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2 years ago

The volume of a cube of ice for an ice sculpture is 64000

Mathematics

1 answer:

-BARSIC- [3]2 years ago

8 0

no question to answer

Step-by-step explanation:

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Find a linear second-order differential equation f(x, y, y', y'') = 0 for which y = c1x + c2x3 is a two-parameter family of solu

Alisiya [41]

Let $y=C_1x+C_2x^3=C_1y_1+C_2y_2$ . Then $y_1$ and $y_2$ are two fundamental, linearly independent solution that satisfy

$f(x,y_1,{y_1}',{y_1}'')=0$
$f(x,y_2,{y_2}',{y_2}'')=0$

Note that ${y_1}'=1$ , so that $x{y_1}'-y_1=0$ . Adding $y''$ doesn't change this, since ${y_1}''=0$ .

So if we suppose

$f(x,y,y',y'')=y''+xy'-y=0$

then substituting $y=y_2$ would give

$6x+x(3x^2)-x^3=6x+2x^3\neq0$

To make sure everything cancels out, multiply the second degree term by $-\dfrac{x^2}3$ , so that

$f(x,y,y',y'')=-\dfrac{x^2}3y''+xy'-y$

Then if $y=y_1+y_2$ , we get

$-\dfrac{x^2}3(0+6x)+x(1+3x^2)-(x+x^3)=-2x^3+x+3x^3-x-x^3=0$

as desired. So one possible ODE would be

$-\dfrac{x^2}3y''+xy'-y=0\iff x^2y''-3xy'+3y=0$

(See "Euler-Cauchy equation" for more info)

6 0

3 years ago

Graph f(x)= x^3 + x^2

ozzi

I would give the answer but there are to many numbers and I don't want you to get confused by the answer I give you

8 0

2 years ago

Write an equation of a quadratic function that has x-intercepts -1 and 4 and a y-intercept of 3.

igomit [66]

Y=(x+1)(x-4)

this should be correct.

5 0

3 years ago

helppp plssssss (10 points)

Margaret [11]

4 + -6 = -2

Hope that helps? Sorry if it doesn’t...

6 0

2 years ago

You need to cover the playground of a child development center with mulch. the playground is 125 feet long and 60 feet wide. you

kirill [66]

The answer is 139 cubic yards

This mulch will be of cylindrical shape.
The volume (V) of a cylinder is:
V = l · w · h (l - length, w - width, h - height (in our example, height = depth)

It is known:
l = 125 feet
w = 60 feet
h = 6 inches = 0.5 feet

V = l · w · h = 125 · 60 · 0.5 = 3750 feet³

Since 1 cubic foot is 0.037 cubic yards, 3750 cubic feet are 139 cubic yards:
0.037 · 3750 feet³ = 138.75 cubic yards ≈ 139 cubic yards

4 0

3 years ago