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Tcecarenko [31]
1 year ago
7

3. What are the roots of the polynomial y = x³ - 8?

Mathematics
1 answer:
zzz [600]1 year ago
4 0

Step-by-step explanation:

x^3 is a perfect cube, 8 is a perfect cube, so we use difference of cubes.

{a}^{3}  -  {b}^{3}  = (a - b)( {a}^{2}  + ab +  {b}^{2} )

Cube root of x^3 is x.

Cube root of 8 is 2

So

a=x

b= 2.

(x - 2)( {x}^{2}  - 2x + 4)

Set these equations equal to zero

x - 2 = 0

x = 2

{x}^{2}  - 2x + 4 = 0

If we do the discriminant, we get a negative answer so we would have two imaginary solutions,

Thus the only real root is 2.

If you want imaginary solutions, apply the quadratic formula.

1 + i  \sqrt{ 3 }

and

1 - i \sqrt{3}

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B) John returns from holiday with these notes.
ivolga24 [154]

Answer:

£290.70

Step-by-step explanation:

Number of notes of $50 = 5

Total value = 50 × 5 = $250

Number of notes of $20 = 2

Total value = 20 × 2 = $40

Number of notes of $10 = 7

Total value = 10 × 7 = $70

Number of notes of $5 = 3

Total value = 5 × 3 = $15

Total value of all notes with John = 250 + 40 + 70 + 15

                                                        = $375

Since, $1.29 = £1

Therefore, $1 = £\frac{1}{1.29}

Therefore, $375 = £ \frac{375}{1.29}

                           = £290.70  

4 0
3 years ago
Please help it is 10th grade Equations of lines and circles 7. Michael is hanging out in the park and needs to keep his so
frosja888 [35]

Step-by-step explanation:

1) the required equation in common form is:

(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - coordinates, where Michael is standing; r - the social distance;

According to the common form and given coordinates (x₀=-5; y₀=2; r=6) it is possible to make up the required equation:

<u>(x+5)²+(y-2)²=6².</u>

2) if the distance between two friends is:

d=\sqrt{(-5-1)^2+(2-1)^2}=\sqrt{37}, \ then

this distance is longer than social (6 ft). For more info see the attachment.

4 0
1 year ago
PLEASE HELP WITH THE FOLLOWING. WILL GIVE BRAINLIEST. THANK YOU
Marina86 [1]

Answer:

<h2>50.8°</h2>

Step-by-step explanation:

First, we need to use the Pythagorean Theorem to find the third side. We will then use the law of cosines to find the angle.

2√15² = 2√6² + b²

60 = 24 + b²

Subtract 24

36 = b²

b = 6

Now, that we have all three sides, we will use the law of cosines to figure out the angle.

c² = a² + b² - 2abCosC°

Substitute the values in.

6² = 2√15² + 2√6² - 2(2√15)(2√6)CosC°

36 = 60 + 24 - 2(37.947331922)CosC°

36 = 60 + 24 - 75.894663844CosC°

36 = 84 - 75.894663844CosC°

Subtract 84

-48 = -75.9CosC°

0.63241106719 = CosC°

Arccos (0.63241106719) = 50.77176844°

The largest acute angle is approximately 50.8°

4 0
2 years ago
One plant container holds 14 tomato seedlings. If you have 1,113 seedlings, how mny containers do you need to hold all the seedl
IRISSAK [1]

Answer:

79

Step-by-step explanation:

1 container----------->14 seedlings

x containers-------------> 1113 seedlings

14x=1113×1

x=1113/14

x=79


5 0
3 years ago
Read 2 more answers
Perform the operation. Enter your answer in scientific notation.<br><br><br> 3.2 × 107 + 7.2 × 108 =
almond37 [142]

Answer:

1, 120

Step-by-step explanation:

    3.2 x 107 = 342.4

                                               

+   7.2 x 108 = 777.6

_____________________

                       1, 120                          

8 0
3 years ago
Read 2 more answers
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