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4 years ago

HELP PLEASE. Find x & y round answer to the nearest tenth!

Mathematics

1 answer:

trapecia [35]4 years ago

3 0

Answer:

y=18.2 x=5.6

Step-by-step explanation:

sin 73 = y/19

19 sin 73 = y

cos 73 = x/19

19 cos 73 = x

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The sum of the first n terms of a geometric series is 364? The sum of their reciprocals 364/243. If the first term is 1, find n

Afina-wow [57]

If the geometric series has first term $a$ and common ratio $r$ , then its $N$ -th partial sum is

$\displaystyle S_N = \sum_{n=1}^N ar^{n-1} = a + ar + ar^2 + \cdots + ar^{N-1}$

Multiply both sides by $r$ , then subtract $rS_N$ from $S_N$ to eliminate all the middle terms and solve for $S_N$ :

$rS_N = ar + ar^2 + ar^3 + \cdots + ar^N$

$\implies (1 - r) S_N = a - ar^N$

$\implies S_N = \dfrac{a(1-r^N)}{1-r}$

The $N$ -th partial sum for the series of reciprocal terms (denoted by $S'_N$ ) can be computed similarly:

$\displaystyle S'_N = \sum_{n=1}^N \frac1{ar^{N-1}} = \frac1a + \frac1{ar} + \frac1{ar^2} + \cdots + \frac1{ar^{N-1}}$

$\dfrac{S'_N}r = \dfrac1{ar} + \dfrac1{ar^2} + \dfrac1{ar^3} + \cdots + \dfrac1{ar^N}$

$\implies \left(1 - \dfrac1r\right) S'_N = \dfrac1a - \dfrac1{ar^N}$

$\implies S'_N = \dfrac{1 - \frac1{r^N}}{a\left(1 - \frac1r\right)} = \dfrac{r^N - 1}{a(r^N - r^{N-1})} = \dfrac{1 - r^N}{a r^{N-1} (1 - r)}$

We're given that $a=1$ , and the sum of the first $n$ terms of the series is

$S_n = \dfrac{1-r^n}{1-r} = 364$

and the sum of their reciprocals is

$S'_n = \dfrac{1 - r^n}{r^{n-1}(1 - r)} = \dfrac{364}{243}$

By substitution,

$\dfrac{1 - r^n}{r^{n-1}(1-r)} = \dfrac{364}{r^{n-1}} = \dfrac{364}{243} \implies r^{n-1} = 243$

Manipulating the $S_n$ equation gives

$\dfrac{1 - r^n}{1-r} = 364 \implies r (364 - r^{n-1}) = 363$

so that substituting again yields

$r (364 - 243) = 363 \implies 121r = 363 \implies \boxed{r=3}$

and it follows that

$r^{n-1} = 243 \implies 3^{n-1} = 3^5 \implies n-1 = 5 \implies \boxed{n=6}$

5 0

2 years ago

A store is selling 10 apples for 5.99 what is a cost of one apple?

OleMash [197]

Answer:

~$0.60

Step-by-step explanation:

Divide 10 with 5.99:

5.99/10 = 0.599

Round to the nearest hundredths.

0.599 rounded to the nearest hundredths = ~0.60

~$0.60 is the cost of one apple.

3 0

3 years ago

4(4-w)=3(2w+2)<br> 20 points

erastova [34]

Answer:

1. Rearrange terms

4(4−

7 0

3 years ago

Read 2 more answers

Gjkrjjfrnfjiejfjejjrn

JulijaS [17]

B is the answer. Because you have to turn the mixed numbers into improper fractions then subtract them. then convert it back into a mixed number

7 0

4 years ago

I’ll give brainliest

Dafna1 [17]

The answer is H, or x = 0.6.

8 0

2 years ago