This is an arithmetic sequence because each term is 7 greater than the previous term, so 7 is what is called the common difference...
Any arithmetic sequence can be expressed as:
a(n)=a+d(n-1), a=first term, d=common difference, n=term number.
We know a=1 and d=7 so:
a(n)=1+7(n-1)
a(n)=1+7n-7
a(n)=7n-6
The above is the "rule" for the nth term.
<h3>
Answer: ds/dt = 11</h3>
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Work Shown:
Before we can use derivatives, we need to find the value of s when (x,y) = (15,20)
s^2 = x^2+y^2
s^2 = 15^2+20^2
s^2 = 225+400
s^2 = 625
s = sqrt(625)
s = 25
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Now we can apply the derivative to both sides to get the following. Don't forget to use the chain rule.
s^2 = x^2 + y^2
d/dt[s^2] = d/dt[x^2 + y^2]
d/dt[s^2] = d/dt[x^2] + d/dt[y^2]
2s*ds/dt = 2x*dx/dt + 2y*dy/dt
2(25)*ds/dt = 2(15)*5 + 2(20)*(10)
50*ds/dt = 150 + 400
50*ds/dt = 550
ds/dt = 550/50
ds/dt = 11
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Side note: The information t = 40 is never used. It's just extra info.
Answer:
24
Step-by-step explanation:
subtract 90-66
Answer:
35000
Step-by-step explanation:
