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3 years ago

Sketch the curve y=x(x-2)^3 showing any stationary points and points of inflection

Mathematics

2 answers:

ycow [4]3 years ago

6 0

Answer:

hshsnwjsbsbskakdbdbsn

elixir [45]3 years ago

3 0

Answer:

Step-by-step explanation:

hello :

let : y=f(x)

f(x)==x(x-2)^3 so : f'(x) = 1.(x-2)^3+3x(x-2)²

f'(x) = (x-2)²(x-2+3x)

f'(x) = (x-2)²(4x-2)

f'(x) =0 : x=2 or x=1/2

the minumum is (1/2 ,f(2))

the inflection points use f"(x) = 0.......continu

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Kaylee has 2 gallons each of red and blue paint, and 1 gallon each of orange and green paint. She paints her bedroom with these

Aleks04 [339]

Answer:

3( 73/84 )left over

Step-by-step explanation:

She had 6 gallons in total

2/3+1/4+1/2+5/7=179/84 = 2 ( 11/84)

6/1-179/84 = 325/84 = 3(73/84)

She used 179/84

She have left 325/84

179/84 + 325/84 = 6

With mixed numbers:

2 11/84

3 73/84

2+3=5 11/84+73/84= 84/84 =1

5+1=6

8 0

3 years ago

A new movie is released each year for 8 years to go along with a popular book series. Each movie is 5 minutes longer than the la

Georgia [21]

Answer:

The total length of all 8 movies is 740 minutes

Step-by-step explanation:

* Lets revise the arithmetic series

- In the arithmetic series there is a constant difference between

each two consecutive numbers

- Ex:

# 2 , 5 , 8 , 11 , ………………………. (constant difference is 3)

# 5 , 10 , 15 , 20 , ………………………… (constant difference is 5)

# 12 , 10 , 8 , 6 , …………………………… (constant difference is -2)

* General term (nth term) of an Arithmetic series:

- If the first term is a and the common diffidence is d, then

U1 = a , U2 = a + d , U3 = a + 2d , U4 = a + 3d , U5 = a + 4d

So the nth term is Un = a + (n – 1)d, where n is the position of the

number in the series

- The formula to find the sum of n terms is

Sn = n/2 [a + l] , where l is the last term in the series

* Lets solve the problem

- A new movie is released each year for 8 years to go along with a

popular book series

∴ n = 8

- Each movie is 5 minutes longer than the last

∴ d = 5

- The first movie is 75 minutes long

∴ a = 75

- To find the total length of all 8 movies find the sum of the 8 terms

∵ Un = a + (n - 1)d

∵ The last term l is u8

∵ a = 75 , d = 5 , n = 8

∴ l = 75 + (8 - 1)(5) = 75 + 7(5) = 75 + 35 = 110

∴ l = 110

∵ Sn = n/2 [a + l]

∴ S8 = 8/2 [75 + 110] = 4 [185] = 740 minutes

* The total length of all 8 movies is 740 minutes

7 0

2 years ago

Find the proportion of observations from a standard Normal distribution that falls in each of the following regions. -2.31 <

Igoryamba

$\mathbb P(-2.31$

4 0

2 years ago

VEEL

Andre45 [30]

Answer:

$a_n=-3(3)^{n-1}$ ; {-3,-9, -27,- 81, -243, ...}

$a_n=-3(-3)^{n-1}$ ; {-3, 9,-27, 81, -243, ...}

$a_n=3(\frac{1}{2})^{n-1}$ ; {3, 1.5, 0.75, 0.375, 0.1875, ...}

$a_n=243(\frac{1}{3})^{n-1}$ ; {243, 81, 27, 9, 3, ...}

Step-by-step explanation:

The first explicit equation is

$a_n=-3(3)^{n-1}$

At n=1,

$a_1=-3(3)^{1-1}=-3$

At n=2,

$a_2=-3(3)^{2-1}=-9$

At n=3,

$a_3=-3(3)^{3-1}=-27$

Therefore, the geometric sequence is {-3,-9, -27,- 81, -243, ...}.

The second explicit equation is

$a_n=-3(-3)^{n-1}$

At n=1,

$a_1=-3(-3)^{1-1}=-3$

At n=2,

$a_2=-3(-3)^{2-1}=9$

At n=3,

$a_3=-3(-3)^{3-1}=-27$

Therefore, the geometric sequence is {-3, 9,-27, 81, -243, ...}.

The third explicit equation is

$a_n=3(\frac{1}{2})^{n-1}$

At n=1,

$a_1=3(\frac{1}{2})^{1-1}=3$

At n=2,

$a_2=3(\frac{1}{2})^{2-1}=1.5$

At n=3,

$a_3=3(\frac{1}{2})^{3-1}=0.75$

Therefore, the geometric sequence is {3, 1.5, 0.75, 0.375, 0.1875, ...}.

The fourth explicit equation is

$a_n=243(\frac{1}{3})^{n-1}$

At n=1,

$a_1=243(\frac{1}{3})^{1-1}=243$

At n=2,

$a_2=243(\frac{1}{3})^{2-1}=81$

At n=3,

$a_3=243(\frac{1}{3})^{3-1}=27$

Therefore, the geometric sequence is {243, 81, 27, 9, 3, ...}.

6 0

3 years ago

Describe the end behavior of the given function f(x)=2/3x-2

Ipatiy [6.2K]

Answer:

The end behavior of f(x)=2/3x-2 is: as x->+ infinity, f(x)->+ infinity

as x->- infinity, f(x)->- infinity

Step-by-step explanation:

When you are asked about the end behavior of a function, look to see where the function is traveling on the graph. For instance, this graph is linear, so you should look to see if the slope is positive or negative. This linear function is positive, so as x is reaching positive infinity the f(x) would also be reaching positive infinity. As x is reaching negative infinity, f(x) would also be reaching negative infinity. The end behavior of a function describes the trend of the graph on the left and right side of the x- axis. (As x approaches negative infinity and as x approaches positive infinity).

4 0

3 years ago