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stellarik [79]
3 years ago
11

How to write distributive property for 7x420

Mathematics
1 answer:
Ugo [173]3 years ago
8 0
<span>7x420
= 7( 400 + 20)
=2800 + 140
=2940

</span>
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Find the value of c that makes each trinomial a perfect square. Then write the trinomial as a perfect square.
musickatia [10]

Answer:

d. c = 100; (x – 10)²

Step-by-step explanation:

Note that (x+a)²=x²+2ax+a².

In our case, 2a=-20, so 'a' must be -10.

Since c=a², and a=-10, c=(-10²)=100.

Since a=-10, the perfect square is (x – 10)²

3 0
3 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
3 years ago
David works at Mc Donald’s, and he made 96.75 for 10 hours of work how much does David earn per hour
Digiron [165]
9.675

Move the decimal back one spot


Mark brainliest please
7 0
2 years ago
Read 2 more answers
Franklin is cutting a 7 1/2 foot rope into 5 equal pieces. how long will each piece of rope be?
chubhunter [2.5K]

Answer:

18 inches or 1 foot 6 inches/1 foot and a half

Step-by-step explanation:

one foot is 12 inches long so you take the number of feet given (7—we'll worry about the half later) and multiply by the number of inches that are in a foot (12)

7×12=84

then half a foot is 6 inches so 84+6=90 inches

then we take 90 and divide it by 5 (to get the length of one piece)

90/5=18 inches

you can keep it as 18 inches or convert it into feet which you subtract 12 from 18, and you have 6 inches left which is 1 foot and a half

5 0
2 years ago
ANSWER IT PLEASEEEE!!!!!!
Roman55 [17]
The answer is C :))






hope that helped
4 0
3 years ago
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