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3 years ago

Solve the equation :)

Mathematics

1 answer:

wariber [46]3 years ago

6 0

12e=-12
e=-1 is the final answer

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Ayudemen porfavor . Determine 4 ala potencia x + 4 ala potencia -x, si se sabe que 2ala potencia x + 2 ala potencia -x =3

Afina-wow [57]

Answer:

Es igual a 7.

Step-by-step explanation:

Ok, sabemos que:

$2^x + 2^{-x} = 3$

Queremos calcular:

$4^x + 4^{-x}$

Tambien sabemos que 4 = 2*2

Entonces:

$4^x + 4^{-x} = (2*2)^x + (2*2)^{-x}$

y sabemos que 2*2 = 2^2

Entonces:

$4^x + 4^{-x} = (2*2)^x + (2*2)^{-x} = (2^2)^x + (2^2)^{-x}$

y ahora podemos usar la relación:

$(a^n)^m = (a^m)^n = a^{m*n}$

entonces:

$(2^2)^x + (2^2)^{-x} = (2^x)^2 + (2^{-x})^2$

Ahora podemos completar cuadrados sumando y restando el termino:

$2*(2^x)*(2^{-x})$

Asi tendremos:

$(2^x)^2 + (2^{-x})^2 = (2^x)^2 + (2^{-x})^2 + 2*(2^x)*(2^{-x}) - 2*(2^x)*(2^{-x}) = (2^x + 2^{-x})^2 - 2*(2^x)*(2^{-x})$

Entonces de momento tenemos que:

$4^x + 4^{-x} = (2^x + 2^{-x})^2 - 2*(2^x)*(2^{-x})$

Sabemos que el termino que esta dentro del parentesis es igual a 3.

Y tambien podemos usar la propiedad:

$a^n*a^m = a^{n + m}$

en el termino de la derecha.

Asi tendremos:

$(2^x + 2^{-x})^2 - 2*(2^x)*(2^{-x}) = (3)^2 - 2*2^{x + (-x)} = 9 - 2 = 7$

7 0

3 years ago

What is the slope of the line y=-4

Vikki [24]

Add more info please

7 0

3 years ago

I need to know how to solve this (Pythagorean theorem) and the answer

Neko [114]

Answer:

≈ 106.4

Step-by-step explanation:

Pythagorean Therorem: $a^{2} + b^{2} = c^{2}$

Equation: $28^{2} + b^{2} = 110^{2}$

$784 + b^{2} = 12100$

-784 -784

$b^{2} = 11316$

$\sqrt{b^{2} } = \sqrt{11316}$

= 106.3766892

Round to nearest tenth:

≈ 106.4

Hope I helped :)

6 0

4 years ago

Read 2 more answers

What is RT, OB, and US equal PLEASE HELP !!!

Lina20 [59]

Answer:

RT = 20, BT = 19, US = 9

Step-by-step explanation:

You calculate the other letters: IR only R is 2, UT, T = 0 and B = 1. US, U = 0 and S = 9.

4 0

4 years ago

A 40% sugar solution is added to an 85% sugar solution to create 1800 mL of a 60% solution. How much of each solution is used? (

denis-greek [22]

Answer:

Number of ml of 40% sugar = x = 1000mL

Number of ml of 85% sugar used = y = 800mL

Step-by-step explanation:

Let the

Number of ml of 40% sugar = x

Number of ml of 85% sugar used = y

From the above question, our system of equations is given as:

x + y = 1800mL ....... Equation 1

x = 1800 - y

40% × x + 85% × y = 60% × 1800mL

0.4x + 0.85y = 1080.... Equation 2

We substitute 1800 - y for x in Equation 2

0.4(1800 - y) + 0.85y = 1080

720 - 0.4y + 0.85y = 1080

- 0.4y + 0.85y = 1080 - 720

0.45y = 360

y = 360/0.45

y = 800mL

Solving for x

x = 1800 - y

x = 1800 - 800

x = 1000mL

Therefore,

Number of ml of 40% sugar = x = 1000mL

Number of ml of 85% sugar used = y = 800mL

4 0

3 years ago