Compare 8/3 and 19/8.

First, find the inverse of f,

[tex]y=e^x[/tex]

[tex]x=e^y[/tex]

Now take the natural logarithm on both sides,

[tex]\ln x=\ln e^y\implies f^{-1}(x)=\boxed{\ln(x)}[/tex]

Second, find the inverse of g,

[tex]y=5x\implies g^{-1}(x)=\boxed{\frac{x}{5}}[/tex]

Now take their composition,

[tex](g\circ f)(x)=g(f(x))=\frac{\ln(x)}{5}[/tex]

Let [tex]y=\frac{\ln(x)}{5}[/tex], now again find the inverse,

[tex]x=\frac{\ln(y)}{5}[/tex]

[tex]5x=\ln y[/tex]

exponentiate both sides to base e,

[tex]e^{5x}=e^{\ln y}\implies (g\circ f)^{-1}(x)=\boxed{e^{5x}}[/tex]

Hope this helps :)

Answer:

[tex]\displaystyle y' = \frac{5x - 2xy^2}{2y(x^2 - 3y)}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Product Rule]:                                                                             [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Implicit Differentiation

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle 5x^2 - 2x^2y^2 + 4y^3 - 7 = 0[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Book: College Calculus 10e

Answer:

The price that maximizes the revenue is $165

Step-by-step explanation:

We can model the price as a function of sold units as a linear relationship.

Remember that a linear relationship is something like:

y = a*x + b

where a is the slope and b is the y-intercept.

We know that if the line passes through the points (x₁, y₁) and (x₂, y₂), then the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

For this line, we have the point (40, $110)

which means that to sell 40 units, the price must be $110

And we know that if the price increases by $11, then he will sell 2 units less.

Then we also have the point (38, $121)

So we know that our line passes through the points (40, $110) and  (38, $121)

Then the slope of the line is:

a = ($121 - $110)/(38 - 40) = $11/-2 = -$5.5

Then the equation of the line is:

p(x) = -$5.5*x + b

to find the value of b, we can use the point (40, $110)

This means that when x = 40, the price is $110

then:

p(40) = $110 = -$5.5*40 + b

            $110 = -$220 + b

       $110 + $220 = b

        $330 = b

Then the price equation is:

p(x) = -$5.5*x + $330

Now we want to find the maximum revenue.

The revenue for selling x items, each at the price p(x), is:

revenue = x*p(x)

replacing the p(x) by the equation we get:

revenue = x*(-$5.5*x + $330)

revenue = -$5.5*x^2 + $330*x

Now we want to find the x-value for the maximum revenue.

You can see that the revenue equation is a quadratic equation with a negative leading coefficient. This means that the maximum is at the vertex.

And remember that for a quadratic equation like:

y = a*x^2 + b*x + c

the x-value of the vertex is:

x = -b/2a

Then for our equation:

revenue = -$5.5*x^2 + $330*x

the x-vale of the vertex will be:

x = -$330/(2*-$5.5) = 30

x = 30

This means that the revenue is maximized when we sell 30 units.

And the price is p(x) evaluated in x = 30

p(30) = -$5.5*30 + $330 = $165

The price that maximizes the revenue is $165

Answer:

b) Y =5.73X +4.36

C)  =5.73225*(21)X +4.359

    124.73625

D) 163.728 = 5.73X +4.36  

     X = (163.728 - 4.36)/5.73

     X = 27.81291449

  Year would be 2027

Step-by-step explanation:

x1 y1  x2 y2

4 27.288  16 96.075

(Y2-Y1) (96.075)-(27.288)=   68.787  ΔY 68.787

(X2-X1) (16)-(4)=    12  ΔX 12

slope= 5 41/56    

B= 4 14/39    

Y =5.73X +4.36      

Answer:

D.

Step-by-step explanation:

2=-2，3=-3

2²=-2²，3²=3²

Answer:

The answer is a.

The equation of the reflected function across the y-axis is g(x) = -4x - 8.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function f(x) = 4x - 8 is reflected across the y-axis.

The function g(x) will be given by putting the negative x in place of x. Then the reflected function is obtained.

g(x) = -4x - 8

Then the equation of the reflected function across the y-axis is g(x) = -4x - 8.

The graph of the reflected graph is given below.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ2

Answer:

[tex]56[/tex] choices

Step-by-step explanation:

We know that we'll have to solve this problem with a permutation or a combination, but which one do we use? The answer is a combination because the order in which the child picks the candy does not matter.

To further demonstrate this, imagine I have 4 pieces of candy labeled A, B, C, and D. I could choose A, then C, then B or I could choose C, then B, then A, but in the end, I still have the same pieces, regardless of what order I pick them in. I hope that helps to understand why this problem will be solved with a combination.

Anyways, back to the solving! Remember that the combination formula is

[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex], where n is the number of objects in the sample (the number of objects you choose from) and r is the number of objects that are to be chosen.

In this case, [tex]n=8[/tex] and [tex]r=3[/tex]. Substituting these values into the formula gives us:

[tex]_8C_3=\frac{8!}{3!5!}[/tex]

[tex]= \frac{8*7*6*5*4*3*2*1}{3*2*1*5*4*3*2*1}[/tex] (Expand the factorials)

[tex]=\frac{8*7*6}{3*2*1}[/tex] (Cancel out [tex]5*4*3*2*1[/tex])

[tex]=\frac{8*7*6}{6}[/tex] (Evaluate denominator)

[tex]=8*7[/tex] (Cancel out [tex]6[/tex])

[tex]=56[/tex]

Therefore, the child has [tex]\bf56[/tex] different ways to pick the candies. Hope this helps!

Answer:

sir she hey Jen Jen Jenn receive surge

Answer:

Hello,

Step-by-step explanation:

z=0.7734

p(z<?)=0.75 ==> ?=0.7734

Answer:

1.5

Step-by-step explanation:

Let the first term be a and the common ratio be r

ATQ, ar=50 and ar^3=112.5, divide these two. r^2=2.25, r=1.5

Answer:40, 80 and 62

Step-by-step explanation:

182-22= 160

160/4 = 40 so,

Shortest side is 40

Longest is 80

Third side is 62

Answer:

12. We use Rational numbers when the number is in P/q form

we don't use integers because they are not in p/q form

13.  Aron is wrong . he is not correct

an opposite of rational number can out be  negative it should be irrational number

opposite of integers are negative  that's why

*so opposite of rational numbers will ne irrational numbers not negative

14. Greatest to least

   -3.02 , -4 , -4.09 , -4.32, -4,35 , -5.11

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the quantity of 80% solution. Then the quantity of 55% solution is (130-x) and the total amount of antifreeze in the mix is ...

  0.55(130 -x) +0.80(x) = 0.70(130)

  0.25x +71.5 = 91 . . . simplify

  0.25x = 19.5 . . . . . . subtract 71.5

  x = 78 . . . . . . . . . . . divide by 0.25; amount of 80%

  130-78 = 52 . . . . amount of 55%

52 gallons of the 55% brand, and 78 gallons of the 80% brand must be used.

Answer:

0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the elements are arranged, so we have to use the arrangements formula.

Arrangements formula:

The number of possible arrangements of n elements is:

[tex]A_{n} = n![/tex]

Desired outcomes:

Pine trees(6!) then the willows(6!) or

Willows(6!) then the pine trees(6!). So

[tex]D = 2*6!*6! = 1036800 [/tex]

Total outcomes:

12 trees, so:

[tex]T = 12! = 479001600 [/tex]

What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other?

[tex]p = \frac{D}{T} = \frac{1036800 }{479001600 } = 0.0022[/tex]

0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.

Answer:

distributive

Step-by-step explanation:

a(b + c)=ab + ac

it's distributive one

Answer:

Step-by-step explanation:

Answer:

The answer is "0.07404893".

Step-by-step explanation:

Applying the binomial distribution:

[tex]n = 22\\\\p= 82\%=0.82\\\\q = 1-0.82 = 0.18\\\\[/tex]

Calculating the probability for not enough seats:

[tex]=P(X>20)\\\\= P(21) + P(22)\\\\[/tex]

[tex]= \binom{22}{21} (0.82)^{21}(0.18)^1+ \binom{22}{22} (0.82)^{22}(0.18)[/tex]

[tex]=0 .06134598+ 0.01270295\\\\=0.07404893[/tex]

Answer:

Step-by-step explanation:

Second and Third which gives in total:

This is under 1/2 and greater than Crew.

Answer: SORRY NEED AN ACCOUNT ON - 10

Step-by-step explanation:

To resolve the proposed issue, an explanation is needed in which the subject is addressed

Base case (n = 1):

• left side = 1×2² = 4

• right side = 1×(1 + 1)×(3×1² + 11×1 + 10)/12 = 4

Induction hypothesis: Assume equality holds for n = k, so that

1×2² + 2×3² + 3×4² + … + k × (k + 1)² = k × (k + 1) × (3k ² + 11k + 10)/12

Induction step (n = k + 1):

1×2² + 2×3² + 3×4² + … + k × (k + 1)² + (k + 1) × (k + 2)²

= k × (k + 1) × (3k ² + 11k + 10)/12 + (k + 1) × (k + 2)²

= (k + 1)/12 × (k × (3k ² + 11k + 10) + 12 × (k + 2)²)

= (k + 1)/12 × ((3k ³ + 11k ² + 10k) + 12 × (k ² + 4k + 4))

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

= (k + 1)/12 × (3k ³ + 23k ² + 58k + 48)

On the right side, we want to end up with

(k + 1) × (k + 2) × (3 (k + 1) ² + 11 (k + 1) + 10)/12

which suggests that k + 2 should be factor of the cubic. Indeed, we have

3k ³ + 23k ² + 58k + 48 = (k + 2) (3k ² + 17k + 24)

and we can rewrite the remaining quadratic as

3k ² + 17k + 24 = 3 (k + 1)² + 11 (k + 1) + 10

so we would arrive at the desired conclusion.

To see how the above rewriting is possible, we want to find coefficients a, b, and c such that

3k ² + 17k + 24 = a (k + 1)² + b (k + 1) + c

Expand the right side and collect like powers of k :

3k ² + 17k + 24 = ak ² + (2a + b) k + a + b + c

==>   a = 3   and   2a + b = 17   and   a + b + c = 24

==>   a = 3, b = 11, c = 10

Answer:

BC^2=10^2+30^2

Step-by-step explanation:

Using pythagorean theorem

[tex]\\ \sf\longmapsto BC^2=10^2+30^2[/tex]

[tex]\\ \sf\longmapsto BC^2=100+300[/tex]

[tex]\\ \sf\longmapsto BC^2=400[/tex]

[tex]\\ \sf\longmapsto BC=\sqrt{400}[/tex]

[tex]\\ \sf\longmapsto BC=20[/tex]

9514 1404 393

Answer:

  A. False

  B. False

  C. True

  D. True

  E. False

Step-by-step explanation:

A. False -- any triangle has at least two acute angles, whether it is acute, right, or obtuse.

B. False -- by definition, any polygon that is not convex is concave.

C. True -- the angle sum is the same regardless of whether the pentagon is convex or concave. (Provided it is a "simple" polygon, with no crossing sides.)

D. True -- the measure of the interior angle of a regular polygon increases as the number of sides increases. (see E)

E. False -- the exterior angles of a regular polygon are 360° divided by the number of sides. As the number of sides increases, the measure of each exterior angle decreases. (Interior angles are the supplement of exterior angles, so they increase as the number of sides increases.)

Answer:

B. 1 + ln 2 - ln x

General Formulas and Concepts:

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle ln(\frac{2e}{x})[/tex]

Step 2: Simplify

9514 1404 393

Answer:

  67.0 square units

Step-by-step explanation:

The formula for the area is ...

  Area = 1/2ab·sin(C)

  Area = (1/2)(14)(28)sin(20°) ≈ 67.036 . . . . square units

The area of the triangle is about 67.0 square units.

Answer:

B. ∆LMN ≅ ∆OPQ because of ASA

Step-by-step explanation:

Two triangles are congruent if two angles and an included side of one triangle are congruent to two corresponding angles and a corresponding included side of the other.

From the information given, we have:

Two angles (<L and <M) in ∆LMN that are congruent to two corresponding angles (<O and <P) in ∆OPQ.

Also, included side in both triangles are congruent (ML ≅ PO).

Therefore, ∆LMN ≅ ∆OPQ by the ASA Theorem.

Answer:

b. The solution is a non empty set.

Step-by-step explanation:

There are no common elements.

Answer:

W=7 and L=11

Step-by-step explanation:

We have two unknowns so we must create two equations.

First the problem states that  length of a rectangle is 10 yd less than three times the width so: L= 3w-10

Next we are given the area so: L X W = 77

Then solve for the variable algebraically. It is just a system of equations.

3W^2 - 10W - 77 = 0

(3W + 11)(W - 7) = 0

W = -11/3 and/or W=7

Discard the negative solution as the width of the rectangle cannot be less then 0.

So W=7

Plug that into the first equation.

3(7)-10= 11 so L=11

Answer:

x is 5

Step-by-step explanation:

[tex] \frac{4x - 5}{9x - 5} = \frac{3}{8} \\ \\ 8(4x - 5) = 3(9x - 5) \\ 32x - 40 = 27x - 15 \\ 5x = 25 \\ x = \frac{25}{5} \\ \\ x = 5[/tex]

Step-by-step explanation:

as you can see as i solved above. all you need to do was to rationalize the both equations

Answer:

Not a function

Domain: {3,4}

Range: {4,5}

Step-by-step explanation:

A function is a relation where each input has its own output. In other words if the x value has multiple corresponding y values then the relation is not a function

For the relation given {(3, 4), (3, 5), (4, 4), (4, 5)} the x value 3 and 4 have more than one corresponding y value therefore the relation shown is not a function

Now let's find the domain and range.

Domain is the set of x values in a relation.

The x values of the given relation are 3 and 4 so the domain is {3,4}

The range is the set of y values in a relation

The y value of the given relation include 4 and 5

So the range would be {4,5}

Notes:

The values of x and y should be written from least to greatest when writing them out as domain and range.

They should be written inside of brackets

Do not repeat numbers when writing the domain and range

Answer:(

fx).(gx)=D. -40x^3+25x^2+45

Step-by-step explanation: