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3 years ago

Are 15:10 and 3:2 ratios equivalent?

Mathematics

2 answers:

Grace [21]3 years ago

7 0

Yes because if u divide 15:10 by 5 you will get 3:2

Grace [21]3 years ago

3 0

YES if you simplify 15:10 by 5 since they can both be divided by 5 the ratio becomes 3:2

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Use Lagrange multipliers to find the maximum and minimum values of

marusya05 [52]

The Lagrangian is

$L(x,y,\lambda)=x+8y+\lambda(x^2+y^2-4)$

It has critical points where the first order derivatives vanish:

$L_x=1+2\lambda x=0\implies\lambda=-\dfrac1{2x}$

$L_y=8+2\lambda y=0\implies\lambda=-\dfrac4y$

$L_\lambda=x^2+y^2-4=0$

From the first two equations we get

$-\dfrac1{2x}=-\dfrac4y\implies y=8x$

Then

$x^2+y^2=65x^2=4\implies x=\pm\dfrac2{\sqrt{65}}\implies y=\pm\dfrac{16}{\sqrt{65}}$

At these critical points, we have

$f\left(\dfrac2{\sqrt{65}},\dfrac{16}{\sqrt{65}}\right)=2\sqrt{65}\approx16.125$ (maximum)

$f\left(-\dfrac2{\sqrt{65}},-\dfrac{16}{\sqrt{65}}\right)=-2\sqrt{65}\approx-16.125$ (minimum)

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3 years ago

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IrinaK [193]

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3 years ago

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tinyurl.com/wpazsebu

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3 years ago

Y is directly related to x and y is 81 when x is 27 the constant of.variation is

suter [353]

Answer:

The constant of variation is 3

Step-by-step explanation:

Given.

$y=81$

$x=27$

And y is directly related to x

$y$ ∝ $x$

Here k is constant of variation

$y=kx$

$k=\frac{y}{x}$ --------------(1)

Put the $y$ and $x$ value in equation 1.

$k=\frac{81}{27}$

$k=3$

So, the constant of variation is 3.

6 0

3 years ago