The line through the points (1/2, 2) and (- 3/2, 4)

Mathematics

1 answer:

Amanda [17]3 years ago

8 0

Answer:

y=-x+2.5

Step-by-step explanation:

You might be interested in

Determine if the following infinite series converges or diverges

Mandarinka [93]

Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.

<h3>How do we verify if a sequence converges of diverges?</h3>

Suppose an infinity sequence defined by:

$\sum_{k = 0}^{\infty} f(k)$

Then we have to calculate the following limit:

$\lim_{k \rightarrow \infty} f(k)$

If the <u>limit goes to infinity</u>, the sequence diverges, otherwise it converges.

In this problem, the function that defines the sequence is:

$f(k) = \frac{k^3}{k^4 + 10}$

Hence the limit is:

$\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0$

Hence, the infinite sequence converges, as the limit does not go to infinity.

More can be learned about convergent sequences at brainly.com/question/6635869

#SPJ1

6 0

2 years ago

Read 2 more answers

(27x^4-18x^3+9x^2)÷3x

Goshia [24]

Answer:

the answer is 9x^3 - 6x^2 + 3x

Step-by-step explanation:

take each number with variable and divided by 3x

3 0

3 years ago

A guy wire to a tower makes a 72 degrees angle with level ground. At a point 30 ft farther from the tower than the wire but on t

Andreyy89

So.. checking the picture below

we can say y = y, or just do a substitution and end up with

$\bf tan(72^o)=tan(30^o)(30+x)\implies 3.08x=\cfrac{30}{\sqrt{3}}+\cfrac{1}{\sqrt{3}}x
\\\\\\
3.08x-\cfrac{1}{\sqrt{3}}x=\cfrac{30}{\sqrt{3}}\implies 2.5x\approx 17.32\implies x\approx \cfrac{17.32}{2.5}$

once you know, how long is "x", then you can simply use the cosine of 72° to get "r"

thus $\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad cos(72^o)=\cfrac{x}{r}\implies r=\cfrac{x}{cos(72^o)}$