Solve 64x^3 +1 =0the back of the texts books gives me the answers -1/4 and 1 plus or minus i√3 all over 8
I understand where the -1/4 comes from . I just don't understand the second answer. I know they used the quadratic formula to get it but I always end up with something to totally different

Answers

Answer 1

Answer: Expand the expression using the formula:
$a^3+b^3=(a+b)(a^2 - ab + b^2)$

$64x^3+1=0 \n(4x)^3+1^3=0 \n(4x+1)((4x)^2- 4x * 1+1^2)=0 \n(4x+1)(16x^2-4x+1)=0 \n4x+1=0 \ \lor \ 16x^2-4x+1=0$

The first equation:
$4x+1=0 \n 4x=-1 \n x=-(1)/(4)$

The second equation:
$16x^2-4x+1=0 \n \na=16 \n b=-4 \n c=1 \n b^2-4ac=(-4)^2-4 * 16 * 1=16-64=-48 \n√(b^2-4ac)=√(-48)=√(48) * √(-1)=√(16 * 3) * √(-1)=\pm 4√(3) i \n \nx=(-b \pm √(b^2-4ac))/(2a)=(-(-4) \pm 4√(3)i)/(2 * 16)=(4 \pm 4√(3)i)/(32)=(4(1 \pm √(3)i))/(4 * 8)=(1 \pm √(3)i)/(8) \nx=(1-√(3)i)/(8) \ \lor \ x=(1+√(3)i)/(8)$

The final answer:
$\boxed{x=-(1)/(4) \hbox{ or } x=(1-√(3)i)/(8) \hbox{ or } x=(1+√(3)i)/(8)}$

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A company has two electric motors that consume varying amounts of power. The power consumed by each motor is a function of the time (t in minutes) for which it runs. The cost of power (in $) to run one motor is given by the function `C_a(t) = t^2 - 2t + 5`. The cost of running the second motor is given by `C_b(t) = 3t + 2`. Which function gives the total cost of running both motors?
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What are numbers that have 24 as its multiple?

Answers

1, 2, 3, 4, 6, 8, 12,
............................

The numbers that have 24 as its multiple are 1, 2, 3, 4, 6, 8, 12, 24.

Hope this helps~

Edgar Anderson earns $300 a week plus a 15% commission on all sales over $1,000. If Mr. Anderson's sales for one week are $2,500, what is his gross pay for that week?

Answers

Basic amount that Edgar Anderson earns per week = $300
Sales of Mr. Anderson for one week = $2500
Percentage of commission on sales above $1000 = 15%
Then
Amount of commission
earned for the week = [2500 - 1000] * (15/100) dollars
= 1500 * (15/100) dollars
= 15 * 15 dollars
= 225 dollars
Then
Gross pay of Edgar Anderson for the week = (300 + 225) dollars
= 525 dollars
So the gross pay of Edgar Anderson for the week is $525.

(a) 3x + 7y = 13, 5x + 2y = 12
How do i solve this linear equation using substitution method??

Answers

Answer:

x= 2, y= 1

Step-by-step explanation:

First label the 2 equations:

3x +7y= 13 -----(1)

5x +2y= 12 -----(2)

Make x or y the subject of formula for one of the equation so that we can substitute its value into the 2nd equation.

Here, I am making y the subject of formula in the 2nd equation.

5x +2y= 12

2y= 12 -5x

$y = 6 - (5)/(2) x$ -----(3)

Substitute (3) into (1):

$3x + 7(6 - (5)/(2) x) = 13$

Expand:

$3x + 42 - (35)/(2) x = 13$

Bringconstantstooneside:

$3x - (35)/(2) x = 13 - 42$

Simplify:

$- (29)/(2) x = - 29$

Multiplyby-2onbothsides:

$- 29x = - 58$

Divideby-29onbothsides:

x=2

Substitute x=2 into (1):

3(2) +7y= 13

7y +6= 13

7y= 13 -6 (-6onbothsides)

7y= 7

y= 7 ÷7

y= 1

The scatter plot shows a hiker's elevation above sea level during a hike from the base to the top of a mountain. The equation of a trend line for the hiker's elevation is y equals=9.069.06xplus+651651, where x represents the number of minutes and y represents the hiker's elevation in feet. Use the equation of the trend line to estimate the hiker's elevation after 175 minutes.

Answers

Answer:

2236.5

Step-by-step explanation:

The regression equation for predicting hiker's elevation is

y=9.06x+651.

Here x is the number of minutes.

We wish to estimate hiker's elevation after 175 minutes. For this purpose we put x=175 in the predicted regression equation.

y=9.06(175)+651

y=1585.5+651

y=2236.5

Thus, the hiker's elevation after 175 minutes is 2236.5 feet.

Camillo estimates the weight of his dog. The veterinarian says that the dog weighs 84 pounds. The percent error in Camillo's estimates is less than 10%.Decide whether each of the following weight estimates could have been Camillo's estimate.
a. 80 pounds yes or no
b. 78 pounds yes or no
c. 94 pounds yes or no
d. 77 pounds yes or no
e. 92 pounds yes or no
f. 75 pounds yes or no

Answers

Answer:

A.Yes B.Yes C.No D.Yes E.No F.No

Step-by-step explanation:

10% of 84 is 8.4 and 84-8.4=76.6 and anything between 76.6-84 could have been the estimate.

Final answer:

Camillo's weight estimate could have been 80 pounds, 78 pounds, 77 pounds, or 92 pounds.

Explanation:

The percent error measures the discrepancy between an estimated value and an actual value. It is calculated using the formula: Percent Error = (|Measured Value - Actual Value| / Actual Value) * 100%. Since the given problem states that Camillo's estimate has a percent error less than 10%, we can calculate the percent error for each weight estimate and determine if it is less than 10%.

a. 80 pounds: Percent Error = (|80 - 84| / 84) * 100% = 4.76%, which is less than 10%. So, yes, this could have been Camillo's estimate.
b. 78 pounds: Percent Error = (|78 - 84| / 84) * 100% = 7.14%, which is less than 10%. So, yes, this could have been Camillo's estimate.
c. 94 pounds: Percent Error = (|94 - 84| / 84) * 100% = 11.9%, which is not less than 10%. So, no, this could not have been Camillo's estimate.
d. 77 pounds: Percent Error = (|77 - 84| / 84) * 100% = 8.33%, which is less than 10%. So, yes, this could have been Camillo's estimate.
e. 92 pounds: Percent Error = (|92 - 84| / 84) * 100% = 9.52%, which is less than 10%. So, yes, this could have been Camillo's estimate.
f. 75 pounds: Percent Error = (|75 - 84| / 84) * 100% = 10.71%, which is not less than 10%. So, no, this could not have been Camillo's estimate.