See question in screenshot below.

The dimensions of the rectangular window that gives a maximum area are as follows;

Width = [tex]\dfrac{12}{2+\pi }[/tex] feet and length = 3 feet

The maximum value of a function is given by the point at which the graph of the function has the highest value.

The parameters of the window are;

Length of the framing material available = 12 ft.

The shape of the window = A semicircle on top of a regular rectangular window

Required; The dimension of the rectangular part of the Norman window that allows the most light

Solution;

Diameter of the semicircular part of the window = The width of the rectangular part

Let x represent the width of the window, we have;

Perimeter of the semicircle = π·x/2

Side length of the rectangular window = (12 - π·x/2 - x)/2

Area of the rectangular part of the window, A = x × (12 - π·x/2 - x)/2

Area of the semicircle = π·x²÷4

Area of the window, is therefore;

[tex]A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} +\dfrac{ \pi \cdot x^2}{4}[/tex]

At the maximum area, of the rectangular part, we have;

[tex]A_r' =\dfrac{d}{dx}\left( A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} \right) = -\dfrac{x\cdot \pi +2\cdot x-12}{2} = 0[/tex]

x·π + 2·x - 12 = 0

The width, x = [tex]\dfrac{12}{2+\pi }[/tex] feet

The length of the rectangle is therefore;

[tex](12 - \pi \cdot \dfrac{6}{2+\pi } - \dfrac{12}{2+\pi })/2 = 6 - \pi \cdot \dfrac{3}{2+\pi } - \dfrac{6}{2+\pi } = 3[/tex]

The length of the rectangular window = 3 feet

Learn more about the maximum value of a function here:

https://brainly.com/question/15300035

#SPJ1

The possible roots for the given equation are, -1,3, -1-2i, -1+2i.

What do you mean by the roots of an equation?

The values of the variable that fulfill the equation are known as the roots of a quadratic equation. In addition, they are referred to as the "solutions" or "zeroes" of the quadratic equation. For instance, x = 2 and x = 5 satisfy the quadratic equation x2 - 7x + 10 = 0 and are hence the roots of the equation.

F(x) = x4-2x2-16x-15 has a root (zero) that you should find.

Finding x values for which F(x)=0 is the goal of the Polynomial Roots Calculator method set.

A tool from the list above is the rational roots test. Only numbers x that can be represented as the quotient of two integers, or rational roots, would be found.

According to the Rational Root Theorem, P and Q are factors of the Leading Coefficient and the Trailing Constant, respectively, if a polynomial zeroes for a rational number P/Q.

The Leading Coefficient is 1 and the Trailing Constant is -15 in this instance.

The component(s) are:

1 is the Leading Coefficient, while 1 is the Trailing Constant.

to learn more about quadratic equations from the given link,

https://brainly.com/question/1214333

#SPJ1

Answer: (D) [tex]y=3x-5[/tex]

Step-by-step explanation:

Using the points (0, -5) and (2, 1), the slope of the line is [tex]\frac{-5-1}{0-2}=3[/tex].

Since the y-intercept is -5, the equation is [tex]y=3x-5[/tex].

Amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.

As given in the question,

Conversion of quarter into dollars is :

1 quarter = 0.25 dollars

Amount of money with Lee in his pocket is equal to :

= ( 7 × 5) dollars + ( 6 × 0.25) dollars

= (35 +1.5) dollars

=$ 36.5

Cost of leather jacket buy by Lee = $35.20

Amount of money left in lee's pockets after purchasing jacket

= $( 36.5 - 35.20)

= $ 1.3

Therefore, amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.

The complete question is :

Lee has seven 5-dollar bills and 6 quarters in his pocket. How much money would he have left in his pocket if he buys a leather jacket

worth $35.20?

Learn more about money here

brainly.com/question/19294126

#SPJ1

Answer:

See below

Step-by-step explanation:

I think you may have left some info out of your question post, but here is something that may help you:

x = walk speed    km/hr

x + 5 = run speed     km/hr

45 min = 3/4 hr  = .75 hr

(.75)(x+5)      +      3 * x   = total distance   in  km

3.75x + 3.75 = total distance

Answer: 3x²(5x+y)

Step-by-step explanation:

15x³ + 3x²y​

Apply exponent rule: 15x²x+3x²y

Rewrite 15 as 5*3: 5*3x²x+3x²y

Factor out common terms 3x²: 3x²(5x+y)

Hope this helps!!! :)

well, one focus point at (9 , 0) and another at (-9 , 0) will mean the major axis runs over the x-axis, with a center at the origin, so the "c" distance will be 9 units, and since the major axis is 36 units, that means its "a" component or namely its half is half of 36 or 18 units, so

[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} a=18\\ h=0\\ k=0 \end{cases}\implies \cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ b^2}=1\qquad \textit{we also know that }C=9[/tex]

[tex]9=\sqrt{18^2 - b^2}\implies 9^2=18^2-b^2\implies 9^2+b^2=18^2\implies b^2=18^2-9^2 \\\\\\ b^2=243\hspace{5em}\cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ 243}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{324}+\cfrac{y^2}{243}=1 \end{array}}[/tex]

Check the picture below.

Answer: The correct statements are:

1 SS before tax costs $19.20

Sales tax for 2 SS is $2.88

Total cost for 2 SS is $41.28

Step-by-step explanation:

$16 x 1.20 = $19.20 cost before tax

$19.20 x 0.075 = $1.44 sales tax, one shirt

Sales tax for 2 shirts = $1.44 x 2 = $2.88

Total cost of a shirt = $19.20 + $1.44 = $20.64

Total cost for 2 shirts = $20.64 x 2 = $41.28

The question that can be answered by finding the quotient of 5/6 divided by 1/20 is C. Jared has 5/6 of an hour left to finish making bags. It takes him 1/20 of an hour's to make each bag. How many bags can he make?

It should be noted that the quotient is the value that is gotten when we divide the numbers given.

In this case, Jared has 5/6 of an hour left to finish making bags. It takes him 1/20 of an hour's to make each bag.

The number of bags will be:

= 5/6 ÷ 1/20

= 5/6 × 20

= 100 / 6

= 17 bags

Learn more about quotient in:

brainly.com/question/11995925

#SPJ1

Answer:

17 bags

Step-by-step explanation:

To solve the given derivative we need to apply the chain rule.

Given that, [ln(g(x))]².

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

The chain rule is a formula that expresses the derivative of the composition of two differentiable functions [tex]f[/tex] and [tex]g[/tex] in terms of the derivatives of [tex]f[/tex] and [tex]g[/tex].

Find the derivative using the chain and power rules.

ln(g²x²)/x

Therefore, to solve the given derivative we need to apply the chain rule.

To learn more about the differentiation of an equations visit:

https://brainly.com/question/25731911.

#SPJ1

Answer:

b= -2

Step-by-step explanation:

This is written in the y=mx+B form. This means that x is our slope, and -2 is our y-intercept (b). This meakes b= -2

-Hope this helped

Answer: x=6.

Step-by-step explanation: First go to the Algebra Calculator.

The 50 pounds of trail mix includes 28.57 pounds of cashews and 21.43 pounds of chocolate candies.

let

x + y = 50

2.75x + y = 50 × 2

Solve the equation simultaneously

x + y = 50

2.75x + y = 100

2.75x - x = 100 - 50

1.75x = 50

x = 50/1.75

x = 28.57 pounds

Substitute into

x + y = 50

28.57 + y = 50

y = 50 + 28.57

y = 21.43 pounds

So therefore, the pounds of cashew and chocolate candies needed are 28.75 and 21.43 respectively.

Read more on simultaneous equation:

https://brainly.com/question/16863577

#SPJ1

From given graph,

a - domain and range:  (-∞, 3) ∪ (3, ∞)

b - intercepts: x = 0 and y = 0

c - horizontal asymptotes: y = 3

d - vertical asymptotes: x = 3

e - oblique asymptotes: No

In this question, we have been given a graph of a function.

From given graph we need to answer the following questions.

1) domain of function: (-∞, 3) ∪ (3, ∞)

the range of function : (-∞, 3) ∪ (3, ∞)

2) the intercepts:

x = 0, y = 0

3) horizontal asymptotes

A red dotted line y = 3 is a horizontal asymptotes

4) vertical asymptotes

A red dotted line x = 3 is a vertical asymptotes

5) Oblique asymptotes

The graph of function does not have any Oblique asymptotes

Therefore, from given graph,

a - domain and range:  (-∞, 3) ∪ (3, ∞)

b - intercepts: x = 0 and y = 0

c - horizontal asymptotes: y = 3

d - vertical asymptotes: x = 3

e - oblique asymptotes: No

Learn more about the asymptotes here:

https://brainly.com/question/4084552

#SPJ1

Answer:

One solution: x =21.6

Step-by-step explanation:

Equation

12x + 6 = 14(2x – 24)                    Remove the brackets

Solution

12x + 6 = 28x - 336                      Add 336 to both sides.

12x + 6+336 = 28x - 336             Combine

12x + 342 = 28x -336+336        

12x + 342 = 28x                            Subtract 12x from both sides.

12x-12x + 342 = 28x - 12x             Combine

342 = 16x                                      Divide by 16

342/16 = 16x/16

21.6=x  

The time the airforce plane needs to before the planes are 3510 miles apart is 8.32 hours.

Time is the duration of an event

Since a jet left paris and flew toward moscow at an average speed of 410 mph. an air force plane left three hours later and flew in the opposite direction with an average speed of 160 mph.

The distance flown by the jet is d = vt where

So, d = 410t

Also, the distance flown by the airplane is D = vt' where

So, D = 160t'

= 160(t + 3)

Since the total distance apart of the both jet and airplane is D' = d + D, we have

D' = 410t + 160(t + 3)

Given that D = 3510 miles, we have that

410t + 160(t + 3) = 3510

Soving for t, we have

410t + 160t + 480 = 3510

570t = 3510 - 480

570t = 3030

t = 3030/570

t = 5.32 hours

Since t' = t + 3, we have

t' = 5.32 + 3

= 8.32 hours

So, the airforce plane needs to fly for 8.32 hours.

Learn more about time of flight of plane here:

https://brainly.com/question/14012337

#SPJ1

Answer:

it is a subset where you are going to make sets from that one set

The constant of variation is 1.75 for every unit increase in x (weight), and the cost(y) value increases by $ 1.75.

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The difference between two consecutive entries is constant, as we can see = 1.75

⇒ 7 - 5.25 = 1.75

⇒ 8.75-7 = 1.75

⇒ Slope(m) = 1.75

The slope represents the variable's rate of change.

y - 3 = m(x - 5.25)

y - 5.25 = 1.75(x-3)

y = 1.76x

Thus, the constant of variation is 1.75

This indicates that for every unit increase in x (weight), the cost(y) value increases by $ 1.75.

Learn more about the equation here:

brainly.com/question/10413253

#SPJ1

The question seems to be incomplete the correct question has been attached

Answer: Gradient: 3. y-intercept: 6

Step-by-step explanation:

By using linear pair, we have found that the value of x is 3.

Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.

Given that  Angle QGP = 80°, Angle ROP = 3 + 59x and Angle ROG= 32x + 4. Find x.

Therefore, we can see that Angle ROG and Angle QGP lie in a straight line.

Thus, by linear pair

Angle ROG + Angle QGP = 180

80° + 32x + 4 = 180

32x = 100 - 4

x = 96/32

x = 3

Hence, the value of x is 3.

Learn more about angles;

https://brainly.com/question/7116550

#SPJ1

The equation of the quadratic function in standard form as required in the task content is; f(x) = -x² + 12x - 43.

It follows from the task content that the standard form equation of the quadratic function is to.be determined.

Since the standard form equation can be derived from the vertex form equation as follows;

f(x) = a (x - h)² + k

f(x) = a (x - 6)² - 7

Hence, to find the value of a, Substitute x = 8 and f(x) = -11 so that we have;

-11 = a (8 - 6)² - 7

-11 = 4a - 7

4a = -4

a = -1.

Hence, the equation in vertex form is; f(x) = -1 (x -6)² - 7 and when expressed in standard form we have;

f(x) = -1(x² - 12x + 36) - 7

f(x) = -x² + 12x - 43

Therefore, the required equation in standard form is; f(x) = -x² + 12x - 43.

Read more on quadratic functions;

https://brainly.com/question/25841119

#SPJ1

When you add polynomials of different degrees, it is not adding up the degrees, in special cases this may end up with smaller degree polynomials.

When you multiply polynomials of different degrees, it adds up the degrees, and the final polynomial is off the higher degree.

The answers:

Answer:

The answers are:

1. 2(x2 + 6x + 9) = 3 + 18

2. 2(x2 + 6x) = 3

Let's take a look at the first choice:

2(x² + 6x + 9) = 3 + 18

Now, we will multiply 2 with every member of the other multiplier on the left side:

2·x² + 2·6x + 2·9 = 3 + 18

2x² + 12x + 18 = 3 + 18

2x² + 12x - 3 = 18 - 18

2x² + 12x - 3 = 0

Let's take a look at the second choice:

2(x² + 6x) = 3

Now, we will multiply 2 with every member of the other multiplier on the left side:

2·x² + 2·6x = 3

2x² + 12x = 3

2x² + 12x - 3 = 0 Man that was so hard MARK ME Brainilest Thanks Peace

Step-by-step explanation:

Answer: Radius is estimated to = 5.2

               Circumference is estimated to = 32.66

The missing values for gallons of gasoline remaining is 11,6,1.

Given that equation shown below can be used to find the gallons of gasoline remaining (g) after distance driven (d).

We want to find the missing values for gallons of gasoline remaining.

The given equation is g=16-(1/20)d

When the distance is 100 then we will find the gallons of gasoline remaining by substituting d=100 in given equation, we get

g=16-(1/20)100

g=16-5

g=11

When the distance is 200 then we will find the gallons of gasoline remaining by substituting d=200 in given equation, we get

g=16-(1/20)200

g=16-10

g=6

When the distance is 300 then we will find the gallons of gasoline remaining by substituting d=300 in given equation, we get

g=16-(1/20)300

g=16-15

g=1

Hence, the missing values for gallons of gasoline remaining when distance 100 is 11, when distance 200 is 6 and when distance 300 is 1.

Learn more about the gallons of gasoline from here brainly.com/question/27517273

#SPJ9

Step-by-step explanation:

the angle TSW is the total angle and is 73°.

from that total angle, we have one part : angle 1 = 36°.

as angle TSW = angle 1 + angle 2

we have

73 = 36 + angle 2

angle 2 = 73 - 36 = 37°

Answer:

John's rate is faster than Paul's Step-by-step explanation: John, 64 push-ups/4min = 16 push-ups per minute Paul,

:

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~1 - (-3)~~)^2 + (~~-1 - 5~~)^2} \implies d=\sqrt{(1 +3)^2 + (-1 -5)^2} \\\\\\ d=\sqrt{( 4 )^2 + ( -6 )^2} \implies d=\sqrt{ 16 + 36 } \implies d=\sqrt{ 52 }\implies d\approx 7.2[/tex]

The statement that is true about the number of rooms that can be painted using inequality is; D.

The hotel can repaint 2 rooms, but this number is neither the maximum nor the minimum.

We are given;

Budget of hotel to repaint the lobby and some hotel rooms; $63750

Amount spent on painting the lobby = $26700

Cost to paint each room = $4250

Thus, the inequality to represent the given situation is;

26,700 + 4,250n ≤ $63,750

where;

n is number of rooms the hotel can repaint

Subtract 26700 from both sides of the inequality to get;

4250n ≤ 37050

n ≤ 37050/4250

n ≤ 8.717

Since we can't paint only a portion, we leave it as a maximum of 8 rooms

Looking at the given options, the only correct one is option D.

Read more about Inequality Word Problems at; https://brainly.com/question/25275758

#SPJ1