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1 year ago

Simplify the expression.

Mathematics

1 answer:

bagirrra123 [75]1 year ago

3 0

Answer:

Step-by-step explanation:

Exponent rule:

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

$(x^{\frac{2}{5}})^{10} = x^{\frac{2}{5}*10} \\\\\\$

$=x^{2*2}\\\\=x^{4}$

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Correct answer gets brainliest and 5 stars

dsp73

Answer:

16 ft

Step-by-step explanation:

Slant Height=sqrt(Radius^2+Height^2)

Height=sqrt(20^2-12^2)=sqrt(256)=16 ft

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2 years ago

Read 2 more answers

Simplify the complex numbers using de Moivre's Theorem and match them with their solutions.

alexandr1967 [171]

For the numbers in $a+bi$ form, convert to polar form:

$1+i=\sqrt2\dfrac{1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)$

By DeMoivre's theorem,

$(1+i)^5=(\sqrt2)^5\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=4\sqrt2\dfrac{-1-i}{\sqrt2}=-4-4i$

$-1+i=\sqrt2\dfrac{-1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4}\right)$

$\implies(-1+i)^6=(\sqrt2)^6\left(\cos\dfrac{18\pi}4+i\sin\dfrac{18\pi}4\right)=8i$

$\sqrt3+i=2\dfrac{\sqrt3+i}2=2\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)$

$\implies2(\sqrt3+i)^{10}=2^{11}\left(\cos\dfrac{10\pi}6+i\sin\dfrac{10\pi}6\right)=2^{11}\dfrac{1-i\sqrt3}2=2^{10}(1-i\sqrt3)$

For the numbers already in polar form, DeMoivre's theorem can be applied directly:

$2\left(\cos20^\circ+i\sin20^\circ\right)^3=2\left(\cos60^\circ+i\sin60^\circ\right)=2\dfrac{1+i\sqrt3}2=1+i\sqrt3$

$2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)^4=2(\cos\pi+i\sin\pi)=-2$

At second glance, I think the 2s in the last two numbers should also be getting raised to the 3rd and 4th powers:

$\left(2(\cos20^\circ+i\sin20^\circ)\right)^3=8\left(\cos60^\circ+i\sin60^\circ\right)=4+4\sqrt3$

$\left(2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)\right)^4=16(\cos\pi+i\sin\pi)=-16$

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2 years ago

What kind of solution is 2(7x-5)=14x- 10?

Alona [7]

~ Simplifying

-2(7x + -5) = -14x + 10

~ Reorder the terms:

-2(-5 + 7x) = -14x + 10

(-5 * -2 + 7x * -2) = -14x + 10

(10 + -14x) = -14x + 10

~ Reorder the terms:

10 + -14x = 10 + -14x

~ Add '-10' to each side of the equation.

10 + -10 + -14x = 10 + -10 + -14x

~ Combine like terms: 10 + -10 = 0

0 + -14x = 10 + -10 + -14x

-14x = 10 + -10 + -14x

~ Combine like terms: 10 + -10 = 0

-14x = 0 + -14x

-14x = -14x

~ Add '14x' to each side of the equation.

-14x + 14x = -14x + 14x

~ Combine like terms: -14x + 14x = 0

0 = -14x + 14x

~ Combine like terms: -14x + 14x = 0

0 = 0

~ Solving

0 = 0

~ This equation is an identity, all real numbers are solutions.

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2 years ago

If Y is between X and Z, then X, Y, and Z are collinear?

gtnhenbr [62]

I think, I'd go with A) Always true. As 2 points is always the line. If you add third one, it will be collinear.

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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:

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3 years ago