Select the correct answer. a number is selected at random from the set {2, 3, 4, ... 10}. which event, by definition, covers the entire sample space of this experiment?

I'll assume the ODE is

[tex]y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}[/tex]

Solve the homogeneous ODE,

[tex]y'' - 3y' + 2y = 0[/tex]

The characteristic equation

[tex]r^2 - 3r + 2 = (r - 1) (r - 2) = 0[/tex]

has roots at [tex]r=1[/tex] and [tex]r=2[/tex]. Then the characteristic solution is

[tex]y = C_1 e^x + C_2 e^{2x}[/tex]

For nonhomogeneous ODE (1),

[tex]y'' - 3y' + 2y = e^x[/tex]

consider the ansatz particular solution

[tex]y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x[/tex]

Substituting this into (1) gives

[tex]a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1[/tex]

For the nonhomogeneous ODE (2),

[tex]y'' - 3y' + 2y = e^{2x}[/tex]

take the ansatz

[tex]y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}[/tex]

Substitute (2) into the ODE to get

[tex]b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1[/tex]

Lastly, for the nonhomogeneous ODE (3)

[tex]y'' - 3y' + 2y = e^{-x}[/tex]

take the ansatz

[tex]y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}[/tex]

and solve for [tex]c[/tex].

[tex]ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16[/tex]

Then the general solution to the ODE is

[tex]\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}[/tex]

The radius of the orange circle is 1.5 unit and  the radius of the blue circle is 2.25 units

The figure that completes the question is added as an attachment

The orange circle

The radius of the green circle is given as:

r = 1

One and half green circle make up the radius of the orange circle.

So, the radius of the orange circle is

R = 1.5 * r

This gives

R = 1.5 * 1

R = 1.5

Hence, the radius of the orange circle is 1.5 unit

The blue circle

The radius of the orange circle is given as:

r = 1.5

One and half orange circle make up the radius of the blue circle.

So, the radius of the blue circle is

R = 1.5 * r

This gives

R = 1.5 * 1.5

R = 2.25

Hence, the radius of the blue circle is 2.25 units

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Answer:

2

-2

Step-by-step explanation:

Use the second equation for x = -4.

f(-4) = 2

Use the third equation for x = 3.

f(x) = -x + 1 = -3 + 1 = -2

Based on Alonso's budget, he can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.

21 = 2.50 + 5x

21 - 2.50 = 5x

18.50 = 5x

x = 18.50 / 5

x = 3.7 bags of avocados

To get 3 bags of avocados or 9 avocados

= $5 × 3

= $15

Therefore, Alonso can get 3.7 bags of avocados and the cost of 3 bags of avacodes or 9 avacadoes is $15.

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Considering the relation built the presence of point M on line LN, the numerical length of LN is of 9 units.

Point M splits line LN into two parts, LM and MN, hence the total length is given by:

LN = LM + MN.

From the given data, we have that:

Hence we first solve for x.

LN = LM + MN.

2x - 5 = 3 + x - 1

x = 7.

Hence the total length is:

LN = 2x - 5 = 2 x 7 - 5 = 14 - 5 = 9 units.

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Answer:

Decreasing at an increasing rate

Step-by-step explanation:

graph looks like an arch

right side is going down

right side is going down as x increases

Answer:

Yes, this is a valid inference because she took a random sample of the neighborhood.

Step-by-step explanation:

As we can see, Sue's survey was perfectly random and without any prejudice.

18% of the families, according to her research, would volunteer at the shelter. According to her, 18% of the local households should be required to volunteer at the animal shelter.

Therefore, given that she chose a representative sample of the area, her conclusion is valid.

Step-by-step explanation:

Yes, an positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval. By definition, a function, f is increasing over an interval [a,b], if f(b)> f(a)

Yes, a positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Yes, a positive average rate of change indicates that the endpoint of our period is higher than the interval's starting point. A function f is rising over the range [a,b] by definition if f(b)> f. (a)

Therefore, the positive average rate of change over an interval must be increasing over that interval.

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Answer:

84m

Step-by-step explanation:

The perimeter of a triangle is the sum of the length of the external sides.

Therefore, the perimeter of the triangle = 21m + 28m + 35m = 84m.

Hey there!

What is the formula for finding the perimeter of a triangle?
a + b + c = perimeter

What does the labels mean?
a = side 1

b = base

c = side 2

What should the equation look like?
21m + 28m + 35m = perimeter

How do should it be solve?
21m + 28m + 35m = perimeter

49m + 35m = perimeter

84m = perimeter

What is the answer to the question?

84m

Good luck on your assignment and enjoy your day!

~Amphitrite1040

dis i know functiin of fx is ♾

Answer:

4th option

Step-by-step explanation:

the end behaviour is what happens when x gets larger and positive (right- hand end )or larger and negative ( left- hand end )

f(x) = [tex]\frac{1}{2}[/tex] x² ← is of even degree (2) and has a positive leading coefficient , then

• even degree and positive leading coefficient

f(x) → +∞ as x → + ∞ and

f(x) → + ∞ as x → - ∞

A pendulum that swings fully once in 1.9 seconds has a length of 2.93 feet.

A basic pendulum is a machine in which the point mass is hung from a fixed support by a light, inextensible string.

Length of pendulum is defined as the distance between the point of suspension to the center of the bob and is denoted by " 1 ".

Given the equation:

[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]

where L is the length in feet and T is the time in seconds.

Given that T = 1.9sec,

Hence:

[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]

L = 2.93 feet

A pendulum that swings fully once in 1.9 sec has a length of 2.93 feet.

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Answer:

Step-by-step explanation:

Comment

There are a number of ways of doing this problem. I don't know which method you are intended to use. One sure way in this case is graphing the equation, I have done this for you. See below. The maximum volume occurs where x = 2

The graph shows that there is a peak at x = 2. That is where the maximum volume is,

Answer

x = 2

The correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

To find which 2 books describe a pair of dependent events:

Therefore, the correct option is (D) one of the non-fiction books on the bottom shelf and a second non-fiction book from the bottom shelf.

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Answer:

If I'm not mistaken that is the answer

The functions f(x) and g(x) are different functions

The function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common feature in both functions is their range

According to the statement

we have given that the some functions and we have to justify these functions.

The functions are given as:

f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2

This means that the function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common key features of the functions

To do this, we plot the graphs of both functions

From the attached graph, we have the following features:

Function f(x)

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y - intercept = 3

x - intercepts = -2.37

Function g(x)

Domain: x > 0

Range: -∞ < y < ∞

y - intercept = None

x - intercepts = 0.01

By comparing the key features above, we can conclude that the common features in both functions is their range.

The functions f(x) and g(x) are different functions

The function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common feature in both functions is their range

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Area of the sphere ≅ 339.62 in².

A sphere is a geometrical object in three-dimensional space that is the surface of a ball. Like a circle in a two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point in a three-dimensional space.

Area of sphere = 4[tex]\pi r^{2}[/tex]

diameter d = 2r

Given that,

diameter d = 10.4 , r =5.2 in

then, Area of sphere =  4[tex]\pi r^{2}[/tex]

                                   =   4×3.14×5.2×5.2                  

                                  ≅  339.62 in²

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Answer:

108.16 to the second power

Step-by-step explanation:

Answer:

B. the second graph.

Step-by-step explanation:

Literally the photo is on the question.

Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2. Therefore, the correct option is option B.

The study of graphs, that are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this sense, a network consists of vertices, also known as nodes or points, linked by edges, also known as links or lines.

Undirected graphs, in which edges connect two vertices symmetrically, are distinguished from directed graphs, in which edges connect two vertices asymmetrically. One of the main topics that are investigated in discrete mathematics is graphs. Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2.

Therefore, the correct option is option B.

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The lifetime of meson according to laboratory clocks would be 14 μs.

In this question,

Meson decay, Δt = 2μs

Velocity, y = 0.99C, where C is the speed of the light

Time measurement depends on the reference frame of clock.

Time dilation, Δt' = y Δt

⇒  [tex]\frac{\Delta t }{\sqrt{1-\frac{v^{2} }{c^{2} } } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-\frac{(0.99c)^{2} }{c^{2} } } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-0.99^{2} } } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-0.9801 } } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{0.0199} } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{0.1410} } }[/tex]

⇒ 14.18 × 10⁻⁶ ≈ 14 μs

Hence we can conclude that the lifetime of meson according to laboratory clocks would be 14 μs.

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[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

▪ [tex]\longrightarrow \sf{f(x) = |x + 4| + 2}[/tex]

You need to remember that the form of an Absolute Value Function is:

• For the vertex:

[tex]\small\longrightarrow \sf{H= \: \: x -coordinate}[/tex]

[tex]\small\longrightarrow \sf{K= y-coordinate}[/tex]

• For the definition:

If "a" is positive (+) , then the range of the function is:

[tex]\small\longrightarrow \sf{R:y \: \underline > \: k}[/tex]

If "a" is negative (-), the range of the function is:

[tex]\small\longrightarrow \sf{R: y \: \underline < \: k}[/tex]

In this case we can identify that:

[tex]\small\longrightarrow \sf{a = 1}[/tex]

[tex] \small\longrightarrow\sf{a = 2}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex] \large \bm{R: {f(x) \in ℝ | f(x) \underline > 2}}[/tex]

Answer:

Cosa/2-tana+sina

Step-by-step explanation:

Cosatana

The roots of the given polynomials exists

[tex]$x=8+\sqrt{10},[/tex]  and [tex]$ x=8-\sqrt{10}[/tex]

For a quadratic equation of the form [tex]$a x^{2}+b x+c=0$[/tex] the solutions are

[tex]$x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

Therefore by using the formula we have

[tex]$x^{2}-16 x+54=0[/tex]

Let, a = 1, b = -16 and c = 54

Substitute the values in the above equation, and we get

[tex]$x_{1,2}=\frac{-(-16) \pm \sqrt{(-16)^{2}-4 \cdot 1 \cdot 54}}{2 \cdot 1}$[/tex]

simplifying the equation, we get

[tex]$x_{1,2}=\frac{-(-16) \pm 2 \sqrt{10}}{2 \cdot 1}[/tex]

[tex]$x_{1}=\frac{-(-16)+2 \sqrt{10}}{2 \cdot 1}, x_{2}=\frac{-(-16)-2 \sqrt{10}}{2 \cdot 1}$[/tex]

[tex]$x=8+\sqrt{10}, x=8-\sqrt{10}[/tex]

Therefore, the roots of the given polynomials are

[tex]$x=8+\sqrt{10},[/tex]  and [tex]$ x=8-\sqrt{10}[/tex].

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4710

4709.94107458

The nearest whole number for 4709.94107458 is 4710 since the number 9 after the decimal is greater than 5. Therefore, if you add 1 to 9 before the decimal, you get 10.

Hope this helps :)

Answer:

34

Step-by-step explanation:

(a + [tex]\frac{1}{a}[/tex] ) = 6← square both sides

(a + [tex]\frac{1}{a}[/tex] )² = 6² ← expand left side using FOIL

a² + 1 + 1 + [tex]\frac{1}{a^2}[/tex] = 36

a² + 2 + [tex]\frac{1}{a^2}[/tex] = 36 ( subtract 2 from both sides )

a² + [tex]\frac{1}{a^2}[/tex] = 34

Answer:

40

Step-by-step explanation:

7 - 3 + 9 x 8 / 2

Multiplication and division left - right.

7 - 3 + 72 / 2

7 - 3 + 36

Add and subtract left to right.

4 + 36 = 40

Answer:

length is (-7,-1) and radius is 6

Step-by-step explanation:

We are given the expression of the equation of a circle that is

x2 + y2 + 14x + 2y + 14 = 0.

Using completing the squares:

x2 + y2 + 14x + 2y + 14 = 0(x+7)^2 + (y+1) ^2 = -14 + 49 + 1(x+7)^2 + (y+1) ^2 = 36 center thus is at (-7,-1) and the radius is equal to square root of 36 equal to 6.

Step-by-step explanation:

its 29 9x4=29 9+4=13 13+4=17

The type of function for f(x) = 2 · ㏒₅ (3 · x) is a logarithmic function. (Correct choice: B)

In this problem we must check the characteristics of an expression and conclude what kind of function is. First, we need to find if any trascendent operator, it not, then the function may be either polynomial or rational. If the function has a trascendent operator, then we must check if it is logarithmic or exponential.

At first glance, we see that the function includes only one trascendent operator, a "log" operator that creates a function of the form f(x) = A · ㏒ₙ (B · x). Therefore, the type of function for f(x) = 2 · ㏒₅ (3 · x) is a logarithmic function. (Correct choice: B)

The statement is poorly formatted, correct form is shown below:

What type of function is f(x) = 2 · ㏒₅ (3 · x)? a) Exponential, b) Logarithmic, c) Polynomial, d) Rational.

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Answer: Logarithmic

Step-by-step explanation: Got the question right on test.

Answer:

Step-by-step explanation:

350 : (5 + 8 + 12) =

350 : 25 = 14

14 * 12 = 168