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3 years ago

True Or False?

Mathematics

1 answer:

MariettaO [177]3 years ago

4 0

False, would mess up your whole geometric figure including the equation.

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The general solution of 2 y ln(x)y' = (y^2 + 4)/x is

Sav [38]

Replace $y'$ with $\dfrac{\mathrm dy}{\mathrm dx}$ to see that this ODE is separable:

$2y\ln x\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y^2+4}x\implies\dfrac{2y}{y^2+4}\,\mathrm dy=\dfrac{\mathrm dx}{x\ln x}$

Integrate both sides; on the left, set $u=y^2+4$ so that $\mathrm du=2y\,\mathrm dy$ ; on the right, set $v=\ln x$ so that $\mathrm dv=\dfrac{\mathrm dx}x$ . Then

$\displaystyle\int\frac{2y}{y^2+4}\,\mathrm dy=\int\dfrac{\mathrm dx}{x\ln x}\iff\int\frac{\mathrm du}u=\int\dfrac{\mathrm dv}v$

$\implies\ln|u|=\ln|v|+C$

$\implies\ln(y^2+4)=\ln|\ln x|+C$

$\implies y^2+4=e^{\ln|\ln x|+C}$

$\implies y^2=C|\ln x|-4$

$\implies y=\pm\sqrt{C|\ln x|-4}$

4 0

2 years ago

A rectangular prism has dimensions of 1/3, 3, and 5/3 in.

julsineya [31]

Answer:

Step-by-step explanation:

The rectangular prism has a volume equal to V=xyz. V=(1/3)3(5/3)=5/3 in^3. The cube has a volume equal to V=s^3. The volume of the cube is equal to the prism when

$s^3=(1/3)(3)(5/3)\\ \\ s^3=5/3\\ \\ s=\sqrt[3]{\frac{5}{3}}in\\ \\ s\approx 1.19in$

5 0

2 years ago

Six friends each use a $2.00 off coupon to buy themselves a movie ticket. They spend a total of 42. What is the price of one mov

attashe74 [19]

Answer:

Step-by-step explanation:

you would do 42 divided by 7 which is 6 then subtract 2 from 7 and you would get 5

5 0

2 years ago

Please answer it correctly and please show work please help me I need it

tamaranim1 [39]

Answer:

the equation is

y = 0.75x

And, the constant of proportionality is 0.75

Step-by-step explanation:

The computation is shown below:

Given that

4y = 3x

And,

12y = 9x

Here the equation that represent proportional relationship is

4y = 3x

Divide both sides by 4

y = 3x ÷ 4

Now

12y = 9x

divides both sides by 12

y = 9 ÷ 12x

y = 3 ÷ 4x

y = 0.75x

so the equation is

y = 0.75x

And, the constant of proportionality is 0.75

4 0

3 years ago

The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.03x2 + 1.53x, where x is the horizont

netineya [11]

This is the equation of an upside down parabola, so the maximum height will be at the vertex. To find the vertex, we'll use the formula for the x-coordinate and then solve for the y-coordinate.
$x=\frac{-1.53}{2*-.03}=25.5$

Plugging this into the given formula:
$y=-0.03(25.5)^2+1.53(25.5)=19.5075$
Since it asks us to round, the maximum height would be 20 yards. To find how far the football travels in total, we need to set the equation equal to 0 and find the roots:
$0=-0.03x^2+1.53x=x(-0.03x+1.53)$

Then by the zero product property (or the no zero divisors rule), we have:
$x=0$ (this is the x value where the ball is kicked from)
$-0.03x+1.53=0$
$-0.03x=-1.53$
$x=51$

So the ball travels 51 yards in total.

4 0

2 years ago

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