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2 years ago

How much would $300 invested at 9% interest compounded monthly be worth after 3 years?

Mathematics

1 answer:

belka [17]2 years ago

8 0

Answer:

F=P(1+(r/n))^(nt)

F=future amount

P=present amount

r=rate in decimal form

n=number of times per year it is compounded

t=time in years

F=P(1+(r/n))^(nt)

F=future amount

P=300

r=0.09

n=1

t=3

F=300(1+(0.09/1))^(1(3))

F=300(1+0.09)^(3)

F=300(1.09)^(3)

F=388.509

it would be worth $388.51 (rounded)

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Which of the following phrases translates to m - 7?

Sindrei [870]

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OPTION A IS WRONG BECAUSE MATHEMATICALLY IT IS WRITTEN AS

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B IS WRONG BECAUSE IT MEANS

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C IS WRONG BECAUSE IT MEANS

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2 years ago

If Vector u=(5,-7) and v=(-11,3), 2v-6u=_____ and ||2v-6u||≈_____

Sauron [17]

<h2>Answer:</h2>

$2\vec{v}-6\vec{u}=(-52,48) \\ \\ ||2\vec{v}-6\vec{u}||=75.28}$

<h2>Step-by-step explanation:</h2>

In this problem we have two vectors:

$\vec{u}=(5,-7) \ and \ \vec{v}=(-11,3)$

So we need to find two things:

$2\vec{v}-6\vec{u}$

and:

$||2\vec{v}-6\vec{u}||$

FIRST:

In this case we have the multiplication of vectors by scalars. A scalar is a simple number, so:

$2\vec{v}-6\vec{u} \\ \\ Replace \ \vec{v} \ and \ \vec{u} \ by \ the \ given \ vectors: \\ \\ 2(-11,3)-6(5,-7) \\ \\ Multiply \ each \ component \ by \ the \ corresponding \ scalar:\\ \\ (2\times (-11),2\times 3)+(-6\times 5,-6\times (-7)) \\ \\ (-22,6)+(-30,42) \\ \\ Sum \ of \ vectors: \\ \\ (-22-30,6+42) \\ \\ \therefore \boxed{(-52,48)}$

SECOND:

If we name:

$\vec{w}=2\vec{v}-6\vec{u}$

Then, $||2\vec{v}-6\vec{u}||$ is the magnitude of the vector $\vec{w}$ . Therefore:

$||\vec{w}||=||2\vec{v}-6\vec{u}|| \\ \\ ||\vec{w}||=||(-52,48)|| \\ \\ ||\vec{w}||=\sqrt{(-58)^2+48^2} \\ \\ ||\vec{w}||=\sqrt{3364+2304} \\ \\ ||\vec{w}||=\sqrt{5668} \\ \\ \boxed{||\vec{w}||=75.28}$

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