How many more whole numbers can “n” satisfy in the inequality shown?

131.12 divided by 44

Arte-miy333 [17]

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6 0

3 years ago

The capacity at the local police 225 people

andreyandreev [35.5K]

If they were 19& people at the pool what is the percentage 16.9

7 0

2 years ago

can some one plz answer my qwestion it is peter weighs 105 kg he want to lose 500 grams per week how many weeks willit take for

svet-max [94.6K]

Answer:

Your answer is he’s going to die out of Obesity

Step-by-step explanation:

8 0

3 years ago

Steve and Abby purchased a set of vases to place on a 12 foot long mantel above their fireplace. They want to place one vase 1/4

Nonamiya [84]

Answer: One vase should be placed 3 feet from the end of the mantel and the other vase should be placed 9 feet from the same end.

Step-by-step explanation:

You know that lenght of the mantel above their fireplace is 12 feet.

They want to place one vase $\frac{1}{4}$ of the distance from one end of the mantel. This distance in feet is:

$distance_{vase1}=(12feet)(\frac{1}{4})\\\\distance_{vase1}=3feet$

They want to place the other vase $\frac{3}{4}$ of the distance from the same end of the mantel. Therefore, this distance in feet is:

$distance_{vase2}=(12feet)(\frac{3}{4})\\\\distance_{vase2}=\frac{36feet}{4}\\\\distance_{vase2}=9feet$

Therefore, one vase should be placed 3 feet from the end of the mantel and the other vase should be placed 9 feet from the same end.

5 0

3 years ago

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0

2 years ago