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2 years ago

What is the midpoint of the segment shown below??

Mathematics

1 answer:

Leno4ka [110]2 years ago

4 0

Answer:

Step-by-step explanation:

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what is the coeffcient of a term that consists of a single variable?For example,what is the coefficient of x

Viktor [21]

1 easy
x=1x

if you have a cow, how many do you have? 1

if ou have an x, how many do you have? 1

1 is coeficinet

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2 years ago

The lengths of the legs of a right triangle are 8 inches and 9 inches. What is the length of the hypotenuse? Round to the neares

patriot [66]

Hyp^2 = 8^2 + 9^2
hyp^2 = 64 + 81
hyp^2 = 145
hot = 12 inch

6 0

3 years ago

(100 points!!!)

Sergio039 [100]

Answer:

this will probably help

Step-by-step explanation:

3 0

2 years ago

14)

klio [65]

Answer:

y = -1/4x -2

Step-by-step explanation:

the perpendicular slope would be -1/4

2 = -1/4 (-16) + b

b = -2

the equation should be y = -1/4x -2

None of the answers you typed could be correct.

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