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RideAnS [48]
2 years ago
12

a theater has 49 seats in the first row, 52 seats in the second row, 55 seats in the third row, and so on. how many seats are th

ere in row 20
Mathematics
1 answer:
Dominik [7]2 years ago
7 0

Answer:

106

Step-by-step explanation:

this question represents an arithmetic sequence problem where you can use this formula: a(n) = a(1) + d(n-1)  where 'n' is value you're solving for, a(1) is the initial value, and 'd' is the common difference

a(20) = 49 + 3(20-1)

= 49 + 3(19)

= 49 + 57

= 106

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Question 4: What is the solution of the system? *<br> .A<br> .B<br> .C<br> .D
DedPeter [7]

Answer:

C

Step-by-step explanation:

x+4y=-12

x+7y=-15

subtract

-3y=3

y=-1

x+4(-1)=-12

x=-12+4=-8

so point is (-8,-1)

4 0
2 years ago
Find the Fourier series of f on the given interval. f(x) = 1, ?7 &lt; x &lt; 0 1 + x, 0 ? x &lt; 7
Zolol [24]
f(x)=\begin{cases}1&\text{for }-7

The Fourier series expansion of f(x) is given by

\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi x}7+\sum_{n\ge1}b_n\sin\frac{n\pi x}7

where we have

a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx
a_0=\displaystyle\frac17\left(\int_{-7}^0\mathrm dx+\int_0^7(1+x)\,\mathrm dx\right)
a_0=\dfrac{7+\frac{63}2}7=\dfrac{11}2

The coefficients of the cosine series are

a_n=\displaystyle\frac17\int_{-7}^7f(x)\cos\dfrac{n\pi x}7\,\mathrm dx
a_n=\displaystyle\frac17\left(\int_{-7}^0\cos\frac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\cos\frac{n\pi x}7\,\mathrm dx\right)
a_n=\dfrac{9\sin n\pi}{n\pi}+\dfrac{7\cos n\pi-7}{n^2\pi^2}
a_n=\dfrac{7(-1)^n-7}{n^2\pi^2}

When n is even, the numerator vanishes, so we consider odd n, i.e. n=2k-1 for k\in\mathbb N, leaving us with

a_n=a_{2k-1}=\dfrac{7(-1)-7}{(2k-1)^2\pi^2}=-\dfrac{14}{(2k-1)^2\pi^2}

Meanwhile, the coefficients of the sine series are given by

b_n=\displaystyle\frac17\int_{-7}^7f(x)\sin\dfrac{n\pi x}7\,\mathrm dx
b_n=\displaystyle\frac17\left(\int_{-7}^0\sin\dfrac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\sin\dfrac{n\pi x}7\,\mathrm dx\right)
b_n=-\dfrac{7\cos n\pi}{n\pi}+\dfrac{7\sin n\pi}{n^2\pi^2}
b_n=\dfrac{7(-1)^{n+1}}{n\pi}

So the Fourier series expansion for f(x) is

f(x)\sim\dfrac{11}4-\dfrac{14}{\pi^2}\displaystyle\sum_{n\ge1}\frac1{(2n-1)^2}\cos\frac{(2n-1)\pi x}7+\frac7\pi\sum_{n\ge1}\frac{(-1)^{n+1}}n\sin\frac{n\pi x}7
3 0
2 years ago
Find 4ab when (a+b)=15 and (a-b)=12
Volgvan
A + b = 15 ..... eq 1
a – b = 12 ...... eq 2

So a = 15 – b
Substitute in eq 2 :

15 – b – b = 12
15 – 2b = 12
–2b = 12 – 15
b = 1.5

So a = 15 – 3/2 = 13.5

4ab = 4 x 13.5 x 1.5 = 81
4 0
3 years ago
Read 2 more answers
What is 98,464 rounded to the nearest ten thousands ?
sleet_krkn [62]
100,000
because the 8 makes the 9 round up into a 10
6 0
3 years ago
Zoe shows her work in finding the solution to 9 – 7x = 7 – 4(2x 3). which choice describes the error in her solution?
FinnZ [79.3K]
I'll assume the above equation is: 9 - 7x = 7 - 4(2x+3)

* do distributive multiplication
9 - 7x = 7 - 8x - 12

*move like terms
-7x + 8x = 7 - 12 - 9

* solve for x
x = 7 - 21
x = -14

To check, substitute x by its value -14

9 - 7x = 7 - 4(2x+3)
9 - 7(-14) = 7 -4[2(-14) + 3]
9 + 98 = 7 - 4(-28 +3)
107  = 7 - 4(-25)
107 = 7 + 100
107 = 107
5 0
3 years ago
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