Which is the correct answer? A) 3.41 m B) 2.29 m C) 1.59 m D) 2.71 m

77julia77 [94]

1/6 divided by 2

Keep, change, flip

1/6 * 1/2 = 1/12

Answer: 1/12

4 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

3 years ago

An antelope can run at a speed of 61 miles per hour. What is the speed in yards per second

jekas [21]

0.489 yards per second

8 0

3 years ago

How do you measure the perimeter of a shape

Advocard [28]

Perimeter is a measure of the area or distance around a two-dimensional shape. On a rectangle, for instance, the perimeter is the total length of the rectangle's outline, including the two widthwise borders and the two lengthwise borders.

To determine the perimeter of a shape, therefore, you add together all the dimensions that make up the shape's outer edge. Being able to find the perimeter of a shape has many applications in the real world. Say, for example, that you wanted to build a fence around your backyard. In order to purchase materials, you need to know how much fencing you'll need, and to determine that you have to figure out the perimeter of the area you want to fence in.

8 0

2 years ago

Of 560 marbles in a bag, 65% are red and the rest are blue. After 28 red marbles are replaced with blue ones, how many blue marb

jonny [76]

Answer: The answer is 400 blue marbles.

Step-by-step explanation: Given that there are 560 marbles in a bag, out of which 65% are red and rest are blue.

So, number of red marbles is

$n_r=65\%\times 560=\dfrac{65}{100}\times 560=364,$

and number of blue marbles is

$n_b=560-364=196.$

Now, if 28 red marbles are replaced by blue marbles, the the new number of red and blue marbles will be

$n_r^\prime=364-28=336~~~\textup{and}~~~n_b^\prime=196+28=224.$

Now, to get 65% of the marbles blue, we need to add some more blue marbles to the bag. Let 'x' number of blue marbles are added to the bag, then

$65\%\times (560+x)=224+x\\\\\Rightarrow \dfrac{65}{100}\times (560+x)=224+x\\\\\Rightarrow 13(560+x)=20(224+x)\\\\\Rightarrow 7280+13x=4480+20x\\\\\Rightarrow 7x=2800\\\\\Rightarrow x=400.$

Thus, 400 blue marbles need to be added to the bag.

5 0

3 years ago

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