3 years ago

2 (2x+1)+2x+x2+x simplified

Mathematics

1 answer:

Maurinko [17]3 years ago

8 0

X^2 + 7x + 2 that’s your answer

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Simplify the expressions by combining like terms 4r + 9r - 11r + 7r

konstantin123 [22]

9r
Explanation:
4r + 9r = 13r
13r-11r = 2r
2r + 7r = 9r

4 0

2 years ago

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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

2 years ago

using the formula v=l×w×h , find the volume of a right rectangular prism when the length of the prism is 45cm , the width is 12c

Natali [406]

The volume of the rectangular of prism is 5400

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2 years ago

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Which expression represents, 8 times the difference of two numbers?

tiny-mole [99]

Answer:

C, the difference is subtraction so 8 times the difference of two numbers is C

4 0

2 years ago

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Whats 1/18 as a decimal can someone please help me

sergij07 [2.7K]

1/18 as a decimal is 0.055555555555556 because you divide one by eighteen and get that number.

Hope this helped!

6 0

2 years ago