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Oksanka [162]
4 years ago
13

Bridget needs an actor. Actor A is offering her services for an initial $250 in addition

Mathematics
1 answer:
Neporo4naja [7]4 years ago
3 0
\textit{Actor A charges 250 plus 50 per day}
\\ \quad \\

\begin{array}{llll}
days&charge
\\---&---\\
1&50\cdot 1\\
2&50\cdot 2\\
3&50\cdot 3\\
4&50\cdot 4\\
d&50\cdot x\implies 50d
\end{array}\quad meaning\implies A=250+50d

\textit{Actor B charges 2500 plus 60 per day}
\\ \quad \\
\begin{array}{llll}
days&charge
\\---&---\\
1&60\cdot 1\\
2&60\cdot 2\\
3&60\cdot 3\\
4&60\cdot 4\\
d&60\cdot x\implies 60d
\end{array}\quad meaning\implies B=200+60d
\\ \quad \\
when\ is A=B?\qquad well
\\ \quad \\

250+50d\quad =\quad 200+60d\impliedby \textit{solve for days "d"}
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3 0
4 years ago
Find the nth term of the sequence 7,25,51,85,127​
olya-2409 [2.1K]

Let <em>a </em>(<em>n</em>) denote the <em>n</em>-th term of the given sequence.

Check the forward differences, and denote the <em>n</em>-th difference by <em>b </em>(<em>n</em>). That is,

<em>b </em>(<em>n</em>) = <em>a </em>(<em>n</em> + 1) - <em>a </em>(<em>n</em>)

These so-called first differences are

<em>b</em> (1) = <em>a</em> (2) - <em>a</em> (1) = 25 - 7 = 18

<em>b</em> (2) = <em>a</em> (3) - <em>a</em> (2) = 51 - 25 = 26

<em>b </em>(3) = <em>a</em> (4) - <em>a</em> (3) = 85 - 51 = 34

<em>b</em> (4) = <em>a </em>(5) - <em>a</em> (4) = 127 - 85 = 42

Now consider this sequence of differences,

18, 26, 34, 42, …

and notice that the difference between consecutive terms in this sequence <em>b</em> is 8:

26 - 18 = 8

34 - 26 = 8

42 - 34 = 8

and so on. This means <em>b</em> is an arithmetic sequence, and in particular follows the rule

<em>b</em> (<em>n</em>) = 18 + 8 (<em>n</em> - 1) = 8<em>n</em> + 10

for <em>n</em> ≥ 1.

So we have

<em>a </em>(<em>n</em> + 1) - <em>a </em>(<em>n</em>) = 8<em>n</em> + 10

or, replacing <em>n</em> + 1 with <em>n</em>,

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 8 (<em>n</em> - 1) + 10

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 8<em>n</em> + 2

We can solve for <em>a</em> (<em>n</em>) by iteratively substituting:

<em>a</em> (<em>n</em>) = [<em>a</em> (<em>n</em> - 2) + 8 (<em>n</em> - 1) + 2] + 8<em>n</em> + 2

<em>a</em> (<em>n</em>) = <em>a </em>(<em>n</em> - 2) + 8 (<em>n</em> + (<em>n</em> - 1)) + 2×2

<em>a</em> (<em>n</em>) = [<em>a</em> (<em>n</em> - 3) + 8 (<em>n</em> - 2) + 2] + 8 (<em>n</em> + (<em>n</em> - 1)) + 2×2

<em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 3) + 8 (<em>n</em> + (<em>n</em> - 1) + (<em>n</em> - 2)) + 3×2

and so on. The pattern should be clear; we end up with

<em>a</em> (<em>n</em>) = <em>a</em> (1) + 8 (<em>n</em> + (<em>n</em> - 1) + … + 3 + 2) + (<em>n</em> - 1)×2

The middle group is the sum,

\displaystyle 8\sum_{k=2}^nk=8\sum_{k=1}^nk-8=\frac{8n(n+1)}2-8=4n^2+4n-8

so that

<em>a</em> (<em>n</em>) = <em>a</em> (1) + (4<em>n</em> ² + 4<em>n</em> - 8) + 2 (<em>n</em> - 1)

<em>a</em> (<em>n</em>) = 4<em>n</em> ² + 6<em>n</em> - 3

4 0
4 years ago
Can some one please do this? thank you !
jenyasd209 [6]

Answer:

Step-by-step explanation:

6)a)

5\sqrt{27}=5\sqrt{3*3*3}\\\\ =5*3\sqrt{3}\\\\ =15\sqrt{3}

7a) y² - 5y - 14 =  y² -7y +2y - 2*7

                       = y*(y - 7) + 2*(y - 7)

                        =(y - 7)(y + 2)

b) Use FOIL method

(2\sqrt{5}+1)(3\sqrt{5}-1)=(2\sqrt{5}*3\sqrt{5})-((2\sqrt{5}*1)+1*3\sqrt{5})-1*1\\\\ =6*5-2\sqrt{5}+3\sqrt{5}-1\\\\  =30+(-2+3)\sqrt{5}-1\\ \\=29+\sqrt{5}

c) Rationalize the denominator by multiplying the denominator and numerator by √12

\frac{6}{\sqrt{12}}=\frac{6*\sqrt{12}}{\sqrt{12}*\sqrt{12}}\\\\=\frac{6\sqrt{2*2*3}}{12}\\\\=\frac{6*2\sqrt{3}}{12}\\\\=\frac{12\sqrt{3}}{12}\\\\=\sqrt{3}

8 0
3 years ago
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