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Tresset [83]
2 years ago
11

Subtract 4p^2-9p+11 from p^2-5p+4 Your answer should be a polynomial in standard form.

Mathematics
1 answer:
pishuonlain [190]2 years ago
3 0

Answer:

p^2 - 5p + 4

4p^2 - 9p + 11

-⠀⠀⠀+⠀⠀-

-3p^2 + 4p -7

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What is the vertex of f(x)= -3/4|x|+7? also how do i graph it?
Harrizon [31]

Rewrite in standard form and use this form to find the vertex

(h,k).(0,7)  

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7 0
3 years ago
Use variation of parameters to find a general solution to the differential equation given that the functions y1 and y2 are linea
Aleks [24]

Recall that variation of parameters is used to solve second-order ODEs of the form

<em>y''(t)</em> + <em>p(t)</em> <em>y'(t)</em> + <em>q(t)</em> <em>y(t)</em> = <em>f(t)</em>

so the first thing you need to do is divide both sides of your equation by <em>t</em> :

<em>y''</em> + (2<em>t</em> - 1)/<em>t</em> <em>y'</em> - 2/<em>t</em> <em>y</em> = 7<em>t</em>

<em />

You're looking for a solution of the form

y=y_1u_1+y_2u_2

where

u_1(t)=\displaystyle-\int\frac{y_2(t)f(t)}{W(y_1,y_2)}\,\mathrm dt

u_2(t)=\displaystyle\int\frac{y_1(t)f(t)}{W(y_1,y_2)}\,\mathrm dt

and <em>W</em> denotes the Wronskian determinant.

Compute the Wronskian:

W(y_1,y_2) = W\left(2t-1,e^{-2t}\right) = \begin{vmatrix}2t-1&e^{-2t}\\2&-2e^{-2t}\end{vmatrix} = -4te^{-2t}

Then

u_1=\displaystyle-\int\frac{7te^{-2t}}{-4te^{-2t}}\,\mathrm dt=\frac74\int\mathrm dt = \frac74t

u_2=\displaystyle\int\frac{7t(2t-1)}{-4te^{-2t}}\,\mathrm dt=-\frac74\int(2t-1)e^{2t}\,\mathrm dt=-\frac74(t-1)e^{2t}

The general solution to the ODE is

y = C_1(2t-1) + C_2e^{-2t} + \dfrac74t(2t-1) - \dfrac74(t-1)e^{2t}e^{-2t}

which simplifies somewhat to

\boxed{y = C_1(2t-1) + C_2e^{-2t} + \dfrac74(2t^2-2t+1)}

4 0
2 years ago
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cluponka [151]

Answer:

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3 years ago
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Butoxors [25]
To determine the answer it would be helpful if we write this equation into the slope intercept form which is expressed as:

y = mx+b

<span> y−2x=816
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We can see that the slope of the two equations are the same. Therefore, they are parallel which means they do not intersect. The correct answer is the third option, there is no solution.</span>
5 0
2 years ago
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