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3 years ago

What are the roots of the equation 16x² + 16x + 5 = 0 in simplest a + bi form?

Mathematics

1 answer:

Greeley [361]3 years ago

4 0

Answer:

Below in bold.

Step-by-step explanation:

Using the quadratic formula :

roots = [-16 +/-√(16^2 - 4*16*5)] / (2*16)

= -0.5 +/- √(-64) /32

= -0.5 +/- 8i/32

= -0.5 + 0.25i and -0.5 - 0.25i

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I needs help with it

Slav-nsk [51]

Answer:

a) initial height = 0 m

b) 8 s

c) vertex = (4, 32)

maximum height = 32 m

Step-by-step explanation:

Given equation:

$h=-2t^2+16t$

where:

h is the height of the arrow about the ground (in metres)
t is the time (in seconds)

The initial height of the arrow will be at the beginning of its journey, so when t = 0

Substitute t = 0 into the equation and solve for h:

$\implies h=-2(0)^2+16(0)$

$\implies h=0$

Therefore, the initial height of the arrow is 0 m.

The arrow will hit the ground when the height is 0 m.

Substitute h = 0 into the given equation:

$\implies -2t^2+16t=0$

Factor out -2t:

$\implies -2t(t-8)=0$

Therefore:

$\implies -2t=0 \implies t=0$

And:

$\implies t-8=0 \implies t=8$

Therefore, the arrow will hit the ground at 8 seconds.

The vertex is the turning point of a parabola - it's minimum or maximum point.

As the leading coefficient for the given equation is negative, the parabola opens downwards and so its vertex is its maximum point.

There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.

We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds. Therefore, t = 0 and t = 8 are the x-intercepts. The midpoint is halfway between zero and 8, so the midpoint is t = 4

To find the y-coordinate, substitute t = 4 into the equation and solve for h:

$\implies h=-2(4)^2+16(4)$

$\implies h=-32+64$

$\implies h=32$

Therefore, the coordinates of the vertex are (4, 32)

The maximum height is the y-coordinate of the vertex.

Therefore, the maximum height is 32 m

6 0

2 years ago

Plz help Elijah wants to know how much wrapping paper is needed to cover a box with the dimensions shown.

alexdok [17]

Answer:

Step-by-step explanation:

we know 4 times 5 is 20. If you add all of the sides for the next shape 4 4 5 and 5 you get 18 18 tomes 8 is 144 144 plus 20 plus 20 is 184. hope this helps!!!

8 0

3 years ago

A can of favorite dog food holds 14 oz. Four cans are $1.00. The price of three cans of delight beef dog food, each containing 1

myrzilka [38]

The 12 ounce can, because it only costs $.58 for 36 ounces, which means each ounce costs $.016, whereas the 14.5 ounce cans cost $1.00 for 58 ounces, which means each ounce costs $.017.

5 0

3 years ago

When 14 is subtracted from 6 times a number, 40 is

Rzqust [24]

Answer:

4.5

Step-by-step explanation:

Let the number be x

6x-14 = 40

Add 14

6x = 40+14

6x = 54

Divide by 6

6x/6 = 54/6

x = 9

We want 1/2 of the number

1/2 of 9 is 4.5

6 0

3 years ago

PLEASEEE HELP !! in two the three sentences, explain how you would find the line of symmetry for the parabola whose equation is

Arada [10]

Answer:

Axis of symmetry line is parallel to y- axis

Equation of the parabola ( x - ( -2 ))² = (y - 12 )

Step-by-step explanation:

Explanation:-

Given equation is y = x²+4 x+16

y = x²+2 (2 ) x + (2)² - (2)² + 16

y = ( x + 2 )² + 12

( x + 2 )² = y - 12

( x - ( -2 ))² = (y - 12 )

( x- h)² = 4 a ( y - k)

Center (h ,k) = ( -2 , 12)

Here 4 a = 1

a = 1/4

Focus S = ( h , K +a) = ( -2 , 12 + 0.25) = ( -2 , 12.25)

Axis of symmetry line is parallel to y- axis

5 0

3 years ago

What are the roots of the equation 16x² + 16x + 5 = 0 in simplest a + bi form?​

What are the roots of the equation 16x² + 16x + 5 = 0 in simplest a + bi form?