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kykrilka [37]
2 years ago
15

Find a quadratic polynomial with integer coefficients which has x = 2/9, ± SQRT23/9 as its real zeros.

Mathematics
1 answer:
melomori [17]2 years ago
5 0

Answer:

The quadratic polynomial with integer coefficients is y = 81\cdot x^{2}-36\cdot x -19.

Step-by-step explanation:

Statement is incorrectly written. Correct form is described below:

<em>Find a quadratic polynomial with integer coefficients which has the following real zeros: </em>x = \frac{2}{9}\pm \frac{\sqrt{23}}{9}<em>. </em>

Let be r_{1} = \frac{2}{9}+\frac{\sqrt{23}}{9} and r_{2} = \frac{2}{9}-\frac{\sqrt{23}}{9} roots of the quadratic function. By Algebra we know that:

y = (x-r_{1})\cdot (x-r_{2}) = x^{2}-(r_{1}+r_{2})\cdot x +r_{1}\cdot r_{2} (1)

Then, the quadratic polynomial is:

y = x^{2}-\frac{4}{9}\cdot x -\frac{19}{81}

y = 81\cdot x^{2}-36\cdot x -19

The quadratic polynomial with integer coefficients is y = 81\cdot x^{2}-36\cdot x -19.

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Alexis is making cookies. The recipe says that she has to mix 192 grams of sugar into the flour. Alexis knows that 1 cup of this
Dmitrij [34]
For this case we can make the following rule of three:
 1 cup ----------------> 128 grams
 x ----------------------> 192 grams
 From here, we clear the value of x.
 We have then:
 x = (192/128) * (1)
 x = 1.5
 x = 1 1/2
 Answer:
 
She needs about 1 1/2 cups.
4 0
3 years ago
Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ &lt; 360°.
umka2103 [35]
A polar coordinate is that which can be written as (r, θ) where r is the radius and θ is the angle. 

The radius, r, is also the hypotenuse of the right triangle that can be formed. Hence, it can be calculated through the equation,
    
                   r² = x² + y²
If we are to simplify this for the r alone, we have,
                     r = sqrt (x² + y²)

Substituting the known values,
               r = sqrt ((4)² + (-4)²) = 4√2

The x and y can be related through the trigonometric function, tangent. 
      tan θ = y/x
To solve for θ
   θ = tan⁻¹(y/x) = tan⁻¹(-4/4) = -45° = 315°

Hence, the polar coordinate is <em>(4√2, 315°)</em>
5 0
3 years ago
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madreJ [45]

Answer:

Where is the question?

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Consider the following. x = 6 sin y , 0 ≤ y ≤ π, x = 0; about y = 4
Fantom [35]

Answer:

12pi(8-pi), or

183.158 to third decimal place

Step-by-step explanation:

The geometry is indicated in the attached figure.

A. by integration

We will find the volume of the solid by the method of shells, i.e. we will integrate strips parallel to the axis of rotation to form many thin shells, then integrate to get the sum of all these shells.

For each shell, of thickness dy, we integrate strips of length located at y

L(x) = y(x)

and area

L(x)dy

Each strip is at a distance of (4-y) from

for which the volume of each shell equals

dV = 2*pi*(4-y)*L(x)dy = 2*pi*(4-y)*y(x) dy

The total volume of the solid can be obtained by integrating y from 0 to pi

integral( dV ) from 0 to pi

= integral (2*pi*(4-y)*y(x) dy) for y from 0 to pi

= 12*pi(-sin(y)+y*cos(y)-4*cos(y)) for y from 0 to pi

=12(8-pi)*pi

= 183.158

B. Using Pappus theorem

Pappus theorem simplifies the calculation of volume of revolution by multiplying the area of the rotating region by 2pi times the distance between the centroid and the rotation axis.

Here the area of the figure is A=2*6=12, (2 is the area under the sine curve from 0 to pi), or

A = integral (6sin(x))dx, x from 0 to pi

= 6 cos(x), x from 0 to pi

= 6(1- (-1))

= 12

Distance from centroid to axis of rotation = (4-pi/2)

Volume = 2*pi*A*(4-pi/2) = 2*pi*12*(4-pi/2)

= 12pi(8-pi)

=183.158    as before

5 0
3 years ago
Simplify: 9 (5x-4) + 4x
m_a_m_a [10]

Answer:

49x+36

Step-by-step explanation:

Hey There!

for this question they would like you to simplify the expression using distributive property

To do this the first step is to distribute the 9 in to everything that is in the parenthesis

9x5x=45x

9x4=36

so now we have

45x+36+4x

the next step is to combine like terms

the only like terms in the expression are 45x and 4x so we just add the two together

45x+4x=49x

so now we have 49x+36

In conclusions the simplified version of that expression is 49x+36

8 0
2 years ago
Read 2 more answers
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