:2=2:1, 2/1=2
the nth term is denoted by
the first term is represented by
for arythmetic sequences, the nth tem is
where d=distance between each term
for geometric sequences the nth term is
[tex] a_{n}=a_{1}r^{n-1} where r=ratio betwen consecutive terms
1. arythmetic sequences: each term is the same distance to the next term, example, 2,4,6,8, distance is 2
2. geometric sequences: the ratio of consecutive terms is the same, example: 2,4,8,16, ratio is 4:2=2:1, 2/1=2
the nth term is denoted by
the first term is represented by
for arythmetic sequences, the nth tem is
for geometric sequences the nth term is
[tex] a_{n}=a_{1}r^{n-1} where r=ratio betwen consecutive terms