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3 years ago

Evaluate 2 1/2 + (- 7/6) - 1 3/4

Mathematics

1 answer:

ladessa [460]3 years ago

8 0

Answer:

-5/12 or .416

Step-by-step explanation:

Convert 2 1/2 to 5/2 and 1 3/4 to 7/4 then just solve from there!

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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

Ms evans paycheck is $850 a week.If she works 49 hours per week, how muxh does she make an hour

Aneli [31]

She would make about 17.35 because $850 divided by 49 is 17.3469388 rounded is 17.35

3 0

3 years ago

Let f(x)=x+2 and g(x)=2x+1 .

gogolik [260]

Step-by-step explanation:

Given g(x) = x+2 and f(x) = $2^x+1$

If f(x) = g(x)

⇔ $2^x+1$ = x+2

⇔ $2^x= x +1$

Only x= 1 and x=0 will be satisfy the above equation.

If x= 1, it gives and x=0 gives

$2^1= 1+1$ $2^0=0+1$

⇔2=2 ⇔1=1

7 0

3 years ago

Read 2 more answers

6/12 is that equivalent to 1/12

prohojiy [21]

No 6/12 is equal to 12/24

5 0

3 years ago

Find the length of a side of the square shown below. х 6V2 X = x = [?]

Leona [35]

Answer:

x=6

Step-by-step explanation:

In a square, its angles are all 90 degrees. So, cutting a square in half into two triangles from corner to corner produces 45 degree angles on both sides. Since the triangles are now 45-45-90 triangles, we can use the rule where the hypotenuse of the triangle is equal to the square root of 2 times the length of either side. So, the side length is 6.

4 0

3 years ago