Determine if 0.054227406110177... is rational or irrational and give a reason for<br> your answer.

5. Find the discriminant of 15x2 = 4x – 1 and describe

diamong [38]

Answer:

a) The discriminant of the equation = - 44

b)The nature of the roots will be imaginary.

c) $x = \frac{2 +\sqrt{11} i}{15} or, x = \frac{2 - \sqrt{11} i}{15}$

Step-by-step explanation:

Here, the given expression is $15x^{2} = 4x -1$

or, $15x^{2} - 4x + 1 = 0$

Now the discriminant (D) of a quadratic equation $ax^{2} +b x + c = 0$

D = $b^{2} - 4ac = (-4)^{2} - 4(15) (1) = 16 - (60) = -44$

Hence, the discriminant of the equation = - 44

As D< 0, so the roots will be imaginary.

Now,by quadratic formula : $x = \frac{-b \pm \sqrt{b^{2} - 4ac} }{2a}$

So, here $x = \frac{-(-4) \pm \sqrt{D} }{2a} = \frac{4 \pm \sqrt{(-44 )} }{30}$

So, either $x = \frac{4 + \sqrt{(-44 )} }{30} or, x = \frac{4 - \sqrt{(-44 )} }{30}$

or, $x = \frac{2 +\sqrt{11} i}{15} or, x = \frac{2 - \sqrt{11} i}{15}$

8 0

2 years ago

Give the domain and range.

alexgriva [62]

Answer:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Step-by-step explanation:

Given:

There are three points on the graph.

Locate the $x$ and $y$ values of the points on the graph.

The points are $(-2,-1),(0,1),\textrm{ and }(2,3)$

Domain is the set of all possible $x$ values. Here, the $x$ values are -2, 0 and 2.

So, domain is: {-2, 0, 2}.

Range is set of all possible $y$ values. Here, the $y$ values are -1, 1 and 3.

So, range is: {-1, 1, 3}

7 0

2 years ago

What is 23 inches in centimetres?

Anettt [7]

Answer: 58.42

Formula: Multiply the length value by 2.54

23×2.54 =58.42

12 Inches = 30.48 Centimetres

7 0

2 years ago

Read 2 more answers

How do i solve this

laila [671]

The ratio is 2:3 for the side lengths of the triangles.

so 6:9 is one side and 5:x would be the other side

2/3 of five is 3.33 and multiplying that by 2 gives you 6.67

4 0

3 years ago

Let v = (v1, v2) be a vector in R2. Show that (v2, −v1) is orthogonal to v, and use this fact to find two unit vectors orthogona

andrey2020 [161]

Answer:

a. v.v' = v₁v₂ - v₁v₂ = 0 b. (20, -21)/29 and (-20,21)/29

Step-by-step explanation:

a. For two vectors a, b to be orthogonal, their dot product is zero. That is a.b = 0.

Given v = (v₁, v₂) = v₁i + v₂j and v' = (v₂, -v₁) = v₂i - v₁j, we need to show that v.v' = 0

So, v.v' = (v₁i + v₂j).(v₂i - v₁j)

= v₁i.v₂i + v₁i.(- v₁j) + v₂j.v₂i + v₂j.(- v₁j)

= v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j

i.i = 1, i.j = 0, j.i = 0 and j.j = 1

So, v.v' = v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j

= v₁v₂ × 1 - v₁v₁ × 0 + v₂v₂ × 0 - v₂v₁ × 1

= v₁v₂ - v₂v₁

= v₁v₂ - v₁v₂ = 0

So, v.v' = 0

b. Now a vector orthogonal to the vector v = (21,20) is v' = (20,-21).

So the first unit vector is thus a = v'/║v'║ = (20, -21)/√[20² + (-21)²] = (20, -21)/√[400 + 441] = (20, -21)/√841 = (20, -21)/29.

A unit vector perpendicular to a and parallel to v is b = (-21, -20)/29. Another unit vector perpendicular to b, parallel to a and perpendicular to v is thus a' = (-20,-(-21))/29 = (-20,21)/29

8 0

2 years ago

Determine if 0.054227406110177... is rational or irrational and give a reason for your answer.