What is 1/3 divided by 1/9

Mathematics

2 answers:

Viktor [21]4 years ago

7 0

.333333/.11111111 = 3

Margarita [4]4 years ago

6 0

1/3 / 1/9 = 1/3 * 9/1 = 9/3 = 3
When dividing fractions, multiply the first fraction by the reciprocal of the second fraction.
1/3 / 1/9 = 3

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Kendra has $6.00 in dimes and quarters. If she has 2 times as many quarters as dimes, how many of each coin does she have?

r-ruslan [8.4K]

Make a system of equations.

$\sf0.10d+0.25q=6$
$\sf~q = 2d$

Plug in 2d for 'q' in the first equation:

$\sf0.10d+0.25q=6$

$\sf0.10d+0.25(2d)=6$

Multiply:

$\sf0.10d+0.50d=6$

Combine like terms:

$\sf0.60d=6$

Divide 0.60 to both sides:

$\sf~d=10$

Now plug this into any of the two equations to find 'q':

$\sf~q = 2d$

$\sf~q = 2(10)$

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Find a solution to the initial value problem, y′′+18x=0,y(0)=5,y′(0)=1.

Serga [27]

We want to find a solution to the initial value problem:

$y'' + 18x = 0 \qquad,\qquad y(0) = 5 \qquad,\qquad y'(0)=1.$

We can start by integrating the equation once:

$\dfrac{\textrm{d}^2 y}{\textrm{d}x^2} + 18 x = 0 \iff \dfrac{\textrm{d}^2 y}{\textrm{d}x^2} = -18 x \iff\\\\\iff \dfrac{\textrm{d}y}{\textrm{d}x} = -18\displaystyle\int x\textrm{ d}x \iff \dfrac{\textrm{d}y}{\textrm{d}x}=-18\dfrac{x^2}{2} + C \iff\\\\\iff \dfrac{\textrm{d}y}{\textrm{d}x} = -9x^2 + C.$

Using the initial condition $y'(0) = 1$ , we can determine the integration constant $C$ :

$\dfrac{\textrm{d}y}{\textrm{d}x}\Big\vert_{x= 0} = 1 \iff -9 \times 0^2 + C = 1 \iff C = 1.$

Therefore, we have:

$\dfrac{\textrm{d}y}{\textrm{d}x} = -9x^2 + 1$

We can now integrate again:

$y(x) = \displaystyle\int\dfrac{\textrm{d}y}{\textrm{d}x}\textrm{ d}x = \int\left(-9x^2+1\right)\textrm{d}x = -9\int x^2\textrm{ d}x + \int\textrm{d}x =\\\\= -9\dfrac{x^3}{3} + x + K = -3x^3 + x + K.$