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2 years ago

Select the graph that represents the following inequality: Ix+2.5I>1.5

Mathematics

1 answer:

fgiga [73]2 years ago

7 0

◆ Linear Reductions ◆

Hey !!

Check the attachment.
Hope it helps you :)

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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

2 Points

sergeinik [125]

Answer:

Step-by-step explanation:

x²+x²=14²

2x²=196

x²=196/2=98

x=7√2 ft

3 0

3 years ago

Solve the problem -8 / (-4) + (6 + 2) =? A. 12 B. 6 C. 8 D. 10

zmey [24]

Answer:

d , 10

Step-by-step explanation:

-8 / -4 = positive 2, + (6+2) (eight) = 10

7 0

3 years ago

Read 2 more answers

In 2004, a survey on computer crime indicated that 7% of reported unauthorized uses of business Web sites came from inside the c

masya89 [10]

Answer:

a) H0 : P = 0.07

Ha : P ≠ 0.07

b) p -value = 0.1770

Step-by-step explanation:

P = 7% = 0.07

x (result ) = 7 , n = 163

p = x / n = 7 / 163 = 0.043

a) Using a significance level ( ∝ ) of 0.05, estimate the appropriate hypothesis

H0 : P = 0.07

Ha : P ≠ 0.07

conduct a Z- test statistic

Z = ( p - P ) / $\sqrt{\frac{P(1-P)}{n} }$

= ( 0.043 - 0.07 ) / $\sqrt{\frac{P(1-P)}{n} }$ = - 1.35

Critical value ( Z₀.₀₂₅ ) = ± 1.96

we fail to reject H0 given that | z | < Zcritical because there is not enough evidence to conclude that proportion change

b) Determine the p-value of the test

P-value = P ( | Z | > Z )

= 2 * P ( Z < -1.35 )

= 0.1770

The p-value ( 0.1770 ) > ∝ ( 0.05 ) hence we fail to reject H0 ( i.e. the conclusion agrees with part a above )

8 0

3 years ago

I give 23 points!!

svlad2 [7]

Answer:

75 miles

Step-by-step explanation:

8 × blank how many times does. 8 go into 120 it goes in 15 times so now we got 15 what is 15×5 because. 8 km is 5m

5 0

2 years ago