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3 years ago

If 48$ is 10% what is 100%

Mathematics

2 answers:

lys-0071 [83]3 years ago

4 0

100 is 480% , times by 48

marishachu [46]3 years ago

4 0

480%. Hope this could help!

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What is 84×22 in standard algorithm for fifth grade

Alekssandra [29.7K]

84.
x22 equals 1848

5 0

3 years ago

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Can someone plz help me plz I beg u the answer choices are at the bottom just pls

enot [183]

Answer:

Step-by-step explanation:

6 0

3 years ago

Use the Laplace transform and inverse Laplace transform to solve in the initial value problem y''-3y'+2y=4t-6 y(0)=1, y'(0)=2

Vesnalui [34]

Denote by $Y(s)$ the Laplace transform of $y(t)$ .

$y''-3y'+2y=4t-6$

Take the Laplace transform of both sides:

$(s^2Y(s)-sy(0)-y'(0))-3(sY(s)-y(0))+2Y(s)=\dfrac4{s^2}-\dfrac6s$

Solve for $Y(s)$ :

$(s^2Y(s)-s-2)-3(sY(s)-1)+2Y(s)=\dfrac4{s^2}-\dfrac6s$

$(s^2-3s+2)Y(s)=\dfrac4{s^2}-\dfrac6s+s-1$

$Y(s)=\dfrac{4-6s-s^2+s^3}{s^2(s^2-3s+2)}$

$Y(s)=\dfrac{4-6s-s^2+s^3}{s^2(s-1)(s-2)}$

Decompose the right side into partial fractions: we're looking for constants $a_1,\ldots,a_4$ such that

$\dfrac{4-6s-s^2+s^3}{s^2(s-1)(s-2)}=\dfrac{a_1}s+\dfrac{a_2}{s^2}+\dfrac{a_3}{s-1}+\dfrac{a_4}{s-2}$

$4-6s-s^2+s^3=a_1s(s-1)(s-2)+a_2(s-1)(s-2)+a_3s^2(s-2)+a_4s^2(s-1)$

Expanding on the right side gives

$2a_2+(2a_1-3a_2)s-(3a_1-a_2+2a_3+a_4)s^2+(a_1+a_3+a_4)s^3$

and matching up coefficients gives the system

$\begin{cases}2a_2=4\\2a_1-3a_2=-6\\3a_1-a_2+2a_3+a_4=1\\a_1+a_3+a_4=1\end{cases}\implies a_1=0,a_2=2,a_3=2,a_4=-1$

So we have

$Y(s)=\dfrac2{s^2}+\dfrac2{s-1}-\dfrac1{s-2}$

and taking the inverse transform of both sides is trivial, giving

$\boxed{y(t)=2t+2e^t-e^{2t}}$

4 0

4 years ago

Answer Choices: 1/12 1/2 1/6 2/3

lyudmila [28]

Answer:

1/12

Step-by-step explanation:

there is 1/2 chance of flipping heads and 1/6 chance of rolling a six

1/2*1/6=1/12

7 0

3 years ago

Find the equation of the line perpendicular to x−5y=15 that passes through the point (−2,5).

Snowcat [4.5K]

First off, let's solve x−5y=15 for "y".

 $\bf x-5y=15\implies x-15=5y\implies \cfrac{x-15}{5}=y\implies \stackrel{slope}{\cfrac{1}{5}}x-3=y$

now, notice the function in slope-intercept form, well, it has a slope of 1/5.

now, a perpendicular line to that one, will have a negative reciprocal to that, let's check what that is.

 $\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{1}{5}\\\\
slope=\cfrac{1}{{{ 5}}}\qquad negative\implies -\cfrac{1}{{{ 5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{1}\implies -5$

so, we're looking for the equation of a line whose slope is -5 and goes through -2,5.

 $\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ -2}}\quad ,&{{ 5}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies -5
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-5=-5[x-(-2)]
\\\\\\
y-5=-5(x+2)\implies y-5=-5x-10\implies y=-5x-5$

4 0

3 years ago

Read 2 more answers