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3 years ago

What is the product of 4.5 × 10-5 and 2.4 × 10-2?

Mathematics

2 answers:

nikitadnepr [17]3 years ago

4 0

4.5 • 10-5 = 40

2.4 • 10-2 = 22

MissTica3 years ago

4 0

Answer is foty n twentytwo

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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

3 years ago

Anyone have any idea? i dont have any idea

ladessa [460]

Answer:

$\tt f(x)=2x^2+20x-10$

let y=f(x)

$\tt y=2x^2+20x-10$

$\tt 2x^2+10x=y+10$

$\tt x^2+10x=\frac{1}{2} y+5$

$\tt x^2+10x+25=\frac{1}{2} y+30$

$\tt (x+5)^2=\frac{1}{2} (y+60)$

$\tt 2(x+5)^2=f(x)+60$

$\boxed{\tt f(x)=2(x+5)^2-60}$

Hope it helps! :)

8 0

2 years ago

6.7.35

tino4ka555 [31]

Answer:

Step-by-step explanation:

dang this one is hard lol

4 0

2 years ago

Read 2 more answers

Heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeh pllll

Romashka-Z-Leto [24]

I think most of them are correct, you might wanna doubke check though! :)

7 0

3 years ago

If 1/2p=2 1/2q, find q:p<br><br>its 2 and a half not 21/2

daser333 [38]

Answer:

1/5 = q/p, or q:p

Step-by-step explanation:

You might want to rewrite 1/2p=2 1/2q as (1/2)p = (2 1/2)q.

To remove the fractions, multiply both sides by 2:

p = 2(2 1/2)q becomes p = 5q.

Dividing both sides by 5 yields p/5 = q.

Dividing both sides by p yields 1/5 = q/p, or q:p

7 0

3 years ago