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3 years ago

13

You buy 24 keyboards for $120 each less 15%. What is your subtotal before taxes?

2 answers:

sineoko [7]3 years ago

7 0

2488 is the answer hope u get it right

kotykmax [81]3 years ago

5 0

<span>First, you need to take the 15% off from the $120 so it will make it easier for you to calculate later. Since there is 15% off, your $120 becomes only $102. Since your keyboards only costs $102 each now, you just have to multiply the number of keyboards you wanted to the less price. $102 multiplied by 24 keyboards is equals to $2,448. We don’t have to add taxes because it is stated that we are just looking for SUBTOTAL before taxes. The answer is A. $2,448. <span>
</span></span>

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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

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

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3 years ago

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AveGali [126]

Answer:

3m and 9m

Step-by-step explanation:

length of the rectangle = 2w+3

width of rectangle = w

area = L*W

if area = 27m²

then (2w+3)w=27

=2w²+3w-27=0

using factorization w= 3 or -4.5

w=3m

L=9m

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