If f(2) = 13 and f '(x) ≥ 2 for 2 ≤ x ≤ 7, how small can f(7) possibly be?​

Answer:

-2, - 1, - 2 and - 3

Step-by-step explanation:

As the graph depicts an odd function, it will follow the rule f(-x) = - f(x)

Answer:

240000

Step-by-step explanation:

Represent the exponential equation.

[tex]10000 (5 {t}^{ \frac{2}{3} } + 4) = [/tex]

Replace 8 with t

[tex]10000(5(8) {}^{ \frac{2}{3} } + 4)[/tex]

[tex]10000(5 \times 4 + 4) [/tex]

[tex]10000(24) = 240000[/tex]

The population of the town after 8 month will be 2,40,000.

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

Let P be the population of the town after 8 months

According to the given question

The current population of the town = 10,000.

Also, the population of the town is changing at the rate of [tex]4+5t^{\frac{2}{3} }[/tex].

Therefore, the population of the town after 8 month is given by the exponential function

[tex]P = 10000(4+5t^{\frac{2}{3} } )[/tex]

Substitute t =8 in the above equation

⇒[tex]P = 10000(4 + 5(8)^{\frac{2}{3} } )[/tex]

⇒[tex]P = 10000(4 + 5(2^{3}) ^{\frac{2}{3} } )[/tex]

⇒[tex]P = 10000(4+5(4))[/tex]

⇒[tex]P = 10000(24)[/tex]

⇒[tex]P = 240000[/tex]

Hence, the population of the town after 8 month will be 2,40,000.

Find out more information about exponential growth here:

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Answer:

4:10

Step-by-step explanation:

if they have to wait for plane B and it arrives every 10 mins then 4:10 is the anser

9514 1404 393

Answer:

  64.1 ft²

Step-by-step explanation:

The area of the cone is given by ...

  A = πr(r +h) . . . . for radius r and slant height h

  A = π(2 ft)(2 ft +8.2 ft) ≈ 64.1 ft²

Answer:

2x^2+4x-16

Step-by-step explanation:

The quadratic can be written as

f(x) = a(x-z1)(x-z2) where z1 and z2 are the roots

f(x) = a (x-2)(x- -4)

a is the leading coefficient

f(x) = 2(x-2)(x+4)

     = 2(x^2 -2x+4x-8)

     = 2(x^2 +2x-8)

     = 2x^2 +4x-16

Answer:

28

Step-by-step explanation:

5 : 2

since this is a simplified ratio, they have a common factor. let's say it is 'x'

so now :

5x : 2x

we know that 5x is lilies, and we also know that she has 20 lilies, so:

5x = 20

x = 4

the daisies would be 2x so 2*4 = 8

total flowers is 20 + 8

28

Answer:

No, -12 is not a solution.

Step-by-step explanation:

8u-1=6u

8(-12)-1=6(-12)

-96-1=-72

-97=-72

Untrue, to it’s not a solution

Answer:

let us do one night

Step-by-step explanation:

Agg-77182882

(#(+2+

Answer:

c) The less than symbol should be replaced with the less than or equal to symbol.

Step-by-step explanation:

3(-4 - n/-2) < 5

The equation written above could be interpreted as :

The product of 3 and the difference of -4 and the quotient of a number, n and -2 is less than 5

This means that the only error in Maddison's representation is the inequality sign, the inequality sign used by Maddison is wrong.

The equation should be used with a ≤ sign and expressed thus :

3(-4 - n/-2) ≤ 5

This means the left hand side (L. H. S) is less than or equal to 5 ; this means the L. H. S is at most 5

Answer:

C

Step-by-step explanation:

Answer:

x = 960

Step-by-step explanation:

x=√{576×(576+1024)}

or, x = √(576×1600)

or, x = √576×√1600

or, x = 24×40

or, x = 960

Answered by GAUTHMATH

Answer:

Step-by-step explanation:

Answer:

The maximum value of f(x) occurs at:

[tex]\displaystyle x = \frac{2a}{a+b}[/tex]

And is given by:

[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are given the function:

[tex]\displaystyle f(x) = x^a (2-x)^b \text{ where } a, b >0[/tex]

And we want to find the maximum value of f(x) on the interval [0, 2].

First, let's evaluate the endpoints of the interval:

[tex]\displaystyle f(0) = (0)^a(2-(0))^b = 0[/tex]

And:

[tex]\displaystyle f(2) = (2)^a(2-(2))^b = 0[/tex]

Recall that extrema occurs at a function's critical points. The critical points of a function at the points where its derivative is either zero or undefined. Thus, find the derivative of the function:

[tex]\displaystyle f'(x) = \frac{d}{dx} \left[ x^a\left(2-x\right)^b\right][/tex]

By the Product Rule:

[tex]\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[x^a\right] (2-x)^b + x^a\frac{d}{dx}\left[(2-x)^b\right]\\ \\ &=\left(ax^{a-1}\right)\left(2-x\right)^b + x^a\left(b(2-x)^{b-1}\cdot -1\right) \\ \\ &= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right] \end{aligned}[/tex]

Set the derivative equal to zero and solve for x:

[tex]\displaystyle 0= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right][/tex]

By the Zero Product Property:

[tex]\displaystyle x^a (2-x)^b = 0\text{ or } \frac{a}{x} - \frac{b}{2-x} = 0[/tex]

The solutions to the first equation are x = 0 and x = 2.

First, for the second equation, note that it is undefined when x = 0 and x = 2.

To solve for x, we can multiply both sides by the denominators.

[tex]\displaystyle\left( \frac{a}{x} - \frac{b}{2-x} \right)\left((x(2-x)\right) = 0(x(2-x))[/tex]

Simplify:

[tex]\displaystyle a(2-x) - b(x) = 0[/tex]

And solve for x:

[tex]\displaystyle \begin{aligned} 2a-ax-bx &= 0 \\ 2a &= ax+bx \\ 2a&= x(a+b) \\ \frac{2a}{a+b} &= x \end{aligned}[/tex]

So, our critical points are:

[tex]\displaystyle x = 0 , 2 , \text{ and } \frac{2a}{a+b}[/tex]

We already know that f(0) = f(2) = 0.

For the third point, we can see that:

[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(2- \frac{2a}{a+b}\right)^b[/tex]

This can be simplified to:

[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]

Since a and b > 0, both factors must be positive. Thus, f(2a / (a + b)) > 0. So, this must be the maximum value.

To confirm that this is indeed a maximum, we can select values to test. Let a = 2 and b = 3. Then:

[tex]\displaystyle f'(x) = x^2(2-x)^3\left(\frac{2}{x} - \frac{3}{2-x}\right)[/tex]

The critical point will be at:

[tex]\displaystyle x= \frac{2(2)}{(2)+(3)} = \frac{4}{5}=0.8[/tex]

Testing x = 0.5 and x = 1 yields that:

[tex]\displaystyle f'(0.5) >0\text{ and } f'(1) <0[/tex]

Since the derivative is positive and then negative, we can conclude that the point is indeed a maximum.

Therefore, the maximum value of f(x) occurs at:

[tex]\displaystyle x = \frac{2a}{a+b}[/tex]

And is given by:

[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]

Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.

g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]

Option C

Hope this helps!

Answer: The area is 22 17/64.

Step-by-step explanation:

base = 7 1/8 = 57/8

height = 6 1/4 = 25/4

area = 1/2*b*h

= 1/2*57/8*25/4

= 1425/64

= 22 17/64

The plane you want is parallel to another plane, x - y + z = -5, so they share a normal vector. In this case, it's ⟨1, -1, 1⟩.

The plane must also pass through the point (0, 4, 4) since it contains r(t). Then the equation of the plane is

⟨x, y - 4, z - 4⟩ • ⟨1, -1, 1⟩ = 0

x - (y - 4) + (z - 4) = 0

x - y + z = 0

Answer:

15km

Step-by-step explanation:

hope it is well understood?

Answer:

5 times.

Step-by-step explanation:

First, look at the values of each line at the 1-hour mark.

For line A (the bicyclist), the distance is about 25 km.

For line B (the pedestrian), the distance is about 5 km.

To determine how many times greater the bicyclist distance is than the pedestrian, divide the values:

[tex]\frac{25\text{km}}{5\text{km}}=5[/tex]

Therefore, the distance covered by the bicyclist for 1 hour is 5 times greater than the distance covered by the pedestrian for the same amount of time.

Answer:

2dollars

Step-by-step explanation:

one bag of popcorn is 4 dollars so 4 bags of popcorn is 16 plus 1 drink which is 2 dollars equal 18.

The cost of each popcorn is $4 and the cost of each drink will be $2.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

If two bags of popcorn and three drinks cost $14, and four bags of popcorn and one drink costs $18.

Let the cost of each popcorn be 'x' and the cost of each drink be 'y'. Then the equations are given as,

2x + 3y = 14           ...1

4x + y = 18            ...2

From equations 1 and 2, then we have

2x + 3(18 - 4x) = 14

2x + 54 - 12x = 14

10x = 40

x = $4

Then the value of the variable 'y' is calculated as,

y = 18 - 4(4)

y = 18 - 16

y = $2

The cost of each popcorn is $4 and the cost of each drink will be $2.

More about the solution of the equation link is given below.

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Answer:

Step-by-step explanation:

I honestly have no idea what you mean by answer by formula, but I'm going to give it my best. I began by squaring both sides to get:

(a² - b²) tan²θ = b² and then distributed to get:

a² tan²θ - b² tan²θ = b² and then got the b terms on the side to get:

a² tan²θ = b² + b² tan²θ and then changed the tans to sin/cos to get:

[tex]\frac{a^2sin^2\theta}{cos^2\theta}=b^2+\frac{b^2sin^2\theta}{cos^2\theta}[/tex] and isolated the sin-squared on the left to get:

[tex]a^2sin^2\theta=cos^2\theta(b^2+\frac{b^2sin^2\theta}{cos^2\theta})[/tex] and distributed to get:

***[tex]a^2sin^2\theta=b^2cos^2\theta+b^2sin^2\theta[/tex]*** and factored the right side to get:

[tex]a^2sin^2\theta=b^2(sin^2\theta+cos^2\theta)[/tex] and utilized a trig Pythagorean identity to get:

[tex]a^2sin^2\theta=b^2(1)[/tex] and then solved for sinθ in the following way:

[tex]sin^2\theta=\frac{b^2}{a^2}[/tex] so

[tex]sin\theta=\frac{b}{a}[/tex] This, along with the *** expression above will be important. I'm picking up at the *** to solve for cosθ:

[tex]a^2sin^2\theta=b^2cos^2\theta+b^2sin^2\theta[/tex] and get the cos²θ alone on the right by subtracting to get:

[tex]a^2sin^2\theta-b^2sin^2\theta=b^2cos^2\theta[/tex] and divide by b² to get:

[tex]\frac{a^2sin^2\theta}{b^2}-sin^2\theta=cos^2\theta[/tex] and factor on the left to get:

[tex]sin^2\theta(\frac{a^2}{b^2}-1)=cos^2\theta[/tex] and take the square root of both sides to get:

[tex]\sqrt{sin^2\theta(\frac{a^2}{b^2}-1) }=cos\theta[/tex] and simplify to get:

[tex]\frac{sin\theta}{b}\sqrt{a^2-b^2}=cos\theta[/tex] and go back to the identity we found for sinθ and sub it in to get:

[tex]\frac{\frac{b}{a} }{b}\sqrt{a^2-b^2}=cos\theta[/tex] and simplifying a bit gives us:

[tex]\frac{1}{a}\sqrt{a^2-b^2}=cos\theta[/tex]

That's my spin on things....not sure if it's what you were looking for. If not.....YIKES

Answer:

The probability of making a correct random guess is 0.00053%.

Step-by-step explanation:

Since Clue is a board game in which you must deduce three details surrounding a murder, and in the original game of Clue, the guilty person can be chosen from 66 people, and there are 66 different possible weapons and 99 possible rooms, and at one point in the game, you have narrowed the possibilities down to 44 people, 55 weapons, and 77 rooms, to determine what is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices , and the guess being correct, the following calculation must be performed:

(1 / (44x55x77)) x 100 = X

(1 / 186,340) x 100 = X

0.0005366 = X

Therefore, the probability of making a correct random guess is 0.00053%.

9514 1404 393

Answer:

  the yield in year 0

Step-by-step explanation:

The y-value is the yield for farms in France in year x. The y-value when x=0 is the yield for farms in France in year 0.

_____

Additional comment

The reasonable domain for this function is approximately 1843 ≤ x ≤ 2186. The function is effectively undefined for values of x outside this domain, so the y-intercept is meaningless by itself.

Answer:

36/39

Step-by-step explanation:

Cos(theta) = Base/Hypotenuse

Cos(X) = 36/39

Answer:

y=9/4x+4

Step-by-step explanation:

Start by finding the slope

m=(-5-4)/(-4-0)

m=-9/-4 = 9/4

next plug the slope and the point (-4,-5) into point slope formula

y-y1=m(x-x1)

y1=-5

x1= -4

m=9/4

y- -5 = 9/4(x - -4)

y+5=9/4(x+4)

Distribute 9/4 first

y+5=9/4x + 9

subtract 5 on both sides

y=9/4x+4

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

I have uploaded a graph for you. The x axis is the number of years. The y axis is the salary multiplied by 1000. I should have made the multiplication factor 10000 but 1000 will do.

The 5 given points are plotted in red. The blue line is the function.

The function is y = 5x + 35. That means for every year you add 5 times the year onto the salary.

No years is 35000

1 year is 1 * 5000 + 35000

2 years is 2 * 5000 + 35000 = 45000

6 years is 5 * 5000 * 35000 = 65000

and so on.

The point you want is x = 12

12 years is 12 * 5000 + 35000 = 95000

Forgot the graph

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Answer:

  5, 10, 20

Step-by-step explanation:

Suppose the three numbers are x, 2x, and 4x. Then they have the required ratios. After the transformation, we have ...

  ((x+3) +(4x -8))/2 = 2x . . . . . 2nd term is average of 1st and 3rd

  5x -5 = 4x   ⇒   x = 5

The original numbers are 5, 10, 20.

_____

After the adjustment, the arithmetic sequence is 8, 10, 12.

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Answer:

  see attached

Step-by-step explanation:

(a) The graph is scaled by a factor of 2, and shifted up 1 unit. The scaling moves each point away from the x-axis by a factor of 2. The points on the x-axis stay there. The translation moves that scaled figure up 1 unit.

__

(b) The graph is reflected across the x-axis and shifted right 4 units. The point on the x-axis stays on the x-axis.

Answer:

c  

Step-by-step explanation:

Answer:

the correct choice is B

Step-by-step explanation:

Answer:

$240,300

Step-by-step explanation:

Given :

Overhead cost :

Computer support = $267000

legal support = $133500

Overheads applied to audit services = (Number of CPU minutes used by Audit services * activity rate per CPU minute)

+

(number of legal hours used by Audit services * activity rate per legal hour)

The overhead applied to audit is thus :

40,000 * (267,000 / (40,000 + 10,000)) +

200 * (133500 / (200 + 800)

(40000 * 5.34) + (200 * 133.5)

= $240,300

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Answer:

  $442.80

Step-by-step explanation:

The formula for the amount of an ordinary annuity is ...

  A = P(12/r)((1 +r/12)^(12t) -1)

where payment P is made n times per year and interest is accrued at annual rate r.

Filling in the given values, we want ...

  50,000 = P(12/0.04)(1 +0.04/12)^(12·8) -1) = 112.91854P

  P = 50,000/112.91854 ≈ 442.80

You would need to deposit $442.80 each month for 8 years.