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3 years ago

A dvd has a diameter of 12 centimeters. What is the area of the dvd? Round your answer to the nearest hundredth.

1 answer:

8 0

1/2 diameter= radius
1/2 (12)= 6 cm

Area= πr^2
A= (3.14)(6)^2
A= (3.14)(36)
A= 113.04 cm to nearest hundredth

ANSWER: The area, rounded to the nearest hundredth, is 113.04 cm.

Hope this helps! :)

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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

2 years ago

A. 60<br> b. 180<br> c. 100<br> d. 120

Leno4ka [110]

Answer:

120 is the correct answer

thanks. please mark brainlist

6 0

3 years ago

What value is a discontinuity of x squared plus 2 x plus 3, all over x squared minus x minus 12 ?

den301095 [7]

X² + 2x +3

If the discriminent Δ = b²-4.a.c <0 , that means the roots (or the zero value) are nit REAL Number (they are imaginary or complex)

Δ = 2² - 4(1)3) = 4 - 12 = -8

since Δ = - 8 < 0 there are no real roots

4 0

3 years ago

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Which graph represents a proportional relationship?

kumpel [21]

Answer:

If the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, ž is equal to k, where k is the unit rate. The point (1, k) is a point on the graph.

Step-by-step explanation:

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3 years ago

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Can u solve these asap pls

irakobra [83]

Step-by-step explanation:

We will use the Thales theorem since ED and CB are parallel and A,D and B are in the same lign wich is the same for C,E and A