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3 years ago

Find Slope (3,2),(-6,2)

Mathematics

2 answers:

NikAS [45]3 years ago

8 0

By using slope formula (x2-x1) ^2 / (y2-y1) ^2 i.e

x1 = 3 x2 = -6

y1 = 2 y2 = 2

Using slope formula,

Slope = {(-6) - 3} ^2 / (2 - 2 ) ^2

*use this and solve and if this was helpful let me know.

dlinn [17]3 years ago

6 0

slope=0

it's a straight horizontal line when you graph it.

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What will be the value of

madreJ [45]

The expression as given doesn't make much sense. I think you're trying to describe an infinitely nested radical. We can express this recursively by

$\begin{cases}a_1=\sqrt{42}\\a_n=\sqrt{42+a_{n-1}}\end{cases}$

Then you want to know the value of

$\displaystyle\lim_{n\to\infty}a_n$

if it exists.

To show the limit exists and that $a_n$ converges to some limit, we can try showing that the sequence is bounded and monotonic.

Boundedness: It's true that $a_1=\sqrt{42}\le\sqrt{49}=7$ . Suppose $a_k\le 7$ . Then $a_{k+1}=\sqrt{42+a_k}\le\sqrt{42+7}=7$ . So by induction, $a_n$ is bounded above by 7 for all $n$ .

Monontonicity: We have $a_1=\sqrt{42}$ and $a_2=\sqrt{42+\sqrt{42}}$ . It should be quite clear that $a_2>a_1$ . Suppose $a_k>a_{k-1}$ . Then $a_{k+1}=\sqrt{42+a_k}>\sqrt{42+a_{k-1}}=a_k$ . So by induction, $a_n$ is monotonically increasing.

Then because $a_n$ is bounded above and strictly increasing, the limit exists. Call it $L$ . Now,

$\displaystyle\lim_{n\to\infty}a_n=\lim_{n\to\infty}a_{n-1}=L$

$\displaystyle\lim_{n\to\infty}a_n=\lim_{n\to\infty}\sqrt{42+a_{n-1}}=\sqrt{42+\lim_{n\to\infty}a_{n-1}}$

$\implies L=\sqrt{42+L}$

Solve for $L$ :

$L^2=42+L\implies L^2-L-42=(L-7)(L+6)=0\implies L=7$

We omit $L=-6$ because our analysis above showed that $L$ must be positive.

So the value of the infinitely nested radical is 7.

4 0

3 years ago

Mr. Takaya can eat three slices of pizza in five minutes. If he continues to eat at the same rate, how many slices

Anna [14]

Answer:

18.

Step-by-step explanation:

3 x 6 = 18. He eats 3 slices every 5 minutes so 5 minutes x 6 is half an hour. so 18 is your answer.

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3 years ago

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State the rule that will result in the transformation below.<br> (x,y) maps to (?, ?)

Anna [14]

Answer:

(x,y) maps to (-y,x).

Step-by-step explanation:

Use vertex I as an example.

Pre-image I is graphed at point (-3,2), while image I' is graphed at point (-2,-3) .

In order to change between these points, the x and y coordinates must be swapped, as well as multiplying the y coordinate by -1.

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3 years ago

Could someone please help and explain how to do this

LiRa [457]

Answer:

Step-by-step explanation:

just remember that $\sqrt{x} = x^{1/2} ....... \sqrt[3]{x} = x^{1/3} \\also that (x^{a})^{b} = x^{a*b}$

1) x^3 = x^ (3/4) ===> FALSE

2) x^3/4 = x^3/4 ===> TRUE

3) x^3/4 = x^3/4 ===> TRUE

4) x^(4/3) = x^(4/3) ===> TRUE

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3 years ago

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Choose the correct ordering, from greatest to least, of the numbers below. L). 0.65 M) 640.23 N) 19.455 0) 6.682 P) 63.08

Neporo4naja [7]

Answer:

640.23. 63.08. 19.455. 6.682. 0.65

Step-by-step explanation:

if you look at the whole number you can see which is greater and which is less, if you still can't figure it out then, look at the tenths then hundredths and finally thousandths

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3 years ago