an iron wire bent in the shape of parabola has rectum of length 60cm what is it's focal length?​

The volume of 20,000 m³, and the cost of $40/m², $100/m², and

$200/m², give the dimensions that give minimum cost as follows;

The dimensions of the cistern = L × W × H

L = 2·H

L × W × H = 20000

2·H² × W = 20000

[tex]W = \mathbf{ \dfrac{20000}{2 \cdot H^2}}[/tex]

Therefore;

A = 40·L·W + 200·L·W + 100·2·L·H + 100·2·W·H

A = 400·H² + 680·W·H

Given that the leading coefficient is positive, the function has a minimum point.

[tex]A = \dfrac{400 \cdot H^4 + 6800000 \cdot H}{H^2}[/tex]

[tex]\dfrac{d}{dH} A = \mathbf{\dfrac{d}{dH} \left( \dfrac{400 \cdot H^4 + 6800000 \cdot H}{H^2} \right)} = 0[/tex]

Which gives;

800·H⁵ - 6800000·H² = 0

800·H⁵ = 6800000·H²

H³ = 6800000 ÷ 800 = 8500

H ≈ 20.4 m

Which gives;

L ≈ 2 × 20.4 m =  40.8 m

[tex]W = \dfrac{20000}{2 \times 20.4^2} \approx \mathbf{24.029}[/tex]

The interior dimensions of the cistern are;

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Answer:

as the following table?y 4 32 7 56 8 64. Choose 3 answers: 1.Step-by-step explanation:

Answer:

1/4 chance for Ephraim and 1/2 chance for Keiko

Answer:

B) a + 2(a - 3) = 15

Step-by-step explanation:

To see which equation has a = 7, we have to plug 7 into a each time until we find a satisfied equation.

A:

B:

Therefore, B is the correct answer.

Answer:

A number less than 45 would be

n<45

n=the number, and the sign is less than

Answer:

Yes, they paid the same price per each ticket.

Step-by-step explanation:

You will have to find each of their individual prices per ticket. For Diego it would be 47/3 or $15.67 per ticket. For Andre it would be 141/9 or $15.67 per ticket. This means that they paid the same price per ticket so they are paying at the same rate for their tickets.

Answer:

1. the set of all real numbers from 0 to 80.

2.  {80, 81, 82, 83, ..., 360}

Step-by-step explanation:

So we know based on the number of days the crew works, a certain amount of road will be completed. The amount of road is dependent on the number of days the crew works.

So, number of days crew works = independent variable =  D

amount of road completed = dependent variable = L

Since the crew can work for at most 80 days, they can work from 0  to 80 days.

The first answer is the set of all real numbers from 0 to 80.

The length of roads is the function L = 2D + 200. You plug in the D variable as it asks for it. D's domain is from (0, 80).

So,

L = 2(0) + 200 = 200

L = 2(80) + 200 = 360

The answer is {80, 81, 82, 83, ..., 360}

[tex] \rm \color{lime}(2,10)[/tex]

step-by-step explanation:

[tex]\rm \color{lime}y = - {x}^{2} + 4x + 6[/tex]

[tex]\rm \color{lime}x = - \frac{4}{2x( - 1)} [/tex]

[tex]\rm \color{lime}y = - {x}^{2} + 4x + 6,x = 2[/tex]

[tex]\rm \color{lime}y = 10[/tex]

[tex] = \rm \color{hotpink} (2,10)[/tex]

hope it helps

Answer:

y = - (x - 2)² + 10

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

y = - x² + 4x + 6 ( factor out - 1 from the first 2 terms )

y = - (x² - 4x) + 6

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 4x

y = - (x² + 2(- 2) + 4 - 4) + 6

y = - (x - 2)² + 4 + 6

y = - (x - 2)² + 10 ← in vertex form

Answer:

Distance between parallel chords is 14 cm or 2 cm. Hope this helps

Step-by-step explanation:

Answer:

can you show a picture

Step-by-step explanation:

it depends on the situation and the problem but normally you would use the other numbers to figure out what number goes in "x"

Need more information to solve for x.

Resolviendo una ecuación cuadratica, veremos que el número puede ser -2 o 1/8.

Partimos de la oración matematica:

"Ocho veces un número es restado de dos veces su recíproco. El resultado es 15. Halla el número."

Primero vamos a definir al número como x.

El reciproco de x es la inversa, es decir, 1/x.

Entonces, a 2 veces ek reciproco de x, le restamos 8 veces x, y eso va a ser igual que 15.

2/x - 8*x = 15

Ahora podemos resolver esto para x, primero multiplicamos a ambos lados por x:

2 - 8x^2 = 15x

-8x^2 - 15x + 2 = 0

Esto es una ecuación cuadratica, las soluciones van a ser:

[tex]x = \frac{-(-15)\pm \sqrt{(-15)^2 - 4*(-8)*2} }{2*(-8)} \\\\x = \frac{15\pm 17}{-16}[/tex]

Entonces tenemos dos soluciones:

x = (15 + 17)/-16 = -2

x = (15 - 17)/(-16) = 1/8

El número puede ser -2 o 1/8.

Sí quieres aprender más sobre ecuaciones cuadraticas, puedes leer:

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Answer:77

Step-by-step explanation:Talk to 8 customers per hour, work 8 hours, so:Talk to 8*8 = 64 customers.

Has to increase by 20%, so 64 is multiplied by 1 + 0.2 = 1.2. Then64*1.2 = 76.8Rounding up, 77 is the answer.

Answer:

Yes

Step-by-step explanation:

Step-by-step explanation:

hello I hope this will help you.

Answer:

52

Step-by-step explanation:

Answer:

8,3

Step-by-step explanation:

The Bedroom is in the Shape of Rectangle

Area of Rectangle = LW

Perimeter of Rectangle = 2(L+W)

Since the Area = 24

Then LW=24                                   --->1

Since the Perimeter = 22

Then 2(L+W)=22, Then L+W=11        --->2

Substitute by L=11-W from Equation 2 into Equation 1

(11-W)*W=24

[tex]11W-W^{2} =24[/tex]

[tex]W^{2} -11W+24=0[/tex]

(W-3)(W-8)=0

W=3  or W=8

Substitute in Equation 1 to Find L

at W=3 , L=24/3=8

at W=8 , L=24/8=3

so the Dimension of the Door is 8 and 3 feet

Answer:

Step-by-step explanation:

I don't know if this is what your looking for but the 38 cars that are 10 years old are 45.78 in percentage and the 5 cars that are more than 20 years are 6.02 in percentage.

(if you are asking how much more percentage to get from 6.02 to 45.78 its 39.76)

I really did not get the question but hope it help a bit.

Answer:

(A) 46% (B) 13%

Step-by-step explanation:

First we can find the percentage of cars that are at least 10 years old by dividing the amount that are 10+ years old by the total amount of cars

[tex]38/83= 0.45783[/tex]

when made into a percentage that is 46%

Now we can find the percentage of those cars that are 20+ years old by dividing the number of 20+ year old cars by our percentage

[tex]5/38=0.13157[/tex]

When made into a percentage That is 13%

Hope this helps! :)

Answer:

20 is my answer and the question is somehow confusing

Answer:

I did not mean to send this blank

Step-by-step explanation:

8

Step-by-step explanation:

you would do 10 divide by 2.25 and that's 4.4 but you can't by half a hamburger so you round down to 4 and then you times 4x2 because it's 2.25 for two hamburgers so your answer is 8.

Answer: Melissa's walking speed is 2mph. Her biking speed is 6mph

Step-by-step explanation:

Her total distance is 6 miles, because she walks 3 miles, and so the returning distance must also be 3.

Let her cycling speed (in mph) be x

Let her walking speed (in mph) be y

We know that x = y + 4

Since we know that S = D/T:

T = D/S

So her cycling time must be: T = 3/x

and her walking time must be: T = 3/y

since we know that x = y + 4, we can substitute this into her cycling time, and rewrite it as T = 3/y+4

we also know that 3/y+4 + 3/y = 2, because the problem says that the total time taken was 2 hours.

We simply need to solve this equation now:

3/y+4 + 3/y = 2

The LCD for y+4 and y is y² + 4y

so now we have:

(3y/y² + 4y) + (3y+12/y² + 4y) = 2

(6y + 12)/y² + 4y = 2

6y + 12 = 2y² + 8y

2y² + 2y - 12 = 0

Solve this using factoring:

2y² + 2y - 12 = 0

2(y² + y - 6) = 0

(y+3)(y-2) = 0

using ab = 0, then a or b =0:

y = -3, or y = 2

Since speed cannot be negative, our answer is 2 for y. So y, or the walking speed is 2mph. Since x = y + 4, we know that x = 6 mph

Melissa's walking speed is 2mph. Her biking speed is 6mph

Answer:

-5/2,-1/4

Step-by-step explanation:

Step-by-step explanation:

both of a and b are correct but I don't know how...

Answer:

options. X -120 27 -110 2 y -100 -95 -90 27 227627 х - 120 -110 27 y 2 100 27 -95 227 -90 ... - did not match any news results.

Step-by-step explanation:

Based on the tables given and the functions represented, the two functions that are inverses of each other are tables 3 and 4. Therefore, the options 3 and 4 are correct answers.

Inverse function is represented by f⁻¹ with regards to the original function  and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.

When two functions are said to be inverses of each other, it means that the value of x is one is the corresponding value of y in the other function.

For instance, when the point is (5, 16) in one function, the other function's point would be (16,5).

Therefore, the options 3 and 4 are correct answers.

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Answer:

2. 131

3. 8

4. 69

Step-by-step explanation:

2.

√5607

=131

3.

10cm, √9cm, 8cm

4.

372−1300

=1369−1300

=69