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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 ____

Mathematics

1 answer:

Tamiku [17]3 years ago

5 0

Answer:x=3/9

Step-by-step explanation:

X directly proportional to Y

X=ky

Make k the subject of formula

k=x/y

K=27/81

Divided by 9

K=3/9

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Please do 9,10,11,12 fast please

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Answer:

9) 1,2,3,6,9,18,27,54

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2 years ago

PLZ help fast I need this I’ll give brainliest

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Answer:

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Step-by-step explanation:

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2 years ago

Martina drove 737 miles in 11 hours. At the same rate, how long would it take her to drive 335 miles?

Dmitriy789 [7]

Answer:

5 hours

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2 years ago

Read 2 more answers

Write a linear inequality in two variables that has (-1, 3) as a solution but does not have (4,0) as a solution.

Stels [109]

Answer: y ≤ -x + 2

Step-by-step explanation:

There are an infinite number of possible solutions.

Plot the two points, draw any line between them such that the two points are NOT connected, then choose the inequality symbol that shades (-1, 3).

Here is one solution that satisfies the requirements. y ≤ -x + 2

Here is another: y < -x + 3

And another: y > x + 3

And one more: y ≥ x + 4

3 0

3 years ago

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

2 years ago