(4Q) Describe how the graph is translated.

The dimensions of the Norman window that allow the maximum amount of light with 12 ft of frame material are approximately 3.83 ft in width and 2.07 ft in height.

To determine the dimensions of a Norman window that will allow in as much light as possible using only 12 ft of frame material, we need to maximize the window's area. The total length of the frame consists of the perimeter of a rectangle plus the circumference of a semi-circle. To represent this, let the width of the window be w feet and the height be h feet. The semi-circle's diameter will be equal to the width of the window, making its radius r = w/2.

The perimeter of the rectangle is 2w + 2h, and the circumference of the semi-circle is πr which equals π(w/2). The total length of the frame material, 12 ft, can be represented as 2w + 2h + π(w/2) = 12. This equation can be rearranged to solve for h in terms of w: h = 6 - w - (πw/4).

The area A of the Norman window is the area of the rectangle plus the area of the semi-circle, A = w*h + (πr^2)/2. Substituting for h and r, we get A = w*(6 - w - (πw/4)) + (πw^2)/8.

To find the maximum area, we take the derivative of A with respect to w, set it to zero, and solve for w. Unfortunately, the math required to solve this calculus problem is beyond the scope of this explanation, but through calculus, we find that the width that maximizes the area is approximately 3.83 ft, and the corresponding height is approximately 2.07 ft.

Thus, the dimensions of the window should be a width of approximately 3.83 ft and a height of approximately 2.07 ft to allow the maximum amount of light.

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A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimensions of the window to allow in as much light as possible, if there are only 12 ft of the frame material available?

The width of the window should be __ft, and the height of the window should be __ft. is:

Answer:

[tex]tan(x/2)=-4[/tex]

Step-by-step explanation:

we know that

The angle x belong to the III quadrant -----> given problem

step 1

Find the angle x

[tex]x=arctan(8/15)=28.07\°[/tex]

Remember that the angle x belong to the III Quadrant

so

[tex]x=28.07\°+180\°=208.07\°[/tex]

step 2

Find angle x/2

[tex]x/2=208.07\°/2=104.035\°[/tex]

step 3

Find tan(x/2)

[tex]tan(104.035\°)=-4[/tex]

Answer:

[tex]\large\boxed{C)\ 2}[/tex]

Step-by-step explanation:

[tex]2.5(6x-4)=10+4(1.5+0.5x)\qquad\text{use the distributive property}\\\\(2.5)(6x)+(2.5)(-4)=10+(4)(1.5)+(4)(0.5x)\\\\15x-10=10+6+2x\qquad\text{subtract 2x from both sides}\\\\13x-10=16\qquad\text{add 10 to both sides}\\\\13x=26\qquad\text{divide both sides by 13}\\\\x=2[/tex]

Answer:

C)2

Step-by-step explanation:

Trust me here boyzz

Answer:

C. [tex]\lim_{x\rightarrow f(x)=2[/tex]

Step-by-step explanation:

Given problem is [tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex].

Now we need to evaluate the given limit.

If we plug [tex]\x=\frac{\pi}{4}[/tex], into given problem then we will get 0/0 form which is an indeterminate form so we can apply L Hospitals rule

take derivative of numerator and denominator

[tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex]

[tex]=\lim_{x\rightarrow \frac{\pi}{4}}\frac{sec^2(x)-0}{1-0}[/tex]

[tex]=\frac{sec^2(\frac{\pi}{4})-0}{1-0}[/tex]

[tex]=\frac{(\sqrt{2})^2}{1}[/tex]

[tex]=\frac{2}{1}[/tex]

=2

Hence choice C is correct.

Answer:

Correct answer is B.) Her monthly average would have increased by $19.57.

Step-by-step explanation:

The true statement about her average monthly tip is (b) Her monthly average would have increased by $19.57.

The average of a dataset is simply the mean value or the expected value of the dataset

The table is given as:

June       July         August       September     October     November

$133.45   $235.31    $239.45     $258.87         $298.45     $115.67

For the 6 months, the average is:

Average = (133.45+235.31+239.45+258.87+298.45+115.67)/6

Average = 213.53

For the 5 months (i.e. exclusive of December), the average is:

Average = (133.45+235.31+239.45+258.87+298.45)/5

Average = 233.10

The 5 months average is greater than the 6 months average.

And the difference (d) is:

d = 233.10 - 213.53

Evaluate

d = 19.57

Hence, Her monthly average would have increased by $19.57.

Read more about average at:

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Answer:

(a-b, c)

Step-by-step explanation:

The midpoints of the two diagonals are the same, so we have ...

(P + (-a, 0))/2 = (O +(-b, c))/2

Multiplying by 2 and subtracting (-a, 0), we get ...

P = (0, 0) +(-b, c) -(-a, 0)

P = (a-b, c)

It is 5/8 because it is 5 per 8. You cut up the cookies and not the people. It does not reduce.

Final answer:

Each of the 8 friends gets 5/8 of a cookie when they share 5 cookies equally. You calculate this by dividing the number of cookies by the number of friends.

Explanation:

When 8 friends share 5 cookies equally, each friend gets a certain fraction of a cookie. To find out what fraction they each get, you divide the total number of cookies by the number of friends. In this case, you divide 5 cookies by 8 friends.

The calculation is 5 cookies ÷ 8 friends = 5/8 of a cookie for each friend.

Therefore, this means each friend gets 5/8 of a cookie. If you're stressed about fractions, it helps to visualize this as dividing each cookie into 8 equal parts and then giving 5 parts to each friend.

Answer:

  A.  y = 5/4x + 2

Step-by-step explanation:

The graph has a positive slope (x-coefficient) and a y-intercept of +2 (constant term in the equation). The only equation with those characteristics is ...

   y = 5/4x + 2

Answer:

[tex]A. \: y = \frac{5}{4} x + 2[/tex]

Step-by-step explanation:

The y-intercept is at (0,2). Starting from this point, go five units up and then 4 units right.

Answer:

5/6 I think

Step-by-step explanation:

Add 2/4 + 2/6 =

2*3/4*3 + 2*2/6*2 =

6/12 + 4/12 =

6+4/12 =

10/12 =

5/6

[tex] \frac{5}{6} \\ hope \: it \: helps \: \\ :)[/tex]

the answer is (a-4)^2

Answer:

Let's factor a2−8a+16

a2−8a+16

The middle number is -8 and the last number is 16.

Factoring means we want something like

(a+_)(a+_)

Which numbers go in the blanks?

We need two numbers that...

Try -4 and -4:

-4+-4 = -8

-4*-4 = 16

Fill in the blanks in

(a+_)(a+_)

with -4 and -4 to get...

(a-4)(a-4)

Answer:

(a−4)(a−4)

Answer:

The width is 51.333

Step-by-step explanation:

l * w = area of rectangle

3 * w = 154

w= 154/3

w=51.333

Answer:

11

Step-by-step explanation:

It right

Answer:

260 total stamps

Step-by-step explanation:

Marlee - 60

Xavier - 60

Nicki - 50

Cameron - 90

60+60+50+90= 260

Final answer:

To determine if the points (-1,3), (4,-2), and (1,-5) form a right triangle, plot them on a coordinate plane, use the distance formula to calculate the lengths of the sides, and then apply the Pythagorean theorem.

Explanation:

To plot the points (-1,3), (4,-2), and (1,-5) on a coordinate plane, mark each point according to its x (horizontal axis) and y (vertical axis) coordinates. Connect these points to form a triangle. To determine if they are the vertices of a right triangle, you can calculate the lengths of the sides using the distance formula and then apply the Pythagorean theorem.

The distance formula is √((x₂-x₁)² + (y₂-y₁)²), and the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

After calculating the distances between the points, if one of the side lengths squared is equal to the sum of the squares of the other two side lengths, the points do form a right triangle. If not, they do not form a right triangle.

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷The dots in between each term means multiply. First, we need to multiply all the like terms.

10 * 10 = 100

a * a = a^2

b = b

You can also multiply a number with a variable to get:

100a^2

You combine all terms together and you get:

100a^2 * b

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

Answer:

you can multiply them all

100ba^2

Answer:

B

Step-by-step explanation:

Domain of a function (Graph) is the set of ALLOWED x-values. Or, the x-values for which the function is defined.

Now, looking at the graph, we can see the line is defined in the region from x = 1 till x = 4, so the domain would be  1 ≤ x ≤ 4.

Answer choice B is right.

Answer:

Maria gets $14 off of the original price of $40

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

3 + 2 = 5

The expression for the total number of dice in b boxes for both a board game, which comes with 2 dice, and a card game, which comes with 3 dice, is 5b. This is calculated by adding the number of dice in each box (2b for the board game and 3b for the card game).

The question is asking for an expression that shows the total number of dice in b boxes of the board game and the card game. The board game comes with 2 dice and the card game comes with 3 dice.

To get the total number of dice, one needs to multiply the number of dice in each type of game by the number of boxes, b, and then add the results together.

The total number of dice in the board game is 2b and the total number of dice in the card game is 3b. The sum of these two amounts gives the total number of dice. So the expression for the total number of dice in b boxes of both games is 2b + 3b, which simplifies to 5b.

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Answer:

Meghan's pencil is shorter than Kim's pencil.

Step-by-step explanation:

Let's denote Meghan's pencil height with M, Tasha's with T and Kim's with K

Now, we know that

M < T

and T < K

So, by transitive property,

M < K

Answer:

yes its c

Step-by-step explanation:

cuz its shaded and i have the line under the greater sign and it lines up

A 1/6% chance because there are six sides and 5 is one of them

Answer:

(1-6) (2-5) (3-4) (4-3) (5-2) (6-1)

Step-by-step explanation:

I was just doing this lesson

Answer:

20

Step-by-step explanation:

ONE QUART IS 0.25 OF A GALLON. SORRY CAPS LOCK IS STUCK TURNED ON!

Answer:

Step-by-step explanation:

She needs to fill the quart container

20 times.

4 quarts make a gallon, so 20 quarts = 5 gallons.

ANSWER

Q(5,-2),S(-3,4)

The given points have coordinates,

P(5,2) and R(-3,-4).

The mapping for a reflection across the x-axis is

[tex](x,y)\to (x,-y)[/tex]

This implies that,

[tex]P(5,2)\to Q( 5,-2)[/tex]

and

[tex]R(-3,-4) \to S(-3,4)[/tex]

The correct choice is A.

Answer:

The correct option is A.

Step-by-step explanation:

Answer:

12.2

Step-by-step explanation:

We can say that FG = FH + HG

Since EH is the median, FH and HG is equal. Thus we can find x.

[tex]FH=HG\\6x-1.1=4x+1.3\\6x-4x=1.3+1.1\\2x=2.4\\x=\frac{2.4}{2}\\x=1.2[/tex]

Now we can find FH = 6x - 1.1 = 6(1.2) - 1.1 = 6.1, and

HG = 4x + 1.3 = 4(1.2) + 1.3 = 6.1

Hence, FG = 6.1 + 6.1 = 12.2

The terms in the sum are given by the sequence

[tex]\left\{\dfrac{5^{n+1}}{3^n}\right\}_{n\ge1}[/tex]

We have

[tex]\dfrac{5^{n+1}}{3^n}>\dfrac{5^n}{3^n}=\left(\dfrac53\right)^n>1[/tex]

for all [tex]n[/tex], and the series [tex]1+1+1+\cdots[/tex] clearly diverges, so [tex]\dfrac{25}3+\dfrac{125}9+\cdots[/tex] must also diverge.

Answer:

B. Divergent

Step-by-step explanation:

Did test

Answer:

do you have a picture?

I can't tell you how I decided it because there's not a picture

Answer: y = 4\5*x

We can get this through slope intercept form.

Slope intercept form is y=mx +b where m is the slope and b is the y intercept.

We plug in 4.5 for the slope and 0 for the y-intercept.

Answer:

It  is the second choice.

Step-by-step explanation:

11.5 + 2*1.5 + 3.25 + 6

when calculating the above you multiply the 2 *and 1.5 first then do the adds.

Answer: B.

Start with 11.5. Multiply 1.5 by 2. Add this product to 11.5. Then add 3.25 and 6 to the answer.

Step-by-step explanation: just because

area of parallelogram=base x height

= 30 x 20

= 600feet

Answer:

  y ≈ 17.32

Step-by-step explanation:

The triangles are all similar, so you have ...

  long-side/hypotenuse = y/(5+15) = 15/y

Cross-multiplying gives ...

  y^2 = 15·20 = 300 . . . . . . . . take the square root to find y

  y = √300 = 10√3 ≈ 17.32