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3 years ago

Solve each equation by finding all roots x^4-16=0

Mathematics

2 answers:

Alexandra [31]3 years ago

4 0

Add both sides by 16
so you'll have x^4 =16
take the 4th root of both sides and you'll get x= 2

SashulF [63]3 years ago

3 0

${ x }^{ 4 }-16=0\\ \\ { x }^{ 4 }=16\\ \\ x=\pm \sqrt [ 4 ]{ 16 } \\ \\ \therefore \quad x=\pm 2$

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Given the figure below, calculate the area

Aleksandr [31]

Answer:

1+√3

Step-by-step explanation:

Area of the triangle = 1/2 * base * height

Area of the triangle = 1/2 * AC * BD

We need to get AC

AC = AD+DC

Get base AD using SOH CAH TOA

tan 45 = 4/AD

AD = 4/tan45

AD = 4/1

AD = 4

Get DC

tan 30 = 4/DC

DC = 4/tan 30

DC = 4/(1/√3)

DC = 4√3

AC = 4 + 4√3

AC = 4(1+√3)

Get the Area of the triangle

Area = 1/2 * 4 * 4(1+√3)

Area of the triangle = 1+√3

6 0

3 years ago

Suppose that you have $6000 to invest. Which investment yields the greater return over four years: 8.25% compounded quarterly or

WARRIOR [948]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$6000\\
r=rate\to 8.25\%\to \frac{8.25}{100}\to &0.0825\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, thus four}
\end{array}\to &4\\
t=years\to &4
\end{cases}
\\\\\\
A=6000\left(1+\frac{0.0825}{4}\right)^{4\cdot 4}\implies A=6000(1.020625)^{16}\\\\
-------------------------------\\\\$

$\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$6000\\
r=rate\to 8.3\%\to \frac{8.3}{100}\to &0.083\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{semiannually, thus two}
\end{array}\to &2\\
t=years\to &4
\end{cases}
\\\\\\
A=6000\left(1+\frac{0.083}{2}\right)^{2\cdot 4}\implies A=6000(1.0415)^8$

compare them away.

4 0

3 years ago

David is shoveling driveways to raise money for his Spring

Anna007 [38]

Answer:

Total savings = $63 + 12 ( m)

: m = number of driveways shoveled

Step-by-step explanation:

Here, the money earned for each road David shovels = $15

The number of driveway shoveled by David = 12

The total money saved David has after he is done with his work = $243

Now, The number of money saved by shoving 12 driveways

= 12 x ( Money earned by shoveling 1 driveway)

= 12 x ( $15) = $ 180

Total savings = His previous savings + Money earned from Shovel work

⇒ $243 = His previous savings + $ 180

⇒ His previous savings = $243 - $180 = $63

Now, we can write his total savings as:

Total savings = $63 + 12 ( m)

: m = number of driveways shoveled

8 0

3 years ago

A bicyclist travels 32 kilometers for 2 hours and then and 13 kilometers for the next hour. Calculate the average speed.

GarryVolchara [31]

Answer:

15 km/h

Step-by-step explanation:

To find the speed, divide the total number of kilometers by the total number of hours:

Find the total number of hours:

32 + 13

= 45

Divide this by 3:

45/3

= 15

So, the average speed was 15 km/h

6 0

3 years ago

There are 100 runners entered in a marathon. How many different groups of three runners can finish in first, second, and third?

DIA [1.3K]

Permutations and Every runner except for the one that was 1st could be 2nd hoep this helps

4 0

4 years ago