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DiKsa [7]
3 years ago
10

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:

<em>1+√3</em>

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

<em>Area = 1/2 * 4 *  4(1+√3)</em>

<em>Area of the triangle = 1+√3</em>

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}&#10;\\\\&#10;A=P\left(1+\frac{r}{n}\right)^{nt}&#10;\quad &#10;\begin{cases}&#10;A=\textit{accumulated amount}\\&#10;P=\textit{original amount deposited}\to &\$6000\\&#10;r=rate\to 8.25\%\to \frac{8.25}{100}\to &0.0825\\&#10;n=&#10;\begin{array}{llll}&#10;\textit{times it compounds per year}\\&#10;\textit{quarterly, thus four}&#10;\end{array}\to &4\\&#10;t=years\to &4&#10;\end{cases}&#10;\\\\\\&#10;A=6000\left(1+\frac{0.0825}{4}\right)^{4\cdot 4}\implies A=6000(1.020625)^{16}\\\\&#10;-------------------------------\\\\



\bf ~~~~~~ \textit{Compound Interest Earned Amount}&#10;\\\\&#10;A=P\left(1+\frac{r}{n}\right)^{nt}&#10;\quad &#10;\begin{cases}&#10;A=\textit{accumulated amount}\\&#10;P=\textit{original amount deposited}\to &\$6000\\&#10;r=rate\to 8.3\%\to \frac{8.3}{100}\to &0.083\\&#10;n=&#10;\begin{array}{llll}&#10;\textit{times it compounds per year}\\&#10;\textit{semiannually, thus two}&#10;\end{array}\to &2\\&#10;t=years\to &4&#10;\end{cases}&#10;\\\\\\&#10;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
3 years ago
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