Find the derivative of f(x) = 6/x at x = -2. (2 points)

Answer:

The two substances will have the same volume after approximately 3.453 hours.

Step-by-step explanation:

The volume of substance A (measured in cubic centimeters) increases at a rate represented by the equation:

[tex]\displaystyle \frac{dA}{dt} = 0.3 A[/tex]

Where t is measured in hours.

And substance B is represented by the equation:

[tex]\displaystyle \frac{dB}{dt} = 1[/tex]

We are also given that at t = 0, A(0) = 3 and B(0) = 5.

And we want to find the time(s) t for which both A and B will have the same volume.  

You are correct in that B(t) is indeed t + 5. The trick here is to multiply both sides by dt. This yields:

[tex]\displaystyle dB = 1 dt[/tex]

Now, we can take the integral of both sides:

[tex]\displaystyle \int 1 \, dB = \int 1 \, dt[/tex]

Integrate. Remember the constant of integration!

[tex]\displaystyle B(t) = t + C[/tex]

Since B(0) = 5:

[tex]\displaystyle B(0) = 5 = (0) + C \Rightarrow C = 5[/tex]

Hence:

[tex]B(t) = t + 5[/tex]

We can apply the same method to substance A. This yields:

[tex]\displaystyle dA = 0.3A \, dt[/tex]

We will have to divide both sides by A:

[tex]\displaystyle \frac{1}{A}\, dA = 0.3\, dt[/tex]

Now, we can take the integral of both sides:

[tex]\displaystyle \int \frac{1}{A} \, dA = \int 0.3\, dt[/tex]

Integrate:

[tex]\displaystyle \ln|A| = 0.3 t + C[/tex]

Raise both sides to e:

[tex]\displaystyle e^{\ln |A|} = e^{0.3t + C}[/tex]

Simplify:

[tex]\displaystyle |A| = e^{0.3t} \cdot e^C = Ce^{0.3t}[/tex]

Note that since C is an arbitrary constant, e raised to C will also be an arbitrary constant.

By definition:

[tex]\displaystyle A(t) = \pm C e^{0.3t} = Ce^{0.3t}[/tex]

Since A(0) = 3:

[tex]\displaystyle A(0) = 3 = Ce^{0.3(0)} \Rightarrow C = 3[/tex]

Therefore, the growth model of substance A is:

[tex]A(t) = 3e^{0.3t}[/tex]

To find the time(s) for which both substances will have the same volume, we can set the two functions equal to each other:

[tex]\displaystyle A(t) = B(t)[/tex]

Substitute:

[tex]\displaystyle 3e^{0.3t} = t + 5[/tex]

Using a graphing calculator, we can see that the intersect twice: at t ≈ -4.131 and again at t ≈ 3.453.

Since time cannot be negative, we can ignore the first solution.

In conclusion, the two substances will have the same volume after approximately 3.453 hours.

Answer:

8.49

Step-by-step explanation:

there is a little formula related to the famous formula of Pythagoras.

it says that the height of a triangle is the square root of the product of both segments of the baseline (the segments the height splits the baseline into).

so, x is actuality the height of the triangle.

x = sqrt(3×24) = sqrt(72) = 8.49

Answer:

535 students passed and 107 students failed

Step-by-step explanation:

Create a system of equations where p is the number of students who passed and f is the number of students who failed:

p + f = 642

p = 5f

Solve by substitution by plugging in 5f as p into the first equation, then solving for f:

p + f = 642

5f + f = 642

6f = 642

f = 107

So, 107 students failed.

Find how many students passed by multiplying this by 5:

107(5)

= 535

535 students passed and 107 students failed.

Answer:

x=4sqrt3 a=4 b=3  ,y=8sqrt3 c=8 d=3

Step-by-step explanation:

because this is a 30-60-90 triangle, it is easy to find the side lengths. the longer leg is sqrt(3) times the shorter leg so x= 12/sqrt(3) or 4sqrt(3). the hypotenuse is 2 times the shorter leg so y= 8sqrt(3)

Suppose there is a function f(x), the definite integral of the function is the difference between the upper and lower x-values.

There are three relationships between the definite integral and the area of the region. The relationships are:

Positive function

The area between the function itself and the x-axis represents the definite integral.

Negative function

The area between the function itself and the x-axis, multiplied by -1 represents the definite integral.

Region between two functions

The definite integral of the function is the difference between the region of both functions.

See attachment for further illustration

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[tex]\\ \sf\longmapsto (m-8)+(m-8)+(m-8)+(m-8)+(m-8)+(m-8)=12[/tex]

[tex]\\ \sf\longmapsto 6(m-8)=12[/tex]

[tex]\\ \sf\longmapsto 6m-48=12[/tex]

[tex]\\ \sf\longmapsto 6m=12+48[/tex]

[tex]\\ \sf\longmapsto 6m=60[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{60}{6}[/tex]

[tex]\\ \sf\longmapsto m=10[/tex]

Answer:

M=14

Step-by-step explanation:

Answer:

9--7

Step-by-step explanation:

Answer:

Step-by-step explanation:

The idea here is to find the area of the circle and then subtract from it the area of the triangle. That will give you the area of what's left in the circle (the shaded part). The area of a circle is:

[tex]A_c=\pi r^2[/tex] so

[tex]A_c=(3.14)(12.4)^2[/tex]   where 12.4 is the radius.

[tex]A_c=482.81[/tex] rounded to the nearest tenth. I used 3.14 for pi.

Now for the area of the triangle. The formula is

[tex]A_t=\frac{1}{2}bh[/tex] where h is the height of 12.4 and the base is the diameter which is 12.4 * 2 = 24.8

[tex]A_t=\frac{1}{2}(24.8)(12.4)[/tex] so

[tex]A_t=153.76[/tex]

Now subtract the triangle's area from the circle's area:

482.81 - 153.76 = 329.05 mm²

Answer:

this is the answer of this question

hoping it will help u

Answer:

16 units

Step-by-step explanation:

period = length of an interval that contains exactly one copy of the repeating pattern, so from one peak to another peak.

in this graph its the peaks are 1 and 17, hence the period is 16

Answer:

c

Step-by-step explanation:

-7.5 is less than 6.5

Answer:

fohohcoufohohcouvhop

Step-by-step explanation:

typing mistake sorry

[tex]\\ \sf\longmapsto x+73=90[/tex]

[tex]\\ \sf\longmapsto x=90-73[/tex]

[tex]\\ \sf\longmapsto x=17[/tex]

Why?

Sum of two complementary angles is 90°

Answer:

l = 2, m = - 1, n = - 6

Step-by-step explanation:

A scalar matrix has its diagonal elements equal and all other elements zero, so

2l - 4 = 0 ( add 4 to both sides )

2l = 4 ( divide both sides by 2 )

l = 2

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

3l + n = 0

3(2) + n = 0

6 + n = 0 ( subtract 6 from both sides )

n = - 6

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

3m - n = 3

3m - (- 6) = 3

3m + 6 = 3 ( subtract 6 from both sides )

3m = - 3 ( divide both sides by m )

m = - 1

Answer:

If the concavity of f changes at a point (c,f(c)), then f′ is changing from increasing to decreasing (or, decreasing to increasing) at x=c. That means that the sign of f″ is changing from positive to negative (or, negative to positive) at x=c. This leads to the following theorem

Step-by-step explanation:

The previous section showed how the first derivative of a function,  f′ , can relay important information about  f . We now apply the same technique to  f′  itself, and learn what this tells us about  f . The key to studying  f′  is to consider its derivative, namely  f′′ , which is the second derivative of  f . When  f′′>0 ,  f′  is increasing. When  f′′<0 ,  f′  is decreasing.  f′  has relative maxima and minima where  f′′=0  or is undefined. This section explores how knowing information about  f′′

Let  f  be differentiable on an interval  I . The graph of  f  is concave up on  I  if  f′  is increasing. The graph of  f  is concave down on  I  if  f′  is decreasing. If  f′  is constant then the graph of  f  is said to have no concavity.

Note: We often state that " f  is concave up" instead of "the graph of  f  is concave up" for simplicity.

The graph of a function  f  is concave up when  f′  is increasing. That means as one looks at a concave up graph from left to right, the slopes of the tangent lines will be increasing. Consider Figure  3.4.1 , where a concave up graph is shown along with some tangent lines. Notice how the tangent line on the left is steep, downward, corresponding to a small value of  f′ . On the right, the tangent line is steep, upward, corresponding to a large value of  f′ .

Answer:

This type of study is called a simulation

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

(y^(4))^(1/5)=y^(4/5)

Answer:

idea how to tell your loved one how you feel? How about a love song?

Answer:

This would be a regular polygon.

Step-by-step explanation:

A regular polygon has congruent sides and interior angles.

An irregular polygon does not have congruent sides and all interior angles.

A convex polygon does not have a interior angle greater than 180°.

Lastly, a concave polygon has only one interior angle greater than 180°.

Using the process of elimination, it would not be a convex or concave polygon. Now we have either a regular or irregular polygon. This polygon can not be a irregular polygon because all the sides are congruent. This means that this polygon is a regular polygon!

The given polygon is a regular convex polygon.

In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain (or polygonal circuit). The bounded plane region, the bounding circuit, or the two together, may be called a polygon.

The segments of a polygonal circuit are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. The interior of a solid polygon is sometimes called its body.

Given,

Polygon has 8 edges and 8 vertices.

1. Regular or Irregular:

A regular polygon has congruent sides and interior angles.

In the figure all sides are of equal length and the angle are same so, It is a regular polygon.

2. Convex or concave:

Convex polygon has all interior angles less than 180° while in concave polygon at least one interior angle should be greater than 180°.

In the given polygon all angles are less than 180°, so it is a convex polygon.

Hence, by the above explanation, the given polygon is regular convex polygon.

Learn more about polygons here:

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#SPJ2

Step-by-step explanation:

Answer in attached picture...

hope it helps

Answer:

–10m4n3 + 8m2n6 + 3m4n3 – 2m2n6 – 6m2n6 = -7m4n3

⇒It is a monomial with a degree of 7 is correct

Step-by-step explanation:

Answer:

i think its all real numbers

Step-by-step explanation:

i think!! im not so sure

Answer:

4

Step-by-step explanation:

64^1/3

cube root of 64 is

4

Answer:

C

Step-by-step explanation:

Using the rule of exponents

[tex]a^{\frac{1}{3} }[/tex] ⇔ [tex]\sqrt[3]{a}[/tex] , then

[tex]64^{\frac{1}{3} }[/tex] = [tex]\sqrt[3]{64}[/tex] = 4 → C

Let numerator be x

ATQ

[tex]\\ \sf\longmapsto x+x+2=12[/tex]

[tex]\\ \sf\longmapsto 2x+2=12[/tex]

[tex]\\ \sf\longmapsto 2x=12-2[/tex]

[tex]\\ \sf\longmapsto 2x=10[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{10}{2}[/tex]

[tex]\\ \sf\longmapsto x=5[/tex]

Now the fraction is

[tex]\\ \sf\longmapsto \dfrac{x}{x+2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{5}{5+2}[/tex]

[tex]\\ \sf\longmapsto \dfrac{5}{7}[/tex]

-- Their sum is 12.

-- If they were equal, each would be 6.

-- To make them differ by 2 without changing their sum, move 1 from the numerator (make it 5), to the denominator (make it 7).

Answer:

x = 3

y = 2

Step-by-step explanation:

3x - y = 7   ------------(i)

2x - 2y = 2 ---------(ii)

Multiply equation (i) by (-2)

(i)*(-2)          - 6x + 2y = -14

(ii)                 2x  - 2y =2     {Add both equation. now y will be eliminated}

                    -4x         = -12          {Divide both sides by -4}

                             x = -12/-4

x = 3

Plug in x = 3 in equation (i)

2*3 - 2y = 2

6 - 2y = 2    

Subtract 6 from both sides

 -2y = 2 - 6

  -2y = -4

Divide both sides by 2

      y = -4/-2

y = 2

Answer:

x = 3, y = 2

Step-by-step explanation:

Given the 2 equations

3x - y = 7 → (1)

2x - 2y = 2 → (2)

Multiplying (1) by - 2 and adding to (2) will eliminate the y- term

- 6x + 2y = - 14 → (3)

Add (2) and (3) term by term to eliminate y

- 4x + 0 = - 12

- 4x = - 12 ( divide both sides by - 4 )

x = 3

Substitute x = 3 into either of the 2 equations and solve for y

Substituting into (1)

3(3) - y = 7

9 - y = 7 ( subtract 9 from both sides )

- y = - 2 ( multiply both sides by - 1 )

y = 2

solution is (3, 2 )

Step-by-step explanation:

5.

[tex](5 + 4 \sqrt{7} ){x}^{2} + (4 - 2 \sqrt{7} ) x- 1 = 0[/tex]

Simplify both radicals.

[tex](5 + \sqrt{112) {x}^{2} } + (4 - \sqrt{28} )x - 1 = 0[/tex]

Apply Quadratic Formula

First. find the discramnint.

[tex](4 - \sqrt{28} ) {}^{2} - 4(5 + \sqrt{112} )( - 1) = 64[/tex]

Now find the divisor 2a.

[tex]2(5 + \sqrt{112} ) = 10 + 8 \sqrt{7} [/tex]

Then,take the square root of the discrimant.

[tex] \sqrt{64} = 8[/tex]

Finally, add -b.

[tex] - (4 + 2 \sqrt{7} )[/tex]

So our possible root is

[tex] - (4 + 2 \sqrt{7} ) + \frac{8}{10 + 8 \sqrt{7} } [/tex]

Which simplified gives us

[tex] \frac{ 4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } [/tex]

Rationalize the denominator.

[tex] \frac{4 + 2 \sqrt{7} }{10 + 8 \sqrt{7} } \times \frac{10 - 8 \sqrt{7} }{10 - 8 \sqrt{7} } = \frac{ - 72 - 12 \sqrt{7} }{ - 348} [/tex]

Which simplified gives us

[tex] \frac{6 + \sqrt{7} }{29} [/tex].

6. The answer is 2.

9514 1404 393

Answer:

  5. x = (6 +√7)/29; a=6, b=1, c=29

  6. x = 2

Step-by-step explanation:

The quadratic formula can be used, where a=(5+4√7), b=(4-2√7), c=-1.

  [tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-(4-2\sqrt{7})+\sqrt{(4-2\sqrt{7})^2-4(5+4\sqrt{7}})(-1)}{2(5+4\sqrt{7})}\\\\=\dfrac{-4+2\sqrt{7}+\sqrt{16-16\sqrt{7}+28+20+16\sqrt{7}}}{10+8\sqrt{7}}=\dfrac{4+2\sqrt{7}}{2(5+4\sqrt{7})}\\\\=\dfrac{(2+\sqrt{7})(5-4\sqrt{7})}{(5+4\sqrt{7})(5-4\sqrt{7})}=\dfrac{10-3\sqrt{7}-28}{25-112}=\boxed{\dfrac{6+\sqrt{7}}{29}}[/tex]

__

Use the substitution z=3^x to put the equation in the form ...

  z² -3z -54 = 0

  (z -9)(z +6) = 0 . . . . . factor

  z = 9 or -6 . . . . . . . . value of z that make the factors zero

Only the positive solution is useful, since 3^x cannot be negative.

  z = 9 = 3^2 = 3^x . . . . use the value of z to find x

  x = 2

Answer:

AED 972

Step-by-step explanation:

Area of the wall = 9² = 81 m²

each m² costs AED 12

so 81 m² will cost 12×81 = AED 972

Answer:

1. Given

2. Def of Vertical Angles

3. Alternate Interior Angles

4. Def of Vertical angles

5. Opposite exterior angles

Step-by-step explanation: