let f be the function given by f(x)= lnx/x for all x>0. the derivative of f is given:
f'(x)= (1-lnx)/x^2
a) write an equation for the line tangent to the graph of f at x=e^2
b) find the x-coordinate of the critical point of f. Determine whether this point is a relative minimum, a relative maximum, or neither. justify your answer.
c) the graph of the function f has exactly one point of inflection. Find the x-coordinate of this point.
d) find thef(x)

By solving a system of equations we will see that the quadratic equation is:

y = 3*x^2 - 10*x - 4

We know that a general quadratic function can be written as:

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

Here we know that the equation passes through (0, -4), replacing these values:

-4 = a*0^2 + b*0 + c

-4 = c

Then the quadratic equation is:

y = a*x^2 + b*x - 4

Now we can use the other two points (-3, -7) and (2, -12), replacing these values we will get a system of equations:

-7 = a*(-3)^2 + b*(-3) - 4

-12 = a*(2)^2 + b*(2) - 4

We can simplify these equations to get:

-3 = 9a + 3b

-8 = 4a + 2b

We can isolate b on the second equation to get:

2b + 4a = -8

2b = -8 - 4a

b = (-8 - 4a)/2

b = -4 - 2a

Now we can replace that in the other equation to get:

-3 = 9a + 3*(-4 - 2a)

-3 = 9a -12 - 6a

-3 + 12 = 3a

9 = 3a

9/3 = a

3 = a

And the value of b is:

b = -4 - 2a

b = -4 - 2*3

b = -4 - 6 = -10

Then the quadratic equation is:

y = 3*x^2 - 10*x - 4

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The actual height of the house is 0.910 feet.

When both the original dimensions and the new dimensions are known, the scale factor may be determined. When employing the scale factor, there are two terms that must be understood. When a figure's size is increased, we refer to this as scaling up, and when its size is decreased, we refer to this as scaling down.

Given:

Scale : 14 inch = 3 feet

So, 1 inch is represented by

= 3/14

So, 4.25 inch represented as

= 3/14 x 4.25

= 0.910 feet

Hence, the actual height is 0.910 feet.

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The markup from cost to sale price is $108.

The pricing system in which a commodity's (goods or services) price is lower than its listed price is referred to as a "discount." Simply put, "discount" refers to a percentage of the advertised price. A discount is a type of price reduction on products that are seen in consumer transactions.

Given,

the selling price of an item = $520

Markdown = 10% = discount

markdown  ​=  percent markdown * selling price

= 10%*520

=  0.10*520

markdown = $52

To find the sale​ price, subtract the markdown from the selling price.

sale/price ​=  selling price - markdown

= 520 - 52

sale price = $468

to find the markup.

cost of item after markdown = $360

mark up cost  ​=  sale price - cost

mark up = 468 - 360

mark up = $108

Therefore,  the markup from cost to sale price is ​$108.

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The solutions for the equation are b = 0, 3.

What is the cubic equation?

A three-degree equation is referred to as a cubic equation. All cubic equations have roots that are either three real roots or one real root and two imaginary roots. Polynomials are referred to as cubic polynomials if they have a degree of three. The opposite of cubing an integer is finding the cube root of that number. It can be determined by first determining how the given integer can be divided into prime factors, and then by using the cube root formula.

To find the solution for the equation 5/3b³ - 2b² - 5, we can factor it or use the quadratic formula.

One way to factor it is to note that it is a cubic equation in terms of b, and can be written as:

5/3b³ - 2b² - 5 = (5/3b³ - 2b²) - 5 = (5/3b³ - 2b²- 5b) + (5b)

= (5/3b)(b² - 3b) + 5

So, b=0 is one solution, but we can also factor the remaining quadratic equation (b² - 3b) = 0,

b=0 and b=3 are the solutions for the equation.

Hence, the solutions for the equation are b = 0, 3.

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Answer:

ΔMDA ≅ ΔMBC by ASA

Step-by-step explanation:

∠DMA ≅ ∠BMC          

MD ≅ MB

∠MDA ≅ ∠MBC

Two angles are congruent and the sides in between the congruent angles are equal. So, the two triangles are congruent by Angle Side Angle congruency.

Answer:

The y value of the point (x, y) is known as the ordinate.

Step-by-step explanation:

It represents the vertical or perpendicular distance of the point from the origin or from the x-axis. The point at which a line intercepts the x-axis is called the x-intercept, and the point at which it intercepts the y-axis is called the y-intercept.

The point-slope form of the horizontal line (-6,0) is y = 0.

Here given point (-6,0).

If the line is horizontal, the slope is zero.

Then the formula in slope-point form, ( y - y 1 ) = m ( x - x 1 )

By substituting,

This is equivalent to y - 0  = 0 ( x - (-6)).

y - 0 = 0

y = 0

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Answer:

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are coefficients and x is the variable.

The roots of a quadratic equation are the values of x that make the equation equal to zero.

Given that the roots of the quadratic equation are (3+√5) and (3-√5), we can set the quadratic equation equal to zero and substitute the roots for x:

ax^2 + bx + c = 0

(x - (3+√5))(x - (3-√5)) = 0

(x - 3 - √5)(x - 3 + √5) = 0

(x - 3 - √5)(x - 3 + √5) = (x-3)^2 - (√5)^2 = (x-3)^2 - 5 = 0

x^2 - 6x + 9 - 5 = 0

x^2 - 6x + 4 = 0

So the quadratic equation whose roots are (3+√5) and (3-√5) is x^2 - 6x + 4 = 0

Step-by-step explanation:

Grace can use the fraction 3 / 5 of the distance from point A and 2 / 5 of the distance from point B to determine the x coordinate of point C.

Herein we find the case of a point partitioning a line segment by observing a given ratio. The equation that observes this fraction is shown below:

AC / BC = 2 / 3

AC / AB = 2 / 5

Vectorially speaking, this is equivalent to the following equation:

C(x, y) - A(x, y) = (2 / 5) · [B(x, y) - A(x, y)]

C(x, y) = (3 / 5) · A(x, y) + (2 / 5) · B(x, y)

If we know that A(x, y) = (3, 2) and B(x, y) = (6, 11), then the coordinates of point C are, respectively:

C(x, y) = (3 / 5) · (3, 2) + (2 / 5) · (6, 11)

C(x, y) = (9 / 5, 6 / 5) + (12 / 5, 22 / 5)

C(x, y) = (21 / 5, 28 / 5)

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The difference in values of the two houses when they are each 15 years old is given as follows:

$22,000.

The home values are modeled using linear functions, which in slope-intercept form are given as follows:

y = mx + b.

In which the parameters are given as follows:

For House A, the points are given as follows:

(3,150) and (8, 180).

Then the slope is given as follows:

m = (180 - 150)/(8 - 3)

m = 6.

Hence:

y = 6x + b

When x = 3, y = 150, hence the intercept b is given as follows:

150 = 18 + b

b = 132.

Then the function for the value of the home after x years is given as follows:

y = 5x + 132.

Meaning that the value of the home after 15 years is given as follows:

y = 5(15) + 132

y = $222,000.

For House B, the points are given as follows:

(1,130) and (5, 150).

Then the slope is given as follows:

m = (150 - 130)/(5 - 1)

m = 5.

Hence:

y = 5x + b

When x = 1, y = 130, hence the intercept b is given as follows:

130 = 5 + b

b = 125.

Then the function for the value of the home after x years is given as follows:

y = 5x + 125.

Meaning that the value of the home after 15 years is given as follows:

y = 5(15) + 125

y = $200,000.

The difference is then given as follows:

$222,000 - $200,000 = $22,000.

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Formula questions are those questions which require an answer that is numerical in value, including a specific value or a set of values.

These questions require you to apply certain mathematical formulas and use numeric data to come up with solutions. It will contain random numerical data that will be changed and the student has to find a solution for the same. Any numeric value can be modified and hence, the answer is not fixed. There can be different answers depending on the set of numbers presented in the formula question. The answer can be found by using the necessary formulas that exist.

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Answer:

where t is in hours since midnight and f(t) represents thousands of gallons of water. The amount of treated water at any given time, t, can be modeled by g(t) = 30e^cos(/2)a) Define a new function, a(t), that would represent the amount of untreated water inside the plant, at any given time, t.b) Find a′ (t).c) Determine the critica

The fraction 1/9 is greater than the fraction 1/11.

Comparing fractions involves a set of rules related to the numerator and the denominator. When any two fractions are compared, we get to know the greater and the smaller fraction.

To compare unlike fractions:

Step 1: Observe the denominators of the given fractions: .

Step 2: Now, let us convert them in such a way that the denominators become the same.

Step 3: Compare the fractions:

Step 4: The fraction with the larger numerator is the larger fraction.

The given fractions are 1/9 and 1/11.

Here, LCM of denominator 9 and 11 is 99

Then, fractions becomes 11/99 and 9/99

11/99>9/99

1/9>1/11

Therefore, the fraction 1/9 is greater than the fraction 1/11.

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For [tex]f(x)[/tex], the axis of symmetry is the vertical line passing through the vertex. Matching with vertex form, we see the vertex of the graph of [tex]f(x)[/tex] has coordinates [tex](4,2)[/tex]. Thus, the axis of symmetry has equation [tex]x=4[/tex].

Similarly, for [tex]h(x)[/tex], the axis of symmetry is the vertical line passing through the vertex. The vertex of the graph of a quadratic function is either the minimum or maximum point (it depends on the leading coefficient of the function). Here, there is a maximum point, which has coordinates [tex](-2,2)[/tex]. Thus, the axis of symmetry has equation [tex]x=-2[/tex].

The increase in the temperature for an increase of 5 chirps per minute is 41.7 Fahrenheit.

What is Linear relationship?

A Linear relationship, describes a straight-line relationship between two variables.

Given that, There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature.  A biologist gives the model = 25.2 + 3.3x, where x is the number of chirps per minute.

there is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. a least-squares fit of some data collected

Here x = 5, putting it in the given model,

Temperature = 25.2 + 3.3 (5) = 41.7 F

Hence, the required prediction of increase in temperature is 41.7 F

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The predicted number of sit ups each person can do in 12 seconds, using a proportional relationship model are;

Janet 18 sit ups

Paulo 10 sit ups

Shah 9 sit ups

A proportional relationship is one in which the values of the output variable are a constant multiple of the values of the variables in the set of the input values.

The data for the number of sit ups each person can do with time are as follows;

1. Janet does 3 sit ups in 2 seconds

2. Paulo does 5 sit ups in 6 seconds

3. Shah does 3 sit ups in 4 seconds

The rates at which each person does sit ups, using a proportional relationship between the number of sit ups and time and the the constant of proportionality in the proportional relationship is the rate of sit ups per person which are;

Rate = (Number of sit ups)/(Time)

The rate at which Janet does sit ups = (3 sit ups)/(2 seconds), m = 1.5 sit ups/second

Rate at which Paulo does sit ups = (5 sit ups)/(6 seconds), m = (5/6) sit ups/second

Rate at which Shah does sit ups = (3 sit ups)/(4 seconds), m = (3/4) sit ups/second

The number of sit ups each person can do, n, in a specified time, t, can be found using the formula;

n = m × t

Where;

n = The number of sit ups

m = The rate at which the person does sit ups

t = The time duration

Therefore, the number of sit ups each person can do in 12 seconds are therefore;

The number of sit ups Janet can do in 12 seconds is; n = 1.5 × 12 = 18

Janet can do 18 sit ups in 12 seconds

Number of sit ups Paulo can do in 12 seconds is; n = (5/6) × 12 = 10

Paulo can do 10 sit ups in 12 seconds

Number of sit ups Shah can do in 12 seconds is; n = (3/4)×12 = 9

Shah can do 9 sit ups in 12 seconds

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Answer:

[tex] \sf \: 9(x + 2)[/tex]

Step-by-step explanation:

Given expression,

→ 9x + 18

Let's factorise the expression,

→ 9x + 18

→ (9 × x) + (9 × 2)

→ 9(x) + 9(2)

→ 9(x + 2)

Hence, the factor is 9(x + 2).

The table that shows the value of the input and output values of g(x) is shown below where x is for the input values and the output values is g(x)

x       g(x)

2       4

1        2

0        0

1         2

2         4

The values are solved by substituting the values of f(x) in the formula as shown in the problem, the formula is

g (x) = 2f (x)

The values of f(x) which is the input values for g(x) are

2 1 0 1 2

this values are substituted in to the function g (x) = 2f (x) to get

4 2 0 2 4

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The zeros of the quadratic function are: x = -3 or x = -4.

The quadratic function is:

f(x) = 2x² + 14x + 24

Set the function equal to 0

2x² + 14x + 24 = 0

Common 2 from the left side,

⇒2(x² + 7x +12) = 0

Factorize the left side

⇒2(x + 3)(x + 4) = 0

Set factors equal to 0 and we get

  x + 3 = 0 or, x + 4 = 0

⇒x = 0-3 or, x = 0-4

⇒x = -3  o, x = -4

Thus,

The zeros of the quadratic function are: x = -3 or x = -4.

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Answer:

2x+6=x+4

2x-x = 4-6

x= -2

Answer:

x=-2

Step-by-step explanation:

cuz , if u added them together the sum would be -2+6=4 , is that ur question? or I've answered smth that has nothing to do?

The value of Double integral will be [tex]\mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}[/tex]

A two-dimensional region can be integrated using double integrals. They enable us to, among other things, calculate the volume beneath a surface.

The integrals of a function in two variables over a region in R2, or the real number plane, are referred to as double integrals in mathematics. It is possible to write the double integral of a function of two variables, such as f(x, y), over a rectangular region as: R f (x, y) d A = R f (x, y) d x d y.

We know that by the property of integral [tex]$\int u \mathrm{udv}=u v-v \int d u$[/tex]

[tex]$$\begin{aligned}& \mathrm{I}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}=\left[\mathrm{x} \ln (1+\mathrm{x})-\int \mathrm{x} \frac{.1}{1+\mathrm{x}} \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4\left[\mathrm{x} \ln (1+\mathrm{x})-\int\left(1-\frac{1}{1+\mathrm{x}}\right) \mathrm{dx}\right]_0^4 \\& \mathrm{I}=4[\mathrm{x} \ln (1+\mathrm{x})-\mathrm{x}+\ln |1+\mathrm{x}|]_0^4 \\& \mathrm{I}=[4 \ln (5)-4+\ln (5)]-[0-0+0] \\& \mathrm{I}=4[5 \ln 5-4] \\& \mathrm{I}=20 \ln 5-16\end{aligned}$$[/tex]

We have to evaluate the given double integral

[tex]$$\iint_{\mathrm{R}} \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dA} \text { where } \mathrm{R}=[0,4] \times[0,1]$$[/tex]

[tex]$$\begin{aligned}& \mathrm{I}=\int_0^4 \int_0^1 \frac{4 \mathrm{x}}{1+\mathrm{xy}} \mathrm{dydx}=\int_0^4 4 \mathrm{x}\left[\frac{|1+\mathrm{xy}|}{\mathrm{x}}\right]_0^1 \mathrm{dx} \\& \mathrm{I}=\int_0^{44}[\ln |1+\mathrm{x}|-0] \mathrm{dx}=4 \int_0^4 \ln |1+\mathrm{x}| \mathrm{dx}\end{aligned}$$[/tex]

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Answer:

N/A

Step-by-step explanation:

1. subtract 3 from both sides to isolate the square root and its coefficient

5√(5-x) = - 10

2. divide both sides by 5 to isolate the square root

√(5-x) = -2

this means that the square root of something would be negative, which is not possible

Answer: From the information provided, it can be inferred that the graph represents a piecewise function, which is a function defined by multiple smaller functions that apply to different parts of the domain.

Based on the information given, we can see that the function is constant for an input of 1. So the output value of 2 is not in the domain of the function.

It's also important to note that a function can only have one output value for a given input value, and the value of 2 is not on the graph of the function provided.

Step-by-step explanation:

Answer: 1478 = Pedro
1196 = Ricky

Step-by-step explanation: 2674-282 = 2392/2 = 1196 = Ricky
1196+282 = 1478 = Pedro

Conversing the conditional statement we get the answer as, if x is odd, then x+ 1 is even.

Two pieces make up a conditional statement: an assumption in the "if" clause and a conclusion in the "then" clause. Conversing, changes the hypothesis and conclusion to create the conditional statement's opposite.

The converse of the first conditional statement is:

If x is odd, then x + 1 is even.

If x is not odd, then x + 1 is not even.

If x + 1 is even, then x is odd.

If x + 1 is not even, then x is not odd.

Hence, in converse of the conditional statement we switch the hypothesis and the conclusion of the statements.

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The simplified form of the expression given is 4.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given is a logarithmic expression.

㏒ 10⁸ - ㏒ 10⁴

We have a rule for logarithms ㏒ aᵇ = b ㏒ a

So the expression becomes,

㏒ 10⁸ - ㏒ 10⁴ = 8 ㏒ (10) - 4 ㏒ (10)

The value of log 10 is 1.

㏒ 10⁸ - ㏒ 10⁴ = 8 - 4 = 4

Hence the expression can be simplified to 4.

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Approximately 34% of observations in a normal distribution lie above one standard deviation below the mean.

In a normal distribution, approximately 68% of observations fall within one standard deviation of the mean. This means that approximately 34% of observations lie below one standard deviation below the mean and 34% of observations lie above one standard deviation above the mean.

The standard normal distribution (also known as the Z-distribution) is a normal distribution with a mean of 0 and a standard deviation of 1. So if you have a normal distribution with a mean of "mu" and a standard deviation of "sigma", you can standardize it by (X - mu)/sigma to obtain the Z-score.

In a standard normal distribution, 34% of observations fall below -1 standard deviation and 34% fall above +1 standard deviation. So, 34% of observations in a normal distribution lie above one standard deviation below the mean.

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Answer:

565.004, 565.040, 565.4

Step-by-step explanation:

If Pham burgers has beginning net fixed assets of $684218 , ending net fixed assets of $679426 and depreciation expense of $48859 , then the net capital spending for the year is $44067  .

For the Pham burgers , the Beginning Net Fixed Assets is = $684218 ;

the ending net fixed assets for Pham burgers is = $679426  ;

the depreciation expense for Pham burgers is = $48859 ;

the tax rate is 21% , which is not relevant for this question ;

The Net capital Spending for the year can be calculated using the formula :

[tex](Ending \; Net \; Fixed \;Assets - Beginning \; Net\; Fixed \; Assets) + Depreciation[/tex] ;

substituting the required values ,

we get ;

Net Capital Spending for year is = ($679426 - $684218) + $48859 ;

On simplifying ,

we get ;

= $44067 .

Therefore , the Net Capital Spending for the year is $44067  .

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The transformation for the graph f(x) to h(x) is a vertical transformation of 2 units.

The graph is given below.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

f(x) = x

h(x) = x + 2

h(x) = f(x) + 2

Now,

f(x) → h(x)

The transformation from f(x) to h(x) is a vertical translation of 2 units.

i.e

f(x) → f(x) + 2

The graph is given below.

The blue line is the function.

The red line is the parent function.

Thus,

The transformation of the function is f(x) → f(x) + 2.

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