What is the midpoint of (10,6) and (4,9)

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

2 years ago

Timothy spends 2.4 hours doing his homework. He did Math, English, History, and Social studies in the ratio 2:2:3:1. How much ti

choli [55]

There are 8 parts in total by adding the ratio. Math 2/8×2.4=0.6 hr Eng. 2/8×2.4=0.6 hr Hist. 3/8×2.4=0.9hr Social. 1/8×2.4=0.3 hr. Add them all will get 2.4

3 0

3 years ago

Read 2 more answers

Please help me with this

Ede4ka [16]

Answer:

A. complementary

Step-by-step explanation:

Complementary is when 2 angles add up to 90°. Therefore, the angle in the image shown is a 90° angle. Hope this helps :)

5 0

3 years ago

The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: M(x) = 13 x - x2. What

My name is Ann [436]

Answer:

The number of mosquitoes is maximum for 6.5 inches rainfall.

Step-by-step explanation:

The given function is

$M(x)=13x-x^2$ .... (1)

where, M(x) is number of mosquitoes in millions and x the June rainfall in inches.

We need to find the rainfall that produces the maximum number of mosquitoes.

Differential the above function with respect to x.

$M'(x)=13-2x$ .... (2)

Equate first derivative equal to 0.

$13-2x=0$

$2x=13$

$x=\frac{13}{2}=6.5$

Differential function (2) with respect to x.

$M''(x)=-2$

Double derivative is negative. So, the value of function is maximum at x=6.5.

Therefore, the number of mosquitoes is maximum for 6.5 inches rainfall.

4 0

3 years ago

Sabrina built a model of one of the office buildings in Dallas shaped like a rectangular prism. The model was 4.1 inches wide, 5

Helen [10]

Answer:

dont kn

Step-by-step explanation:

6 0

3 years ago