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3 years ago

The height of a mountain is 29,027 feet. Which measure is the best estimate for the height of the mountain?

Mathematics

1 answer:

Shalnov [3]3 years ago

4 0

D 3x10^4 since it equals 30000.

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I NEED HELP PLEASE FOR FINALS What is f(4) for the function f(x) = 3x + 5?

Igoryamba

Answer: F(4) = 17

Step-by-step explanation:

Just plug in 4 for X.

F(4)= 3(4)+5

F(4)=12+5

F(4)=17

7 0

2 years ago

1/3 (x – 10) = -4, x =

Len [333]

Answer:

Step-by-step explanation:

Divide both sides by 1/3, which is equivalent to mulitplying by 3

x - 10 = -12

Add 10 to both sides

x = -2

4 0

2 years ago

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:

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

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

4 0

3 years ago

How to know a triangle is congruent

yan [13]

The answer is SAS (side, angle, side) SAS stands for "side, angle, side" and means that we have two triangles where we know two sides and the included angle are equal. If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, thetriangles are congruent.

3 0

3 years ago

Read 2 more answers

A circle has a ridius of 16 inches. If the radius is doubled, what is the area of the larger circle

Ostrovityanka [42]

Radius of larger circle = 32

Area of larger circle:

= π • r²
= 3.14 • 32²
= 3.14 • 1024
= 3,215.36

Answer : 3,215.36 in²

7 0

3 years ago