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3 years ago

Amber is a foster mother. She took care of 8 children in 2003 and in 2004 she had only 5 children. What is the percent decrease?

Mathematics

1 answer:

mylen [45]3 years ago

6 0

Answer:

62.5% i hope that this helped you.

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On Saturday, 4 groups of people went to the restaurant at the ski resort. Each group had 5 people in it. Everyone ordered a cup

VMariaS [17]

Answer: 23 cups

Step-by-step explanation:

There were 4 groups with 5 people each and all of them ordered a cup of hot chocolate:

= 4 * 5

= 20 cups

Rebecca, Malaki, and Jeffrey each ordered an extra cup of hot chocolate so that's 3 extra cups:

= 20 + 3

= 23 cups

4 0

3 years ago

12. If ln(2x – 2) = 2t – 2, what is the value of x?

Katyanochek1 [597]

ln(2x – 2) = 2t – 2

2x-2=e^(2t-2)

x=e^(2t-2)/2+1

8 0

3 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

A mass weighting 64 pounds, attached to the end of a spring and stretches the spring 0.32 foot. There is no damping and no exter

scoundrel [369]

Answer:

Step-by-step explanation:

Check attachment for solution

Download pdf

pdf

8 0

3 years ago

What is the value of x? (x + 40) (3x) O 20 R O O 35 O O ASAP

Natasha2012 [34]

Angles TRS and VRW are vertical angles, so we can set them equal to each other to get x:

x+40=3x

40=2x

20=x

So the value of x is 20

3 0

3 years ago