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2 years ago

Can someone please help me with this problem ASAP thank you

Mathematics

1 answer:

Step2247 [10]2 years ago

6 0

3-degree polynomial is f(x )= $[x^{3 }-\frac{9}{7} x^{2}+9x-\frac{81}{7} ]$

Step-by-step explanation:

Given that polynomial f(x) is 3-degree polynomial and Zeros/Roots at x= $\frac{9}{7}$ and x= -3i

In order to find the equation of a 3-degree polynomial, we need 3 roots.

Here, One of Root is real number x= $\frac{9}{7}$ and another root is an imaginary number x=(-3i)

It is necessary to note that imaginary roots always come in pair of conjugates

Therefore, Comjugate0 of x =(-3i) is 3rd root

Conjugate of (-3i) is 3i

Evaluting equation of polynomial,

= $[x-3i][x+3i][x-\frac{9}{7} ]$

= $[x^{2}-(3i)^{2}][x-\frac{9}{7} ]$

= $[x^{2}-(9)(i)^{2}][x-\frac{9}{7} ]$

= $[x^{2}+9][x-\frac{9}{7} ]$

f(x )= $[x^{3 }-\frac{9}{7} x^{2}+9x-\frac{81}{7} ]$

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Insert grouping symbols so that the given expression has a value of 25. 12 – 7 + 2 • 4 + 6

katovenus [111]

(12-7)+2(4+6) is the one thats value is 25

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2 years ago

The equation 4x-45=y is used to find your profit y in dollars from buying $45 of supplies and washing cars for $4 what does the

Mrrafil [7]

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3 years ago

Find the absolute maximum and absolute minimum values of the function f(x, y) = x 2 + y 2 − x 2 y + 7 on the set d = {(x, y) : |

dsp73

Looks like $f(x,y)=x^2+y^2-x^2y+7$ .

$f_x=2x-2xy=0\implies2x(1-y)=0\implies x=0\text{ or }y=1$

$f_y=2y-x^2=0\implies2y=x^2$

If $x=0$ , then $y=0$ - critical point at (0, 0).
If $y=1$ , then $x=\pm\sqrt2$ - two critical points at $(-\sqrt2,1)$ and $(\sqrt2,1)$

The latter two critical points occur outside of $D$ since $|\pm\sqrt2|>1$ so we ignore those points.

The Hessian matrix for this function is

$H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2-2y&-2x\\-2x&2\end{bmatrix}$

The value of its determinant at (0, 0) is $\det H(0,0)=4>0$ , which means a minimum occurs at the point, and we have $f(0,0)=7$ .

Now consider each boundary:

If $x=1$ , then

$f(1,y)=8-y+y^2=\left(y-\dfrac12\right)^2+\dfrac{31}4$

which has 3 extreme values over the interval $-1\le y\le1$ of 31/4 = 7.75 at the point (1, 1/2); 8 at (1, 1); and 10 at (1, -1).

If $x=-1$ , then

$f(-1,y)=8-y+y^2$

and we get the same extrema as in the previous case: 8 at (-1, 1), and 10 at (-1, -1).

If $y=1$ , then

$f(x,1)=8$

which doesn't tell us about anything we don't already know (namely that 8 is an extreme value).

If $y=-1$ , then

$f(x,-1)=2x^2+8$

which has 3 extreme values, but the previous cases already include them.

Hence $f(x,y)$ has absolute maxima of 10 at the points (1, -1) and (-1, -1) and an absolute minimum of 0 at (0, 0).

3 0

2 years ago

Write an equation of the graph:

katrin [286]

1. To translate to the left, add to x.
The equation is: y = |x + 2|

2. To translate down, add to y.
The equation is: y + 2 = |x| OR y = |x| - 2 (subtract 2 from each side)

Hope this helps!

5 0

3 years ago

Based on a study of population projections for 2000 to 2050, the projected population of a group of people (in millions) can b

Olegator [25]

Answer:

(a) 0.107 million per year

(b) 0.114 million per year

Step-by-step explanation:

$A(t) = 11.19(1.009)^t$

(a) The average rate of change between 2000 and 2014 is determined by dividing the difference in the populations in the two years by the number of years. In the year 2000, $t=0$ and in 2014, $t=14$ . Mathematically,

$\text{Rate}=\dfrac{A(2014) - A(2000)}{2014-2000}=\dfrac{11.19(1.009)^14-11.19(1.009)^0} {14}$

$A(0)=\dfrac{12.69-11.19}{14}=\dfrac{1.5}{14}=0.107$

(b) The instantaneous rate of change is determined by finding the differential derivative at that year.

The result of differentiating functions of the firm $y=a^x$ (where $a$ is a constant) is $\dfrac{dy}{dx}=a^x\ln a$ . Let's use in this in finding the derivative of $A(t)$ .

$A\prime(t) = \dfrac{A}{t}=11.19\cdot1.009^t\ln1.009$

In the year 2014, $t=14$ .

$A\prime(14) =11.19\cdot1.009^14\ln1.009=0.114$

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3 years ago