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kvv77 [185]
3 years ago
5

Determine the discriminant for the given equation x^2+4x+5=0. Then describe the roots(how many and what type).

Mathematics
1 answer:
Fed [463]3 years ago
3 0

Discriminant = b^2 - 4ac, where a, b and c come from the form of the quadratic equation as ax^2 + bx + c

Discriminant = (4)^2 - 4(1)(5)
= 16 - 20
= -4

-4 < 0, therefor there are no roots

(If the discriminant = 0, then there is one root
If the discriminant > 0, there are two roots, and if it is a perfect square (eg. 4, 9, 16, etc.) then there are two rational roots
If the discriminant < 0, there are no roots)
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A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t
xz_007 [3.2K]

Full Question

A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time t = 0, the resulting mass—spring system is disturbed from its rest state by the force F (t) = 20 cos(8t). The force F (t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds.

Determine the spring constant k.

Answer:

Spring Constant = 1000Nm^-1

Step-by-step explanation:

Given

Mass = 10kg

Spring Extension = 9.8cm

Spring Constant K = Force/Extension

Force = Mass * Acceleration

Force = 10 * 9.8 = 9.8N

Spring Extension = 9.8 cm = 9.8 /100 = 0.098 m

Spring constant = 98 / 0.098

Spring Constant = 1000Nm^-1

3 0
2 years ago
Express each of the following percentages as a fraction. 45%
vesna_86 [32]

Answer:

9/20

Step-by-step explanation:

45% can be written as

= 45/100

= 9/20

Hope it will help u..

3 0
3 years ago
Read 2 more answers
Find the median of the data.<br> 12, 33, 18, 28, 29, 12, 17, 4, 2<br> The median is
Reptile [31]

Answer:

The median is 29

Step-by-step explanation:

So you have to cross out 12 then 2 then 33 then 4 then 18 then 17 then 28 then 12 and the last number that's standing is 29.

3 0
3 years ago
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An airplane flies due north from ikeja airport for 500km.It then flies on a bearing of 060 from a further distance of 300km befo
Nata [24]

Answer:

482 km

63.94 degrees

Step-by-step explanation:

to solve this question we will use the cosine rule. For starters, draw your diagram. From point A, up north is 500km and 060 from there, another 300. If you join the point from the road junction back to the starting point, yoou have a triangle.

Cosine rule states that

C = \sqrt{A^{2} + B^{2} -2AB   cos(c)  }

where both A and B are the given distances, 500 and 300 respectively, C is the 3rd distance we're looking for and c is the given angle, 060

solving now, we have

C = \sqrt{500^{2} + 300^{2} -2 * 500 * 300 cos(60)  }

C = \sqrt{250000 + 90000 - [215000   cos(60)  }]

C = \sqrt{340000 - [215000 * 0.5  }]

C = \sqrt{340000 - [107500  }]

C =\sqrt{232500}

C = 482 km

The bearing can be gotten by using the Sine Rule.

\frac{sina}{A} = \frac{sinc}{C}

sina/500 = sin60/482

482 sina = 500 sin60

sina = \frac{500 sin60}{482}

sina = 0.8983

a = sin^-1(0.8983)

a = 63.94 degrees

6 0
2 years ago
What are the common factors of 12 and 28?
AlexFokin [52]

Answer: 1,2 and 4

Step-by-step explanation:

factors of 12 are :  1,2,3,4,6,12

factors of 28 are :1,2,4,7,14,28

commom  factors are= 1,2,4

8 0
2 years ago
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