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2 years ago

-9(m + 2) + 4(6 – 7m)

Mathematics

1 answer:

Travka [436]2 years ago

4 0

I think it is -37m+17 but I am not sure

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I need help w this pls :)

Llana [10]

Answer:

x8 y6

Step-by-step explanation:

5 0

2 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

How do you write the equation of the horizontal line passing through (1,9)?

Leviafan [203]

he equation of any horizontal line is

y = .. a number

The x-value has no effect on the equation or on the line at all, as long as y-value stays the same.

In this case the line passes though the point (−8,9)

which tells us that the y-value we want is 9.

Therefore the equation is y=9

4 0

2 years ago

Plz help giveing 10 pints

erik [133]

Just plug in the variables so you would have -(-3) - 4^2 / 4(-3) - (5-4). Next you solve it for 3 - 16 / -12 - 1, -13/-13 = 1. Your final answer is 1. If this is right could you possibly give me brainliest? Hope this helped.

7 0

3 years ago

Ravi and his wife are each starting a saving plan. Ravi will initially set aside $125 and then add $40.75 every week to the savi

katen-ka-za [31]

Answer:

T = 125 +116.40N

Step-by-step explanation:

The total savings is the sum of the two plan values:

T = A + B

T = (125 +40.75N) +(75.65N) . . . . substitute the given formulas

T = 125 + (40.75+75.65)N . . . . . . .combine like terms

T = 125 +116.40N

7 0

2 years ago

Read 2 more answers