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mestny [16]
3 years ago
6

Simplify 4n 5 + 3.5n 5 + (-2.1n 5).

Mathematics
2 answers:
Mars2501 [29]3 years ago
8 0

Answer:

5.4n^5

Step-by-step explanation:

Given:

Expression, 4n^5+3.5n^5+(-2.1)n^5

Simplify the given polynomial.

\Rightarrow 4n^5+3.5n^5+(-2.1)n^5

Sign rule: (+)(-) = -

\Rightarrow 4n^5+3.5n^5-2.1n^5

Each term has variable n with degree 5.

Combine the coefficients of variable.

\Rightarrow (4+3.5-2.1)n^5

\Rightarrow 5.4n^5

Hence, The simplest form of polynomial is 5.4n⁵

lyudmila [28]3 years ago
3 0
4n 5 + 3.5n 5 - 2.1n 5 = n 5 (4 + 3.5 - 2.1) = n 5 * 5.4 = 5.4n 5
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-3 + x = -22

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What should be subtracted from -8xy + 2x^2 + 3y^2 to get x^2 + 2
Minchanka [31]

Answer:

x^2 - 8xy + 3y^2 - 2

Step-by-step explanation:

(-8xy + 2x^2 + 3y^2) - unknown = x^2 + 2

- unknown = x^2 + 2 + 8xy - 2x^2 - 3y^2

- unknown = -x^2 + 8xy - 3y^2 + 2

Unknown = x^2 - 8xy + 3y^2 - 2

Check:

(-8xy + 2x^2 + 3y^2) - (x^2 - 8xy + 3y^2 - 2)

= -8xy + 2x^2 + 3y^2 - x^2 + 8xy - 3y^2 + 2

= -8xy + 8xy + 2x^2 - x^2 + 3y^2 - 3y^2 + 2

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8 0
2 years ago
Find the Fourier series of f on the given interval. f(x) = 1, ?7 < x < 0 1 + x, 0 ? x < 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
Charli bought 2 3/4 pounds of pears for 0.76 per pound and 2 3/4 pounds of grapes for 1.40 per pound. how much money in dollars
MArishka [77]

Answer:

Total = \$5.94 ---- in dollars

Total = 594\ cents ---- in cents

5 dollars 94 cents

Step-by-step explanation:

Given

Pears

Weight = 2\frac{3}{4}\ lb

Amount = \$0.76 per pound

Grapes

Weight = 2\frac{3}{4}\ lb

Amount = \$1.40 per pound

Required

Determine the amount paid for the fruit in dollar and cents

First, we need to calculate the amount paid for each fruit.

This is calculated by multiplying the amount per pound by the number of pounds bought.

For Pears:

Total_{Pears} = 2\frac{3}{4} * \$0.76

Convert fraction to decimal

Total_{Pears} = 2.75 * \$0.76

Total_{Pears} = \$2.09

For Grapes

Total_{Grapes} = 2\frac{3}{4} * \$1.40

Convert fraction to decimal

Total_{Grapes} = 2.75 * \$1.40

Total_{Grapes} = \$3.85

Next, we add both amounts together to get the total amount spent in dollars.

Total = Total_{Pears} + Total_{Grapes}

Total = \$2.09 + \$3.85

Total = \$5.94

Multiply by 100 to convert this amount to cents

Total = 5.94 * 100\ cents

Total = 594\ cents

And it can be represented as dollars and cents as:

5 dollars 94 cents

8 0
2 years ago
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