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Sliva [168]
2 years ago
14

Can a math god help me out?

Mathematics
1 answer:
Taya2010 [7]2 years ago
3 0

Answer:

f(1)=70

f(n)=f(n-1)+6

Step-by-step explanation:

One is given the following function:

f(n)=64+6n

One is asked to evaluate the function for (f(1)), substitute (1) in place of (n), and simplify to evaluate:

f(1)=64+6(1)

f(1)=64+6

f(1)=70

A recursive formula is another method used to represent the formula of a sequence such that each term is expressed as a function of the last term in the sequence. In this case, one is asked to find the recursive formula of an arithmetic sequence: that is, a sequence of numbers where the difference between any two consecutive terms is constant. The following general formula is used to represent the recursive formula of an arithmetic sequence:

a_n=a_(_n_-_1_)+d

Where (a_n) is the evaluator term (a_(_n_-_1_)) represents the term before the evaluator term, and (d) represents the common difference (the result attained from subtracting two consecutive terms). In this case (and in the case for most arithmetic sequences), the common difference can be found in the standard formula of the function. It is the coefficient of the variable (n) or the input variable. Substitute this into the recursive formula, then rewrite the recursive formula such that it suits the needs of the given problem,

a_n=a_(_n_-_1_)+d

a_n=a_(_n_-_1_)+6

f(n)=f(n-1)+6

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b = 55

d = 55

Step-by-step explanation:

Part B:

1. We can see that m∠C (25 degrees), the angle with 100 degrees, and ∠B are adjacent angles that add up to 180 degrees.

  • This means that b + 25 + 100 = 180

2. (Solving equation above)

Step 1: Simplify both sides of the equation.

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Therefore, b = 55.

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5 0
2 years ago
A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks along the x-axis from the spotlight toward the bui
Sedbober [7]

Answer:

0.675 m/s

Step-by-step explanation:

Let height of shadow= y,CD=x

Height of man=2 m

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x\frac{dy}{dt}+y\frac{dx}{dt}=0

x\frac{dy}{dt}=-y\frac{dx}{dt}

\frac{dy}{dt}=-\frac{y}{x}\frac{dx}{dt}

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Substitute the values in above equation then, we get

8y=24

y=\frac{24}{8}=3

Substitute the values then we get

\frac{dy}{dt}=-\frac{3}{8}\times 1.8=-0.675 m/s

Hence, the length of his shadow on the building decreasing at the rate 0.675 m/s.

8 0
3 years ago
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