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2 years ago

8

A company is expanding its building area from 14,000 square feet to 17,640 square feet. What is the percentage increase of the a

rea of the building space

1 answer:

natali 33 [55]2 years ago

6 0

Answer:

its about 7.9% I think .... ............

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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

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

4 0

2 years ago

X+45+38 +231=360 help again

nikdorinn [45]

Are you tryna solve for x?

4 0

2 years ago

Alpha false and true Which of the following statements are true? If false, explain briefly.

solmaris [256]

Answer:

A. False

B. True

C. True

D.True

Step-by-step explanation:

A. False . The significance level or alpha is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. 0.01 alpha is better than 0.05 alpha . 0.01 indicate a 1% risk of rejecting the null hypothesis when it is true .

B. True . If the p-value is less than alpha, we reject the null hypothesis . Therefore statistically significant.

C . True . If the p-value is less than alpha, we reject the null hypothesis

D. True . Alpha will be greater than p-value . Therefore we will reject .

8 0

2 years ago

Bezzdna [24]

50 per share hope this helped

6 0

2 years ago

A seamstress needs to cut 15-inch pieces of ribbon from a roll of ribbon that is 9 feet length. What is the greatest number of 1

yan [13]

STEP 1:
Divide the length of the ribbon by the size of the pieces.

12 inches= 1 foot

= 9 ft ÷ 15 inch pieces
convert ft to inches
= (12)(9) ÷ 15
= 108 ÷ 15
= 7.2 pieces from one roll

STEP 2:
multiply the number of pieces that can be cut from one roll by the number of rolls

= 7.2 pieces * 5 rolls
= 36 pieces total from 5 rolls

ANSWER: The greatest number of 15-inch pieces that can be cut from five 9-foot rolls is 36.

Hope this helps! :)

4 0

3 years ago