generate a continuous and differentiable function f(x) with the following properties: f(x) is decreasing at x=−6 f(x) has a local minimum at x=−3 f(x) has a local maximum at x=3

Answer:

[tex]\displaystyle \frac{1}{\pi}\approx0.318[/tex]

Step-by-step explanation:

The velocity of an object moving on a line is given by the function:

[tex]\displaystyle v(t)=\frac{1}{\pi}+\sin(3t),\; \frac{\pi}{2}\leq x\leq\pi[/tex]

And we want to determine the velocity of the object when its acceleration is 3.

So, we will need to determine our acceleration function. Remember that acceleration is simply the derivative of speed. Therefore, our acceleration function a(t) will be:

[tex]\displaystyle a(t)=v^\prime(t)=\frac{d}{dt}[\frac{1}{\pi}+\sin(3t)][/tex]

Differentiate. We will use the chain rule on the second part. Hence, our acceleration function is:

[tex]\displaystyle a(t)=3\cos(3t)[/tex]

We want to find the velocity when the acceleration is 3.

So, let’s set a(t) equal to 3 and determine at what time t our function equals 3. Hence:

[tex]3=3\cos(3t)[/tex]

Divide both sides by 3:

[tex]\cos(3t)=1[/tex]

Take the inverse cosine of both sides.

Remember that cosine is 1 for every 2π. Hence:

[tex]3t=2\pi n[/tex]

Where n is an integer.

Divide both sides by 3. Therefore, our solutions are:

[tex]\displaystyle t=\frac{2\pi n}{3}[/tex]

However, our domain was π/2≤x≤π.

Hence, we can test values of n such that it is within our domain.

Testing for n=0, 1, and 2, we see that:

[tex]\displaystyle t=0, \, t=\frac{2\pi}{3},\, t=\frac{4\pi}{3}...[/tex]

However, the only solution that is within our domain is the second solution.

Hence, the acceleration is 3 when the t is 2π/3.

Therefore, our velocity at that time t is:

[tex]\begin{aligned}\displaystyle v(\frac{2\pi}{3})&=\frac{1}{\pi}+\sin(3(\frac{2\pi}{3}))\\ &=\frac{1}{\pi}+\sin(2\pi)\\&=\frac{1}{\pi}+0\\&=\frac{1}{\pi}\approx 0.318\end{aligned}[/tex]

Answer:

answer to your question is 4

what happen is there is a glitch probably

yes this is what happened to me. if u get too far behind they will change the due dates to your "pace" and make it easier for you.

Answer:

(5,-1)

Step-by-step explanation:

TAKE ONE SIDE

(X-5)2=0

2X-10= 0

2X=10

X=10/2

X=5

THEN TAKE OTHE SIDE

-2(y+1) =0

-2y-2=0

-2y=2

y=2/-2

y=-1

So the answer is (5,-1)

And it should be in right down

(-5,1) , the graph opens down

'An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.'

.Given equation: 2(x-5) = -2(y+1)

Evaluating left-hand side,

⇒ (x-5)2 = 0

⇒2x-10 = 0

⇒2x = 10

⇒x =10/2

⇒x = 5

Evaluating RHS,

⇒-2(y+1) = 0

⇒-2y-2 = 0

⇒-2y = 2

⇒y = 2/-2

⇒y = -1

Hence, we can conclude the vertex is at (-5,1) and the graph opens down.

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Answer:

4 + 8 / 2 * 3 = 18

4 + 8 = 12

12 / 2 = 6

6 * 3 = 18

Step-by-step explanation:

*Hope this helps*

Answer:

t = ln1.5/0.25

t = 1.622

Step-by-step explanation:

Gives the equation, 6*e^{0.25t}=9

We are to find t

6*e^{0.25t}=9

e^{0.25t}=9/6

e^{0.25t}= 1.5

Apply ln to both Sides

ln( e^{0.25t) = ln1.5

0.25t = ln1.5

t = ln1.5/0.25

t = 1.622

Answer:

Raphael sells paintings for $200 each at a market, but has to pay $100 to reserve a table. :)

Step-by-step explanation:

The scenario that describes a proportional relationship is D; Raphael sells paintings for $200 each at a market but has to pay $100 to reserve a table.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

p = kq

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

[tex]p \propto q[/tex]where that middle sign is the sign of proportionality.

This inversely proportional relationship is denoted by;

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

Thus, the scenario that describes a proportional relationship is D; Raphael sells paintings for $200 each at a market but has to pay $100 to reserve a table.

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Answer:

The 5 in the () is what the x is

Step-by-step explanation:

3(5)+2=17

Answer:

Step-by-step explanation:

Replace the X with 5

3(5)+2

Follow PEMDAS

so multiplication goes first

15+2

Then add

17

Answer:

The ratio of the similar triangles is 6/4=3/2. Since BC-YZ in this case, 3*3/2=9/2=4.5 which is B.

Answer:

b

Step-by-step explanation:

Answer:

2nd one

Step-by-step explanation:

Answer:

b= infinity

Step-by-step explanation:

Because is b>1 than b can be 2, 3, 44, 100, 1000, 100000000213981623 and higher. There is no way to find the exact number though.

Answer:

21 millimeters

Step-by-step explanation:

ummmm yes

Answer:

25 because is the steep between card

Answer:

32

I hope this helps

Answer:

The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.

Step-by-step explanation:

To compare the intensities, we first need to convert the magnitudes to intensities using the log formula. Then we will set up a ratio to compare the intensities.

Convert the magnitudes to intensities and write them in exponential form.

R=logI

2011 earthquake:

9.1I=logI=109.1

2003 earthquake:

8.3I=logI=108.3

Form a ratio of the intensities.

intensity for 2011intensity for 2003

Substitute in the values and divide by subtracting the exponents to find

109.1108.3100.8≈6.

The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.

Your answer:

The intensity of the 2011 earthquake was about 15 times the intensity of the 2003 earthquake.

The intensities of the two earthquakes will be 6.3095.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

In 2011, Japan encountered a serious quake with an extent of 9.1 on the Richter scale. In 2003, Japan encountered another extraordinary seismic tremor that deliberate 8.3 on the Richter scale.

The intensity of the earthquake is given as,

㏒ (I₁ / I₂) = M₁ - M₂

㏒ (I₁ / I₂) = 9.1 - 8.3

Simplify the equation, then we have

㏒ (I₁ / I₂) = 9.1 - 8.3

㏒ (I₁ / I₂) = 0.8

Take anti log, then we have

(I₁ / I₂) = 6.3095

The intensities of the two earthquakes will be 6.3095.

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Answer:

-8

Step-by-step explanation:

I got 8 from my calculations so im sure thats the anwser

Answer:

The value of R is 0.7482.

Step-by-step explanation:

X Values

∑ = 35

Mean = 5

∑(X - Mx)2 = SSx = 68

Y Values

∑ = 34

Mean = 4.857

∑(Y - My)2 = SSy = 50.857

X and Y Combined

N = 7

∑(X - Mx)(Y - My) = 44

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 44 / √((68)(50.857)) = 0.7482

r = 0.7482

Sorry if I get this wrong Because not for sure how you need the awnsers I dont know if this is the right way

Mx: 5.000

My: 4.857

Sum: 68.000

Sum: 50.857

sum: 44.000

X Values

∑ = 35

Mean = 5

∑(X - Mx)2 = SSx = 68

Y Values

∑ = 34

Mean = 4.857

∑(Y - My)2 = SSy = 50.857

X and Y Combined

N = 7

∑(X - Mx)(Y - My) = 44

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 44 / √((68)(50.857)) = 0.7482

Meta Numerics (cross-check)

r = 0.7482

Answer:

top is -2,4 and bottom is 3,-2 ??

hope that what u need

Step-by-step explanation:

???

Answer:

A

Step-by-step explanation:

87.75-7.25=80.50

Answer:

A. 80.50

Step-by-step explanation:

Answer:

-3/4

Step-by-step explanation:

Get the coordinates of the two points and use the slope formula to find the slope.

We'll call the points point A and point B.

Point A's coordinates are (-3,1) and point B's coordinates are (1,-2)

Now, plug the numbers into the slope formula

Slope formula is: y2-y1/x2-x1

-2-1/1--3

-3/4

Answer:

12

Step-by-step explanation:

Step one:

given data

total players in the league

60

we are told that 20% are right-handed.

Required

The number of right-handed players

Step two:

=20/100*60

=0.2*60

=12

There are 12 right-handed players.

Answer:

30,000

Step-by-step explanation:

If she gets all 50 at 600 per month, 50x600 is 30,000.

I hope this helped!

17

2(1) + 3(5) = 2+15 = 17