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iogann1982 [59]
3 years ago
7

Find the distance between the points (4, 7) and (2, 2)

Mathematics
1 answer:
ch4aika [34]3 years ago
5 0

Answer:

5.38516

Step-by-step explanation:

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Consider the function below. (If an answer does not exist, enter DNE.) f(x) = x3 − 27x + 3 (a) Find the interval of increase. (E
xxTIMURxx [149]

Answer:

(-∞,-3) and (3,∞)  

Step-by-step explanation:

f(x) = x³ − 27x + 3

1. Find the critical points

(a) Calculate the first derivative of the function.

f'(x) = 3x² -27  

(b) Factor the first derivative

f'(x)= 3(x² - 9) = 3(x + 3) (x - 3)

(c) Find the zeros

3(x + 3) (x - 3) = 0

x + 3 = 0      x - 3 = 0

     x = -3          x = 3

The critical points are at <em>x = -3</em> and x = 3.

2. Find the local extrema

(a) x = -3

f(x) = x³ − 27x + 3 = (-3)³ - 27(-3) + 3 = -27 +81 + 3 = 57

(b) x = 3

f(x) = x³ − 27x + 3 = 3³ - 27(3) + 3 = 27 - 81 + 3 = -51

The local extrema are at (-3,57) and (3,-51).

3, Identify the local extrema as maxima or minima

Test the first derivative (the slope) over the intervals (-∞, -3), (-3,3), (3,∞)

f'(-4) = 3x² -27 = 3(4)² - 27  = 21

f'(0) = 3(0)² -27 = -27

f'(4) = 3(4)² - 27 = 51

The function is increasing on the intervals (-∞,-3) and (3,∞).

The graph below shows the critical points of your function.

6 0
3 years ago
Pls help me in these two little exercises about the slope.
den301095 [7]

Answer:

3)  y=\dfrac35x+\dfrac25

4) a)  y=-2x+7

  b)  y=\dfrac12x+\dfrac92

Step-by-step explanation:

<u>Exercise 3</u>

-3x + 5y = 2

\implies 5y = 3x + 2

\implies y=\dfrac35x+\dfrac25

<u>Exercise 4</u>

a) If L2 is parallel to L1, it has the same slope (gradient) ⇒ m = -2

If L2 passes through point (3, 1):

y-y_1=m(x-x_1)

\implies y-1=-2(x-3)

\implies y=-2x+7

So L2 = L1

b) If L3 is perpendicular to L1, then the slope of L3 is the negative reciprocals of the slope of L1  ⇒  m = \dfrac12

If L3 passes through point (-5, 2):

y-y_1=m(x-x_1)

\implies y-2=\dfrac12(x+5)

\implies y=\dfrac12x+\dfrac92

4 0
2 years ago
Read 2 more answers
If the clothing maker bought 500 m2 of this fabric, how much money did he lose? Use 1tepiz=0.625dollar and 0.9144m=1yard.
Ivanshal [37]
1 yard^2 = 0.8361m^2.? 

<span>The solution to the problem is as follows:

So he spent (.625 x 400) = $250.00 per m^2. </span>
He paid out (500 x 250) = $125,000 on the deal. 
He received (500 / 0.8361) = 598.014592 yard^2 of fabric. 
That would have cost (598.014592 x 120) = $71,761.75 locally. 
He lost (125,000 - 71,761.75) = $53,238.25 on the deal. 

<span>You can rework with the incorrect conversion factor.

I hope my answer has come to your help. God bless and have a nice day ahead!
</span>
7 0
3 years ago
Read 2 more answers
A.Pictograph
guajiro [1.7K]

..Answer:

Step-by-step explanation:

...

3 0
3 years ago
How many times can 5 go into 78
creativ13 [48]

Answer:

15.6

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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