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Zepler [3.9K]
3 years ago
12

Find the vertex and the axis of symmetry of the graph of the function?

Mathematics
1 answer:
Orlov [11]3 years ago
5 0
3) Vertex: (-7, 0) Axis of Symmetry: x=-7
6) Vertex: (-2, -1) Axis of Symmetry: x=-2
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Divide 80 in a ratio of 3:2
Alecsey [184]
The 3:2 ratio can be calculated by dividing the total by the sum of the factors (3 + 2) i.e. 80/5 = 16 
<span>Then multiply the factors by the answer above (i.e. 3 x 16 and 2 x 16) </span>

<span>48:32
hope this helps you ! =')</span>
3 0
3 years ago
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A 40-m-long chain hangs vertically from a cylinder attached to a winch. Assume there is no friction in the system and the chain
daser333 [38]

Answer:

a) W₁ = 78400 [J]

b)Wt = 82320 [J]  

Step-by-step explanation:

a) W = ∫ f*dl      general expression for work

If we have a chain with density of 10 Kg/m, distributed weight would be

9.8 m/s² * 10 kg   = mg

Total length of th chain is 40 m, and the function of y at any time is

f(y) = (40 - y ) mg   where ( 40 - y ) is te length of chain to be winded

At the beggining we have to wind 40 meters   y = 0 at the end of the proccess  y = 40 and there is nothing to wind then:

f(y) = mg* (40 - y )

W₁ =  ∫f(y) * dy    ⇒ W₁ = ∫₀⁴⁰ mg* (40 - y ) dy  ⇒ W₁ = mg [ ∫₀⁴⁰ 40dy - ∫₀⁴⁰ ydy

W₁ = mg [ 40*y |₀⁴⁰   -  1/2 * y²  |₀⁴⁰    ⇒  W₁ = mg* [ 40*40 - 1/2 (40)² ]

W₁ = mg * [1/2]     W₁ = 10*9,8* ( 800 )

W₁ = 78400 [J]

b) Now we can calculate work to do if we have a 25 block and the chain is weightless

W₂ = ∫ mg* dy     ⇒    W₂  = ∫₀⁴⁰ mg*dy   ⇒    W₂  = mg y |₀⁴⁰

W₂ = mg* 40   = 10*9.8* 40  

W₂ = 3920 [J]

Total work

Wt = W₁  +  W₂        ⇒    Wt = 78400 + 3920

Wt = 82320 [J]

6 0
3 years ago
H(x)=
UNO [17]

The average rate of change of the function over −2 ≤ x ≤ 2 is 1/2

<h3>How to determine the average rate of change?</h3>

The function is given as:

h(x) = \frac 18x^3 - x^2

The interval is given as:

−2 ≤ x ≤ 2

Calculate h(2) and h(-2)

h(2) = \frac 18 * 2^3 - (2)^2

h(2) = -3

h(-2) = \frac 18 * (-2)^3 - (-2)^2

h(-2) = -5

The average rate of change is then calculated as:

m = \frac{h(-2) - h(2)}{-2-2}

This gives

m = \frac{-5 + 3}{-4}

Evaluate

m = 1/2

Hence, the average rate of change of the function over −2 ≤ x ≤ 2 is 1/2

Read more about average rate of change at

brainly.com/question/23715190

#SPJ1

<u>Complete question</u>

h(x) = \frac 18x^3 - x^2

What is the average rate of change of h over the interval −2 ≤ x ≤ 2

7 0
1 year ago
How do I put 3(x+7) in distributive property
inysia [295]

Answer:

3(x+7) = 3x +21

Step-by-step explanation:


3 0
3 years ago
Read 2 more answers
Mr. Sol records the daily high temperatures for a week. He creates the box plot below to display his data.
andriy [413]
Select 3? Probably C,E,A
7 0
2 years ago
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