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3 years ago

Hank Wants to divide 345 pieces of construction paper evenly among his 23 classmates. How many pieces will be left over?

Mathematics

1 answer:

sleet_krkn [62]3 years ago

5 0

Answer:

There will be no pieces of paper left over. Each student will receive 15 pieces of paper.

Step-by-step explanation:

If you divide the 345 pieces of paper between the 23 classmates, you will end up with 15. There is no remainder or decimal, just 15, a whole number. That means that there will be no pieces of paper left over.

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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

y''(t) + p(t) y'(t) + q(t) y(t) = f(t)

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

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

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 W 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

How to slove step by step

wariber [46]

$\frac{x+3}{12}$ = $\frac{2}{7}$

Multiply both sides by 12, so that we get rid of the fraction in x.

12 · (x+3)/12 = 2/7 · 12

Simplify.

x + 3 = 24/7

Then, subtract 3 from both sides, so that "x" gets isolated.

x = 24/7 - 3

Turn "3" into an improper fraction so that we could find the value of x easier.

3 = 21/3

So :

x = 24/7 - 21/7

Simplify.

x = 3/7

~Hope this helps!~

7 0

3 years ago

Simplify the following expression : (2x + 7y) (x – 3y) – (9x + 4) (3x - 2)

Dmitriy789 [7]

-25x^2+xy-21y^2+6x+8

8 0

3 years ago

Sally has decided to spend some time over two days soving math problems. She figures that on the first day she wil be able to so

erastova [34]

A system of equations for this would be

19x + 11y = 273

and

12x + 17y = 283.

X is the amount of minutes to solve one long division problem and y is the amount of minutes to solve a graphing problem.

How To Solve This System of Equations.

Multiply both by 17 and 11 respectively for them to have the greatest common factor for y. So now both equations are:

323x + 187y= 4641

132x + 187y= 3113.

Subtract both equations and you have left:

191x = 1528.

Divide both sides by 191 and you find x.

X = 8.

Answer

It takes Sally 8 minutes to do one Long Division Problem.

Hope this helped. ;)

6 0

3 years ago

Read 2 more answers

What is the area of this composite figure?

Gelneren [198K]

Answer:

249 centimeters squared

Step-by-step Explanation:

The area of the rectangle: l x w, where l is the length and w is the width.

= 15.5 x 18

= 279

Area of the smaller rectangle: l x w, where l is the length and w is the width.

= 4 x 7.5

= 30

We do not need this 30.

Area of the shaded region:

= 279 - 30

= 249 cm²

5 0

2 years ago