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3 years ago

stickers are made with the same ratio of width to length. a sticker 2 inches has a length of 6 inches. complete the table

Mathematics

1 answer:

Furkat [3]3 years ago

4 0

The answer is 2 x10 = 20
To the power of b which is 15

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Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:

ryzh [129]

First find the critical points of f :

$f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7$

$\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1$

$\dfrac{\partial f}{\partial y}=6y=0\implies y=0$

so the point (1, 0) is the only critical point, at which we have

$f(1,0)=-7$

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

$f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t$

Find the critical points of g :

$\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0$

$\implies\sin t=0\text{ OR }1+5\cos t=0$

$\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi$

where n is any integer. We get 4 critical points in the interval [0, 2π) at

$t=0\implies f(10,0)=155$

$t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299$

$t=\pi\implies f(-10,0)=235$

$t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299$

So f has a minimum of -7 and a maximum of 299.

4 0

3 years ago

The distance Max's bike moves is directly proportional to how many rotations his bike's crank shaft has

Gemiola [76]

Answer:

187.5 feet

Step-by-step explanation:

we know that

Max's bike moves 25 feet after two rotations

using proportion

Find out how many feet will the bike move after 15 rotations

Let

x ----> the distance in feet

$\frac{25}{2}\frac{ft}{rev}=\frac{x}{15}\frac{ft}{rev}\\\\x=15(25)/2\\\\x=187.5\ ft$

7 0

3 years ago

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What’s the password. Pleas help

Alecsey [184]

Password to what exactly?

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3 years ago

In 56 years,Kevin will be 9 times as old as he is right now . How old is he right now ?

grandymaker [24]

6 bc if you divide 56 by 9 you’ll get 6.2 but i’m not sure the ( .2 ) will matter therefore just get the first digit which is 6

8 0

3 years ago

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Chris earns four times Vesna's wage v and Vesna earns $17 more than Dawn. How many dollars does Chris earn if their combined wag

guajiro [1.7K]

Call Dawn's wage x, we will have Vesna's wage = x + 17 and Chris' wage = 4x(x + 17). So we have the equation:
$x + (x + 17) + 4 \times (x + 17) = 163 \\ 2x + 17 + 4x + 68 = 163 \\ 6x = 78 \\ x = 13$
Therefore, Chris's wage:
$4 \times (13 + 17) = 120$

7 0

3 years ago

stickers are made with the same ratio of width to length. a sticker 2 inches has a length of 6 inches. complete the table​

stickers are made with the same ratio of width to length. a sticker 2 inches has a length of 6 inches. complete the table