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3 years ago

Javier is 175% heavier than his brother. If Javier’s brother weighs 80 pounds, how much does Javier weigh?

Mathematics

1 answer:

bija089 [108]3 years ago

7 0

Answer:

140

Step-by-step explanation:

175% of 80 = 140

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What is the domain of y = log Subscript 4 Baseline (x + 3)?

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Answer:

All real numbers greater than -3

Step-by-step explanation:

The domain of a log is the baseline is greater than 0.

Set x + 3 greater than zero and solve

x + 3 > 0

x > -3

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2 years ago

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Find the volume of the composite solid. Round your answer to the nearest tenth.

amm1812

Answer:

Volume of the Figure $=825.38m^3$

Step-by-step explanation:

Volume of the figure = Volume of the Upper cone+Volume of the lower cone

Volume of a cone = $\pi *r^2*\frac{h}{3}$

Volume of the Upper Cone with

$height=12m$

$radius=6m$

$3.14*6*6*\frac{12}{3}$

$=3.14*6*6*4\\\\=3.14*36*4\\\\=3.14*144\\\\=147.14m^3$

Volume of the Lower cone with $radius=6m$ and $height=18m$

$=3.14*6*6*\frac{18}{3} \\\\=3.14*6*6*6\\\\=3.14*36*6\\\\=3.14*216\\\\=678.24m^3$

Volume of the Whole Figure = $147.14+678.24$

Volume of the Figure $=825.38m^3$

4 0

3 years ago

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