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3 years ago

Which of the following expressions can be used to find the perimeter of a rectangle?

Mathematics

1 answer:

morpeh [17]3 years ago

5 0

Answer:

2l + 2w. l+l+w+w. l+l+2w. 2(l+w)

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Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=x+4y subject to the constraint x2+y2=9, if such values

Vesnalui [34]

The Lagrangian is

$L(x,y,\lambda)=x+4y+\lambda(x^2+y^2-9)$

with critical points where the partial derivatives vanish.

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

$L_y=4+2\lambda y=0\implies y=-\dfrac2\lambda$

$L_\lambda=x^2+y^2-9=0$

Substitute $x,y$ into the last equation and solve for $\lambda$ :

$\left(-\dfrac1{2\lambda}\right)^2+\left(-\dfrac2\lambda\right)^2=9\implies\lambda=\pm\dfrac{\sqrt{17}}6$

Then we get two critical points,

$(x,y)=\left(-\dfrac3{\sqrt{17}},-\dfrac{12}{\sqrt{17}}\right)\text{ and }(x,y)=\left(\dfrac3{\sqrt{17}},\dfrac{12}{\sqrt{17}}\right)$

We get an absolute maximum of $3\sqrt{17}\approx12.369$ at the second point, and an absolute minimum of $-3\sqrt{17}\approx-12.369$ at the first point.

4 0

3 years ago

Write an equation of the line with the given slope, m and y intercept (0,b) m=-6, b =-1/2 plss

Arlecino [84]

Recall that an equation in slope-intercept form is as follows:

$y=mx+b,$

where m is the slope of the line, and (0,b) is the y-intercept.

Substituting m=-6, and b=-1/2 we get:

$y=-6x+(-\frac{1}{2})\text{.}$

Simplifying the above result we get:

$y=-6x-\frac{1}{2}\text{.}$

Answer:

$y=-6x-\frac{1}{2}\text{.}$

5 0

1 year ago

For a science project, James needs to fill a tennis ball with sand but he doesn't know how much he will need. He measured the di

klio [65]

Do not go to that link it is a virus and if you go to “goggle” and press the camera icon on the top right and take a picture of the question you should get the answer there

8 0

2 years ago

And ice cream factory makes 190 quarts of ice cream in five hours how many quarts could be made in 36 hours what was the rate pe

levacccp [35]

190/5 = 38

So, they can make 38 quarts in an hour.

38 * 36 = 1,368

They can make 1,368 quarts in 36 hours.

3 0

3 years ago

A radio talk show host asked listeners to respond either yes or no to the question, "Is the candidate who spends the most on a c

IgorLugansk [536]

Answer:

Implied population is all listeners of the radio talk show

the variable is opinion of a listener

Yes, bias is voluntary response. Those with the strongest opinions are most likely to call in.

Step-by-step explanation:

Radio talk show host asked listeners to respond therefore the population is all listeners of the radio talk show.

The variable is the response "yes" or "no"

There is voluntary response bias, because the respondents are volunteered to answer, therefore sample is consisted of self-selected listeners.

3 0

4 years ago