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3 years ago

10

Juan tiene 15 años más que Antonio. Dentro 10 años, la edad de Juan será el doble que la de Antonio¿ Cuantos años tienen los dos

?

1 answer:

adoni [48]3 years ago

6 0

Antonio tiene 5 y Juan tiene 20

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10^(x+3) = 6^(2x) solve for x

Bumek [7]

10×+30=12×
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-2×=-30
×=15

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3 years ago

I need the answers please help me help me help me<br>

Katena32 [7]

Answer:

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Step-by-step explanation:

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3 years ago

(1-i)^2 find 4 th root

sergiy2304 [10]

By de Moivre's theorem,

$1 - i = \sqrt2\,e^{-i\pi/4} \implies (1-i)^2 = 2\,e^{-i\pi/2}$

$\implies \sqrt[4]{(1 - i)^2} = \sqrt[4]{2}\,e^{i(2\pi k-\pi/2)/4} = \sqrt[4]{2}\,e^{i(4k-1)\pi/8}$

where $k\in\{0,1,2,3\}$ . The fourth roots of $(1-i)^2$ are then

$k = 0 \implies \sqrt[4]{2}\,e^{-i\pi/8}$

$k = 1 \implies \sqrt[4]{2}\,e^{i3\pi/8}$

$k = 2 \implies \sqrt[4]{2}\,e^{i7\pi/8}$

$k = 3 \implies \sqrt[4]{2}\,e^{i11\pi/8}$

or more simply

$\boxed{\pm\sqrt[4]{2}\,e^{-i\pi/8} \text{ and } \pm\sqrt[4]{2}\,e^{i3\pi/8}}$

We can go on to put these in rectangular form. Recall

$\cos^2(x) = \dfrac{1 + \cos(2x)}2$

$\sin^2(x) = \dfrac{1 - \cos(2x)}2$

Then

$\cos\left(-\dfrac\pi8\right) = \cos\left(\dfrac\pi8\right) = \sqrt{\dfrac{1 + \cos\left(\frac\pi4\right)}2} = \sqrt{\dfrac12 + \dfrac1{2\sqrt2}}$

$\sin\left(-\dfrac\pi8\right) = -\sin\left(\dfrac\pi8\right) = -\sqrt{\dfrac{1 - \cos\left(\frac\pi4\right)}2} = -\sqrt{\dfrac12 - \dfrac1{2\sqrt2}}$

$\cos\left(\dfrac{3\pi}8\right) = \sin\left(\dfrac\pi8\right) = \sqrt{\dfrac12 - \dfrac1{2\sqrt2}}$

$\sin\left(\dfrac{3\pi}8\right) = \cos\left(\dfrac\pi8\right) = \sqrt{\dfrac12 + \dfrac1{2\sqrt2}}$

and the roots are equivalently

$\boxed{\pm\sqrt[4]{2}\left(\sqrt{\dfrac12 + \dfrac1{2\sqrt2}} - i\sqrt{\dfrac12 - \dfrac1{2\sqrt2}}\right) \text{ and } \pm\sqrt[4]{2}\left(\sqrt{\dfrac12 + \dfrac1{2\sqrt2}} + i \sqrt{\dfrac12 - \dfrac1{2\sqrt2}}\right)}$

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2 years ago

16) MZGFS = 26°, mZSFE = 114x + 1,<br> and mZGFE = 142x – 1. Find mZSFE.<br> F<br> S<br> E<br> u

oee [108]

f por q a todos los numeros no les entendi y por eso sacaras f

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3 years ago

Write the equation in point slope form for a line that passes through the points (-2,3) and (6,-1)

diamong [38]

Answer:

y - 3 = -1/2(x + 2)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

<u>Algebra I</u>

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Point-Slope Form: y - y₁ = m(x - x₁)

x₁ - x coordinate

y₁ - y coordinate

m - slope

Step-by-step explanation:

<u>Step 1: Define</u>

Point (-2, 3)

Point (6, -1)

<u>Step 2: Find slope </u><em><u>m</u></em>

Substitute: $m=\frac{-1-3}{6+2}$
Subtract/Add: $m=\frac{-4}{8}$
Simplify: $m=\frac{-1}{2}$

<u>Step 3: Write linear equation</u>

Point-Slope Form: y - 3 = -1/2(x + 2)

3 0

3 years ago

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