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2 years ago

Find the slope of a line parallel to y=(2/5)x + (4/5)

Mathematics

2 answers:

GaryK [48]2 years ago

7 0

Answer:

m=2/5

Step-by-step explanation:

Lines that are parallel have the exact same slope.

We have an equation in point slope form.

y=mx+b

where m is the slope and b is the y-intercept.

The slope is the number being multiplied by x. In the equation

y=2/5x+4/5

2/5 and x are being multiplied. Therefore, 2/5 is the slope. A line that is parallel will have the same slope of 2/5.

Tcecarenko [31]2 years ago

6 0

Answer:

So if a line was parallel it would have same slope. You can search up what slope-intercept form means. But if you have an equation like this:

y = mx+b

The slope will be m. Your question is written in the form. 2/5 = m.

The slope is 2/5

The y-intercept is 4/5

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4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

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Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$

$=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}$

What we use?

We use that

$e^{i\pi n}=cos(\pi n)+i sin(\pi n)$

and

$\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}$

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