Chứng minh các hàm số sau là liên tục tại mọi điểm x R 
a. f x x ( ) 6 3  
b. f x( ) = mx +b
c. Hãy nêu ý nghĩa của hàm liên tục trong kinh tế? Trình bày một vài ví dụ minh
họa?

Step-by-step explanation:

Any number that can be divided by 2 without having remainder is considered an even number.

I hope it helped U

stay safe stay happy

--------------------------------------------------

Just a correction, the characteristic roots of the equation are [tex]y = 7[/tex] and [tex]y = -\frac{1}{2}[/tex], thus, we should test for:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

--------------------------------------------------

Question a:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]

[tex]y^{\prime\prime} = 49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}[/tex]

[tex]2y^{\prime\prime} - 13y^{\prime} - 7y = 0[/tex]

[tex]2(49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}) - 13(7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}) - 7(Ae^{7x} + Be^{-\frac{x}{2}}) = 0[/tex]

[tex]98Ae^{-7x} + \frac{1}{2}Be^{\frac{x}{2}} - 91Ae^{-7x} + \frac{13}{2}e^{-\frac{x}{2}} - 7Ae^{7x} - 7Be^{-\frac{x}{2}} = 0[/tex]

[tex]98Ae^{-7x} - 91Ae^{-7x} - 7Be^{-\frac{x}{2}} + \frac{1}{2}Be^{\frac{x}{2}}  + \frac{13}{2}e^{-\frac{x}{2}} - 7Be^{-\frac{x}{2}} = 0[/tex]

[tex]0A + 0B = 0[/tex]

[tex]0 = 0[/tex], thus, we found the identity, and for each constant A and B, the following is a solution.

--------------------------------------------------

Question b:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

[tex]A + B = 3 \rightarrow B = 3 - A[/tex]

--------------------------------------------------

[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]

[tex]7A - \frac{1}{2}B = -5[/tex]

Using [tex]B = 3 - A[/tex]

[tex]7A - \frac{3}{2} + \frac{A}{2} = -5[/tex]

[tex]\frac{14A}{2} + \frac{A}{2} = -\frac{10}{2} + \frac{3}{2}[/tex]

[tex]\frac{15A}{2} = -\frac{7}{2}[/tex]

[tex]15A = -7[/tex]

[tex]A = -\frac{7}{15}[/tex]

--------------------------------------------------

Then, B is given by:

[tex]B = 3 - A = 3 - (-\frac{7}{15}) = \frac{45}{15} + \frac{7}{15} = \frac{52}{15}[/tex]

Thus, the values are: [tex]A = -\frac{7}{15}, B = \frac{52}{15}[/tex]

A similar problem is given at https://brainly.com/question/2456414

Answer: $ 39.60

Step-by-step explanation:

36 + (36*0.10) = 39.60

Let y = x + 22 and dy = dx, so the integral becomes

[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{25}^{31} \frac{\mathrm dy}{(y-1)\sqrt{y}}[/tex]

Now let z = √y, so that z ² = y. Then 2z dz = dy, and the integral becomes

[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{\sqrt{25}}^{\sqrt{31}} \frac{2z}{(z^2-1)z} \\\\ = \int_5^{\sqrt{31}} \frac{2}{z^2-1}\,\mathrm dz[/tex]

Expand the integrand into partial fractions:

[tex]\dfrac{2}{z^2-1} = \dfrac1{z-1}-\dfrac1{z+1}[/tex]

Then we have

[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_5^{\sqrt{31}}\left(\frac1{z-1}-\frac1{z+1}\right)\,\mathrm dz \\\\ = \left(\ln|z-1|-\ln|z+1|\right)\bigg|_5^{\sqrt{31}} \\\\ =\left[\ln\left|\frac{z-1}{z+1}\right|\right]\bigg|_5^{\sqrt{31}} \\\\ =\ln\left(\frac{\sqrt{31}-1}{\sqrt{31}+1}\right) - \ln\left(\frac{4}{6}\right) \\\\ =\ln\left(32-2\sqrt{31}\right) - \ln\left(\frac23\right) \\\\ =\boxed{\ln\left(48-3\sqrt{31}\right)}[/tex]

Answer:

B

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

D. This contains an x^2 and is called a parabola ( curved line like a U).

Answer:D

Step-by-step explanation: d is the correct answer

Answer:

A = 2025 ft^2

Step-by-step explanation:

The area of a square is given by

A = s^2 where s is the side length

A = 45^2

A = 2025 ft^2

Answer:

Step-by-step explanation:

The area of any square is s^2

s in this case is 45

Area = s^2

Area = 45 * 45

Area = 2025 m^2

Answer:

114 cm²

Step-by-step explanation:

Surface area of the rectangular prism,

2(wl+hl+hw)

=2×(3×8+3×8+3×3)

=2×(24+24+9)

=2×(57)

=114 cm²

Answer:

A=1024 yd.^2

Step-by-step explanation:

A=s^2

Substitute,

A=32^2

So,

A=1024 yd.^2

Answer:

1024 yd²

Step-by-step explanation:

Since it's a square, the side lengths will all be the same length. Due to this, you can square the given value to find the area.

A(Square) = 32² = 1024

Answer:

what is this sy man i dnt get it

Step-by-step explanation:

Answer:

9z-2y-3x

Step-by-step explanation:

(6z-4y+2x)+(3z-5x+2y)

Combine like terms

6z+3z-4y+2y+2x-5x

9z-2y-3x

Answer:

-3x - 2y + 9z

Step-by-step explanation:

Since you are adding two polynomials, the parentheses are unnecessary, so you can just drop them. Then combine like terms. Like terms are terms that have the same variable part such as 6z and 3z.

(6z - 4y + 2x) + (3z - 5x + 2y) =             Original problem.

= 6z - 4y + 2x + 3z - 5x + 2y                 Drop unnecessary parentheses.

= 2x - 5x - 4y + 2y + 6z + 3z                 Rearrange terms to group like terms.

= -3x - 2y + 9z                                        Combine each set of like terms.

Answer: -3x - 2y + 9z

Answer:

x = 50

Step-by-step explanation:

When two secants intersect in the interior of a circle, the angles formed are the average of the arc an angle and its vertical intercept. In this case, our angle, 73, should be the average of x and 96. We can translate this to an equation and solve:

[tex]\frac{x+96}{2} = 73[/tex]

x + 96 = 146

x = 50

Answer:

∠ A ≈ 79.0°

Step-by-step explanation:

Using the Cosine rule to find the angle

cosA = [tex]\frac{b^2+c^2-a^2}{2bc}[/tex]

        = [tex]\frac{15^2+29^2-30^2}{2(15)(29)}[/tex]

        = [tex]\frac{225+841-900}{870}[/tex]

        = [tex]\frac{166}{870}[/tex] , then

A = [tex]cos^{-1}[/tex] ([tex]\frac{166}{870}[/tex] ) ≈ 79.0° ( to the nearest tenth )

Answer:

2) - 12

3) - 1

4)y = 8

5)r = 4

6)x= -7/29

Hope it helps you

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  2^6 = 64

Step-by-step explanation:

Each hour the initial value (1) is multiplied by 2 (again). So the number of times 2 multiplies the initial value is the number of passing hours (t).

The number of cells after t hours is ...

  c(t) = 1×2^t = 2^t

After 6 hours, this is

  c(6) = 2^6 = 64 . . . . cells after 6 hours

_____

Additional comment

As you know, multiplication simplifies repeated addition.

  x + x + x = 3x

In a similar way, exponentiation simplifies repeated multiplication.

 x·x·x = x³ . . . . (written as x^3 in plain text)

In this problem, we're repeatedly multiplying by 2. After we do that t times, the initial value is multiplied by 2^t.

Answer: Volume is 4.19

Step-by-step explanation:

The equation for the volume of a cone is πr^2(h/3)

r = 1

h = 4

Fill in values into the equation

π(1)^2(4/3) = 4.19

Answer:

A square is a retangle

Step-by-step explanation:

Because a squre is a rectangle

Answer:

first choice..

first choice

Answer:

FIRST CHOISE FIRST CHOISE

Step-by-step explanation:

[tex]\\ \sf\longmapsto 10x=\dfrac{1}{0.001}[/tex]

[tex]\\ \sf\longmapsto 10x=\dfrac{1}{\dfrac{1}{1000}}[/tex]

[tex]\\ \sf\longmapsto 10x=1000[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{1000}{10}[/tex]

[tex]\\ \sf\longmapsto x=100[/tex]

We want to make a system of linear equations that would allow us to find the measure of the angles (we only want to find the system, not solving it)

Here we will find that we do not have a system of linear equations, we have:

s + t = 90°

t < 2*s

Here we have two complementary angles s and t.

Remember that two angles are complementary if their sum is equal to 90°, then we can write:

s + t = 90°

We also know that "t is less than twice s"

this can be written as:

t < 2*s

Notice that the above one is not an equation, is an inequality.

Then the system that we should use to

s + t = 90°

t < 2*s

If we want to force our system to be a system of linear equations, we can write:

s + t = 90°

t = 2*s

But naturally;

s + t = 90°

t < 2*s

has more solutions than:

s + t = 90°

t = 2*s

So we should not replace the inequality with an equation.

If you want to learn more, you can read:

https://brainly.com/question/9446123

Answer:

totally 16 numbers can be formed

It is hard and the condition of repeat of number should be clear if you have formula ( it is obvious to have) you can use that.

This is of Both

Range = Highest - Lowest data

Range = 45 - 10

Range = 35

Only A

Range = 45 - 10

Range = 35

Only B

Range = 40 - 15

Range = 25

Must click thanks and mark brainliest

Answer: 1,526.04 yd³ (this is what i got on my calculator others may vary use any rounding you need)

VOLUME of CONE is: V= Pir² h / 3

Pi= 3.14

r= 9

h= 18

V= (3.14) x (9)² x (18)

9²= 81

3.14 x 81= 254.34 x 18= 4,578.12

4,578.12 / 3= 1,526.04 <-- answer

Answer:

width: 3

Step-by-step explanation:

Given a length l and a width w, we can say that the perimeter is equal to

2 * l + 2 * w. Then, we also know that the perimeter is 27 plus its width, so

2 * l + 2 * w = 27 + w

and the length is 4 times its width, so length = 4 * width = l = 4 * w

We therefore have the two equations

2 * l + 2 * w = 27 + w

l = 4 * w

What we can do is plug 4* w for l in the first equation and solve from there. We thus have

2 * ( 4 * w) + 2 * w = 27 + w

8 * w + 2 * w = 27 + w

10 * w = 27 + w

subtract w from both sides to isolate the w and its coefficient

9 * w = 27

divide both sides by 9 to isolate w

w = 3

l = 4 * w = 12

Therefore, the width is 3 and the length is 12

Answer:

9

Step-by-step explanation:

use Tangent-chord formula for finding the arc knowing E

x=1/2n

4x+19=1/2n

n=8x+38

both arcs = 360

28x-2+8x+38=360

x=9

Answer:

16 once is the better one.

Answer: 12-ounce bag is better by $0.02 per ounce

Concept:

When coming across questions that ask for a comparison between prices, we should make the final unit [price per object].

In finding [price per object], simply do [Total price / number of objects].

Solve:

A 12-ounce bag of rice costs $4.08

Total price / number of objects = 4.08 / 12 = $0.34 per ounce

A 16-ounce bag of rice costs $5.76

Total price / number of objects = 5.76 / 16 = $0.36 per ounce

$0.36 - $0.34 = $0.02

$0.34 < $0.36, therefore, 12-ounce bag is better by $0.02 per ounce.

Hope this helps!! :)

Please let me know if you have any questions