Một người tiêu dùng có thu nhập I = 1.200 đ dùng để mua hai sản phẩm X và Y với giá tương ứng là PX = 100đ/sp và PY = 300đ/sp. Mức thoả mãn được thể hiện qua hàm số:

TUX = -1/3X2 + 10X

TUY = -1/2Y2 + 20Y

a. Hãy xác định phương án tiêu dùng tối ưu của người này?

b. Tính tổng hữu dụng tương ứng đạt được?

The height of the pole above the level of the observer's eyes is 31.42 ft

Let the angle of elevation of the top of the pole from a point 47 ft away be α.

Let the angle of elevation of the top of the pole from the point 13 ft away be β.

Since the angle of elevation of a point 13 feet away is twice that from 47 ft away, we have that β = 2α.

If the height of the pole above the level of the observer's eye is h, we have that

tanβ = tan2α = h/13 and tanα = h/47

From trigonometric identities tan2α = 2tanα/(1 - tan²α)

Substituting the values of the variables into the equation, we have

tan2α = 2tanα/(1 - tan²α)

h/13 = 2h/47 ÷ [1 - (h/47)²]

Dividing through by h, we have

1/13 = 2/47 ÷ [1 - (h/47)²]

Cross-multiplying, we have

1/13 = 2/47 ÷ [1 - (h/47)²]

1 - (h/47)² = 2/47 × 13

1 - (h/47)² = 26/47

(h/47)² = 1 - 26/47

(h/47)² = (47 - 26)/47

(h/47)² = 21/47

Taking square-root of both sides, we have

h/47 = √(21/47)

Cross-multiplyng, we have

h = √(21/47) × 47

h = √(21 × 47)

h = √987

h = 31.42 ft

The height of the pole above the level of the observer's eyes is 31.42 ft

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y=3/4x+1/4

I hope this helped :)

Answer:

Step-by-step explanation:

two points on the line are (-3,-2) and (5,4)

slope=(4-(-2))/(5-(-3)=(4+2)/(5+3)=6/8=3/4

eq. of line is

y+2=3/4(x+3)

4y+8=3x+9

4y=3x+9-8

4y=3x+1

y=3/4 x+1/4

Hey there!

32/8

= 32 ÷ 8 / 8 ÷ 8

= 4 / 1

Therefore, your answer should be: 4:1 or 4/1

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

A and E

Step-by-step explanation:

Answer:

54,400

Step-by-step explanation:

Answer:

  A) 20 pounds

  B.2) (increasing) 60 pounds per minute

Step-by-step explanation:

A) The graph shows the container has 20 pounds in it at x=0 minutes.

__

B) The graph goes up to the right (is increasing).

At minute 0, the container has 20 pounds.

At minute 1, the container has 80 pounds.

The increase in one minute is 80-20 = 60 pounds per minute.

The initial amount of candy in the container is 2 pounds.  As time increases, the amount of candy in the container decreases at a rate of 1 pound per minute.

A.) The amount of candy in the container at 0 minutes is 2 pounds.

B1.) As time increases, the amount of candy in the container decreases. The rate at which the amount of candy is decreasing is 1 pound per minute.

B2.) As time increases, the amount of candy in the container increases. However, this option is not applicable in this case as the graph shows a decreasing trend.

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Answer:

-115/69

Step-by-step explanation:

12(6x + 10) + x = 9x + 5(1 - x)

72x + 120 + x = 9x + 5 - 5x

73x + 120 = 4x + 5

69x = 5 - 120

69x = -115

x = -115/69

Answer:

+4.5B+0.5B-1.5B+0.5‐0.5+0.5

Answer:

9 x + 42.

Step-by-step explanation:

Answer:

72x+178" role="presentation" style="outline: 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 17.017px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">72x+17872x+178

Answer/Step-by-step explanation:

[tex]\frac{1-\cos \left(x\right)}{\sin \left(x\right)}=\frac{\sin \left(x\right)}{1+\cos \left(x\right)}[/tex]

When you have an equation like this, you can start from either side. So, let us start from the left side.

[tex]\underline{\mathrm{Left\:side:}} \quad\frac{1-\cos \left(x\right)}{\sin \left(x\right)}[/tex]

[tex]\sf{Rewrite\: using \:Trig \:identities=\frac{\sin \left(x\right)}{1+\cos \left(x\right)}}\\\\\mathrm{Therefore,\: it \:is \:true}[/tex]

Answer:

I don't see any statements, but Tamara paid less. She paid 19.8 after the discount. David spent a little more at 19.95

Step-by-step explanation:

OOOO

BYE

Answer: -3x

Step-by-step explanation:

(-x)+(-x)=-2x

-2x+(-x)=-3x

Answer:

207,974.375

I'm not sure if you need an explanation, and I myself, am not sure I can explain it to you, so I'll just give the answer to you.

Hope this helps!

Answer:

-3

Step-by-step explanation:

using pemdas, we first divide -18 by 6 to get -3. next, we subtract -3 from -6: -6-(-3)=-6+3=-3

Answer: -3

Step-by-step explanation:

For this, you want to use PEDMAS

This is Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction. The first step would be to divide -18/6. This will come out to -3

Balance the reaction:

a FeS₂ + b O₂   =>   c Fe₂O₃ + d SO₂

Matching up the atoms on either side gives the system of equations

• Fe: a = 2c

• S: 2a = d

• O: 2b = 3c + 2d

We have 3 equations with 4 unknowns. Suppose we fix one of the variables, say a = 2. Then

2 = 2c   ===>   c = 1

2•2 = d   ===>   d = 4

2b = 3•1 + 2•4   ===>   b = 11/2

and so the balanced reaction is

2 FeS₂ + 11/2 O₂   =>   Fe₂O₃ + 4 SO₂

or

4 FeS₂ + 11 O₂   =>   2 Fe₂O₃ + 8 SO₂

Look up the molar masses of each component element:

• Fe: 55.845 g/mol

• S: 32.06 g/mol

• O: 15.999 g/mol

Then the molar masses of the reactants are

• FeS₂: 119.965 g/mol

• O₂: 31.998 g/mol

Convert the given masses to moles:

• (882 g FeS₂) (1/119.965 mol/g) ≈ 7.35 mol FeS₂

• (528 g O₂) (1/31.998 mol/g) ≈ 16.5 mol O₂

In the balanced reaction, 4 moles of FeS₂ combine with 11 moles of O₂, or equivalently 1 mol FeS₂ is needed for every 11/4 = 2.75 mol O₂. Now,

(16.5 mol O₂) / (2.75 mol O₂) = 6

while

(7.35 mol FeS₂) / (1 mol FeS₂) = 7.35

which means the reaction consumes all of the available O₂ and we're left with 7.35 - 6 = 1.35 mol FeS₂.

For every 11 mol O₂ among the reactants, 2 mol Fe₂O₃ are produced. Then 16.5 mol O₂ makes for

(11 mol O₂) / (2 mol Fe₂O₃) = (16.5 mol O₂) / x

===>   x = 3.00 mol Fe₂O₃

which has a mass of

(3.00 mol Fe₂O₃) (160. g/mol) ≈ 479 g Fe₂O₃

To find the mass of Fe2O3 produced, we convert the given masses of FeS2 and O2 into moles and use the molar ratio in the balanced chemical equation. The mass of Fe2O3 produced is 1170.68 grams.

To solve this problem, we need to convert the given masses of FeS2 and O2 into moles. From the balanced chemical equation, we can see that the molar ratio between FeS2 and Fe2O3 is 1:1.

This means that the number of moles of Fe2O3 produced will be equal to the number of moles of FeS2. We can use the molar mass of Fe2O3 to convert moles to grams.

First, we calculate the number of moles of FeS2 and O2:

Moles of FeS2 = 882 g / 120.17 g/mol = 7.34 mol

Moles of O2 = 528 g / 32 g/mol = 16.5 mol

Since the molar ratio between FeS2 and Fe2O3 is 1:1, we know that 7.34 moles of FeS2 will produce 7.34 moles of Fe2O3.

Now, we can calculate the mass of Fe2O3:

Mass of Fe2O3 = Moles of Fe2O3 x Molar mass of Fe2O3

Mass of Fe2O3 = 7.34 mol x 159.69 g/mol = 1170.68 g

Therefore, 1170.68 grams of Fe2O3 are produced.

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Answer:

Step-by-step explanation:

Answer:

For a;

The answer will be 3

For b;

The answer will be -4

Step-by-step explanation:

To find the gradient of the lines, you must pick 2 points on the line and then find  [tex]dy/dx[/tex]

I hope this helped!

Can I have brainliest?

Have a great day/night/afternoon!

- ❤ 7272033Alt ❤

Answer:

Answer: The answer is $20

Multiply 400 by .05 or 5%.

If you wanna know 6 years it would be 536 usd

Explanation:

This would be an compound interest. Meaning that your gain every year would increase exponentially.

The equation to calculate this would be: Kn = K0⋅

(1+p100)n Kn is your savings after the period nK0 is your starting deposit p is the percentage n is the period of interest for your example we would have.

Kn=400⋅

(1+5100)6

Step-by-step explanation:

CREDIT FOR ANSWER GOES TO  

calderonj4588

Multiplication equations can be modeled using decimal models.

The multiplication equation is: [tex]\mathbf{0.50 \times 0.90 = 0.45}[/tex]

From Phil model, we have the following highlights

So, the multiplication expression is:

[tex]\mathbf{\frac{50}{100} \times \frac{90}{100}}[/tex]

Express as decimals

[tex]\mathbf{0.50 \times 0.90}[/tex]

Multiply

[tex]\mathbf{0.50 \times 0.90 = 0.45}[/tex]

Hence, the multiplication equation is: [tex]\mathbf{0.50 \times 0.90 = 0.45}[/tex]

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Step-by-step explanation:

No, it is not possible for a regular polygon to have 240° as the measure of each of

its interior angles.

according to the formula:

A = 180 - (360 /n)

where A is the interior angle

therefore, the A could be less than 180°

Answer:

Line A:  constant of proportionality is 4/3

Step-by-step explanation:

The equation in question is y = (4/3)x, where (4/3) is the constant of proportionality as well s the slope of the line.  The only line here that has a slope greater than 1 is the blue line (A).

Answer:

28% are green or red

Step-by-step explanation:

Answer:

20.5

Step-by-step explanation:

Use Pythagorean theorem,

[tex]x^2 = 14^2 +15^2 \\\\\implies x^2 =421\\\\\implies x =\sqrt{421}\\\\\implies x =20.5[/tex]

Answer:

120

Step-by-step explanation:

The LCM of 24 and 30 is 120. To find the least common multiple (LCM) of 24 and 30, we need to find the multiples of 24 and 30 (multiples of 24 = 24, 48, 72, 96 . . . 120; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 24 and 30, i.e., 120.

Usando técnicas de conteo, se encuentra que

1. Un cliente puede ordenar una comida de 784 formas.

2. 420 grupos de 4 letras se pueden formar con las letras de la palabra TECNICA.

3. 840 números de 4 dígitos se pueden formar con los primeros 7 números naturales.

4. 10 partidos distintos se pueden realizar.

5. Pueden colocarse de 3,628,800 formas.

6. 1260 señales distintas pueden indicarse.

Item 1:

La técnica usada es el principio fundamental de conteo, que afirma que si hay n cosas, cada una con [tex]n_1, n_2, \cdots, n_n[/tex] maneras de seren realizadas, el número total de maneras de ser realizadas es:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

En este problema, [tex]n_1 = 14, n_2 = 8, n_3 = 7[/tex], por eso:

[tex]T = 14 \times 8 \times 7 = 784[/tex]

Un cliente puede ordenar una comida de 784 formas.

Item 2:

El orden es importante, ya que TECN es una palabra diferente de NCET, por lo tanto, la fórmula de permutaciones se usa para resolver este problema.

Fórmula de permutaciociones:

El número de permutaciones de x elementos en un conjunto de n elementos es dada por:

[tex]P_{n,x} = \frac{n!}{(n - x)!}[/tex]

En este problema, 4 letras de 7, enconteces:

[tex]P_{7,4} = \frac{7!}{3!} = 840[/tex]

La letra C se repite dos veces, o sea:

[tex]T = \frac{P_{7,4}}{2} = \frac{840}{2} = 420[/tex]

420 grupos de 4 letras se pueden formar con las letras de la palabra TECNICA.

Item 3:

Permutaciones de 4 dígitos de 7, sin repeticiones, o sea:

[tex]P_{7,4} = \frac{7!}{3!} = 840[/tex]

840 números de 4 dígitos se pueden formar con los primeros 7 números naturales.

Item 4:

El orden no es importante, ya que Time 1 x Time 2 es la misma partida de Time 2 x Time 1, por lo tanto, la fórmula de combinaciones se usa para resolver este problema.

Fórmula de combinaciones:

El número de combinaciones de x elementos en un conjunto de n elementos es dada por:

[tex]C_{n,x} = \frac{n!}{x!(n - x)!}[/tex]

En este problema, combinaciones de 2 elementos de un conjunto de 5, entonces:

[tex]C_{5,2} = \frac{5!}{2!3!} = 10[/tex]

10 partidos distintos se pueden realizar.

Item 5:

El número de arreglos de n elementos viene dado por

[tex]A_n = n![/tex]

En este problema, arreglo de 10 elementos, o sea:

[tex]A_{10} = 10! = 3628800[/tex]

Pueden colocarse de 3,628,800 formas.

Item 6:

El número de arreglos de n elementos, con repeticiones de [tex]n_1, n_2, \cdots n_n[/tex] elementos viene dado por

[tex]A_n^{n_1,n_2,\cdots,n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]

En este problema, [tex]n = 9, n_1 = 3, n_2 = 2, n_3 = 4[/tex], por eso:

[tex]A_9^{3,2,4} = \frac{9!}{3!2!4!} = 1260[/tex]

1260 señales distintas pueden indicarse.

Un problema similar es dado en https://brainly.com/question/19022577

The distance Pilar's bike travel when the wheel makes  10 complete rotations is 753.6 inches

Since the wheel is circular in nature, we will take the circumference to determine the distance travelled for 1 revolution

Circumference of a circle = πr²

r is the radius of the wheel.

Given that d = 24 in, r = 24/2 = 12in

C = 2(3.14)(12)

C = 75.36 in

Hence the distance completed by 1 revolution is 75.36. If Pilar's bike makes 10 revolutions, hence the required distance will be:

D = 10 * 75.36

D = 753.6in

Hence the distance Pilar's bike travel when the wheel makes  10 complete rotations is 753.6 inches

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Answer:

no se bro no se inglés así no se que bas a aaer

Step-by-step explanation:

pero puedes consultar por