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3 years ago

(1/125x^3)-1/3 Simplify the expression

Mathematics

1 answer:

bija089 [108]3 years ago

3 0

Step-by-step explanation:

Simplify 1/125

1/125 . (x3))-1) ÷ 3

(x3

(———)-1) ÷ 3

125

3.1 x3 raised to the minus 1 st power = x( 3 * -1 ) = x-3

3.2 125 = 53 (125)-1 = (53)(-1) = (5)(-3)

x(-3)

——————— ÷ 3

(5)(-3)

x(-3)

Divide ——————— by 3

(5)(-3)

Answer: 125

/3x3

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3 years ago

Estimate the quotient of 57.8 divided by 81

Rudik [331]

Right answer is 1.4013841

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3 years ago

This table gives a few (x,y) pairs of a line in the coordinate plane.

fomenos

Answer:

(-22,0)

explanation:

You subtract 10 from 8 and you get -2 and if you subtract 10 from -2 you get -12 so there for you are subtracting by 10 on the x-values so if you do -12 - 10 = -22 making your answer (-22,0).

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3 years ago

Dy/dx = 2xy^2 and y(-1) = 2 find y(2)

Anarel [89]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2887301

—————

Solve the initial value problem:

dy
——— = 2xy², y = 2, when x = – 1.
dx

Separate the variables in the equation above:

$\mathsf{\dfrac{dy}{y^2}=2x\,dx}\\\\
\mathsf{y^{-2}\,dy=2x\,dx}$

Integrate both sides:

$\mathsf{\displaystyle\int\!y^{-2}\,dy=\int\!2x\,dx}\\\\\\
\mathsf{\dfrac{y^{-2+1}}{-2+1}=2\cdot \dfrac{x^{1+1}}{1+1}+C_1}\\\\\\
\mathsf{\dfrac{y^{-1}}{-1}=\diagup\hspace{-7}2\cdot \dfrac{x^2}{\diagup\hspace{-7}2}+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{y}=x^2+C_1}$

$\mathsf{\dfrac{1}{y}=-(x^2+C_1)}$

Take the reciprocal of both sides, and then you have

$\mathsf{y=-\,\dfrac{1}{x^2+C_1}\qquad\qquad where~C_1~is~a~constant\qquad (i)}$

In order to find the value of C₁ , just plug in the equation above those known values for x and y, then solve it for C₁:

y = 2, when x = – 1. So,

$\mathsf{2=-\,\dfrac{1}{1^2+C_1}}\\\\\\
\mathsf{2=-\,\dfrac{1}{1+C_1}}\\\\\\
\mathsf{-\,\dfrac{1}{2}=1+C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-1=C_1}\\\\\\
\mathsf{-\,\dfrac{1}{2}-\dfrac{2}{2}=C_1}$

$\mathsf{C_1=-\,\dfrac{3}{2}}$

Substitute that for C₁ into (i), and you have

$\mathsf{y=-\,\dfrac{1}{x^2-\frac{3}{2}}}\\\\\\
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\mathsf{y=-\,\dfrac{2}{2x^2-3}}$

So y(– 2) is

$\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot (-2)^2-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{2\cdot 4-3}}\\\\\\
\mathsf{y\big|_{x=-2}=-\,\dfrac{2}{8-3}}\\\\\\
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I hope this helps. =)

Tags: <em>ordinary differential equation ode integration separable variables initial value problem differential integral calculus</em>

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3 years ago

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Murrr4er [49]

Answer:

$43,512

Step-by-step explanation:

3.6% = 0.036

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42,000 + 1,512 = 43,512

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3 years ago