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3 years ago

Write the equation of the line that passes through the points (-6,8) and (-6,2).

Mathematics

1 answer:

just olya [345]3 years ago

6 0

Answer:

x = -6

Step-by-step solution:

The two points you have are (-6, 8) and (-6, 2).

1) First, you want to find the slope.

The equation for slope is $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

Let's have (-6, 8) be x_{1} and y_{1}, and (-6, 2 ) x_{2} and y_{2}.

So, you would get $\frac{2 - 8}{-6 - (-6)}$ = $\frac{-6}{0}$ = 0.

Since there is no slope, you know this is a horizontal or vertical line.

Because the two points have the same x- value, you know that it is a vertical line at x = -6.

You can see the two points and the line in the graph I've attached below.

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If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.

Pie

Given that $f^{(n)}(0)=(n+1)!$ , we have for $f(x)$ the Taylor series expansion about 0 as

$f(x)=\displaystyle\sum_{n=0}^\infty\frac{(n+1)!}{n!}x^n=\sum_{n=0}^\infty(n+1)x^n$

Replace $n+1$ with $n$ , so that the series is equivalent to

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}$

and notice that

$\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}$

Recall that for $|x|$ , we have

$\displaystyle\sum_{n=0}^\infty x^n=\frac1{1-x}$

which means

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}=\frac{\mathrm d}{\mathrm dx}\frac1{1-x}$
$\implies f(x)=\dfrac1{(1-x)^2}$

5 0

3 years ago

Jerry deposited 20,000 on an investment that will give 1,750 for every year that his money stays in the account. How much money

lesya692 [45]

Answer:

$34,000

Step-by-step explanation:

Jerry will get $1,750 for every year that his money stays in the account thus for 8 years he will get:

8*1,750 = $14,000

Together with the deposited money:

$20,000 + $14,000 = $34,000

By the end of year 8 there will be $34,000 of Jerry's account.

3 0

2 years ago

Paula used these steps to solve an equation:

Nookie1986 [14]

Answer:

steps 4 and 5

Step-by-step explanation:

When we look at example, we can see that we have :

-6r=57

So we divide by -6 and we got

$r=-\frac{57}{6}$

So, our final answer is steps 4 and 5

5 0

3 years ago

Juan has 12 muffins. He puts 1/4 of the muffins in a bag. How many muffins does Juan put in the bag?

Kitty [74]

12 divided my four is 3. So three is your answer.

3 0

3 years ago

Read 2 more answers

A cake is made out of 2 identical trapezoids. Each trapezoid has a height of 11 inches and base of 9 inches and 14 inches . What

a_sh-v [17]

Answer:

Area is 126.5 inches^2

Step-by-step explanation:

Mathematically, to calculate the area of the trapezoid, we use the following mathematical formula;

A = 1/2(a + b) h

here, a and b represents the two parallel sides which is 9 and 14 inches here and h which is the height is 11

Plugging these values into the equation, we have

A = 1/2(9 + 14)11

= 1/2(23)11 = (23*11)/2 = 126.5 inches^2

8 0

3 years ago