What is the balance point for this data set? Type the NUMBER ONLY (please give a description)

What is the average rate of change of the function over the interval x = 0 to x = 6? f(x)=2x−1 3x+5 Enter your answer, as a frac

Tatiana [17]

Answer:

-11

Step-by-step explanation:

Our function is 2x-13x+5

2x-13x+5= -11x+5
F(0)= 5 and F(6)= -11*6+5 = -61
let m be the average change : m= (-61-5)/6= -11

8 0

3 years ago

Write the equation of a line perpendicular to y= 2x+ 2 that passes through the point (-1, -7).

Nataly [62]

Answer:

all work is shown and pictured

5 0

3 years ago

A ½in diameter rod of 5in length is being considered as part of a mechanical linkagein which it can experience a tensile loading

Evgesh-ka [11]

Answer:

a. Maximum Load = Force = 27085.09 N

b. Maximum Energy = 3.440 Joules

Step-by-step explanation:

Given

Rod diameter = ½in = 0.5in

Length = 5in

Young's modulus = 15.5Msi

By applying the 0.2% offset rule,

The maximum load the rod can hold before it gets to breaking point is given as follows by taking the strain as 0.2%

Young Modulus = Stress/Strain ------- Make Stress the Subject of Formula

Stress = Strain * Young Modulus

Stress = 0.2% * 15.5

Stress = 0.002 * 15.5

Stress = 0.031Msi

Calculating the area of the rod

Area = πr² or πd²/4

Area, A = 22/7 * 0.5^4 / 4

A = 22/7 * 0.25 / 4

A = 5.5/28

A = 0.1964in²

The maximum load that the rod would take before it starts to permanently elongate is given by

Force = Stress * Atea

Force = 0.031Msi * 0.1964in²

Force = 31Ksi * 0.1964in²

Force = 6.089Ksi in²

Force = 6.089 * 1000lbf

Force = 6089 lbf

1 lbf = 4.4482N

So, Force = 6089 * 4.4482N

Force = 27085.09 N

b.

Using Strain to Energy Formula

U = V×σ²/2·E

Where V = Volume

V = Length * Area

V = 5 in * 0.1964in²

V = 0.982in³

σ = Stress = 0.031Msi

= 0.031 * 1000Ksi

= 31Ksi

= 31 * 1000psi

= 31000psi

E = Young Modulus = 15.5Msi

= 15.5 * 1000Ksi

= 15.5 * 1000 * 1000psi

= 15500000psi

So,

Energy = 0.982 * 31000²/ ( 2 * 15500000)

Energy = 943,702,000/31000000

Energy = 30.442in³psi

------- Converted to ftlbf

Energy = 2.537 ftlbf

-------- Converted to Joules

Energy = 3.440 Joules

7 0

4 years ago

What is the equivalent of 3/6

Maslowich

$\frac{3}{6}^{/3}= \frac{1}{2}$

3 0

3 years ago

Read 2 more answers

The length of a rectangle is 5 metres less than twice the breadth. If the perimeter is 50 meters,find the length and breadth

MAXImum [283]

As per the given question, it is stated that the length of a rectangle is 5 m less than twice the breadth.

Assumption : Let us assume the length as "l" and width as "b". So,

$\twoheadrightarrow \quad\sf{ Length =2(Width)-5}$

$\twoheadrightarrow \quad\sf{ \ell=(2b-5) \; m}$

Also, we are given that the perimeter of the rectangle is 50 m. Basically, we need to apply here the formula of perimeter of rectangle which will act as a linear equation here.

$\\ \twoheadrightarrow \quad\sf{ Perimeter_{(Rectangle)} = 2(\ell +b) } \\$

l denotes length
b denotes breadth

$\\ \twoheadrightarrow \quad\sf{50= 2(2b-5+b)} \\$

$\\ \twoheadrightarrow \quad\sf{50= 2(3b-5)} \\$

$\\ \twoheadrightarrow \quad\sf{50= 6b - 10} \\$

$\\ \twoheadrightarrow \quad\sf{50+10= 6b} \\$

$\\ \twoheadrightarrow \quad\sf{60= 6b} \\$

$\\ \twoheadrightarrow \quad\sf{\cancel{\dfrac{60}{6}}=b} \\$

$\\ \twoheadrightarrow \quad\underline{\bf{10\; m = Width }} \\$

Now, finding the length. According to the question,

$\twoheadrightarrow \quad\sf{ \ell=(2b-5) \; m}$

$\twoheadrightarrow \quad\sf{ \ell=2(10)-5\; m}$

$\twoheadrightarrow \quad\sf{ \ell=20-5\; m}$

$\\ \twoheadrightarrow \quad\underline{\bf{15\; m = Length }} \\$

Therefore, length and breadth of the rectangle is 15 m and 10 m. 

7 0

3 years ago