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2 years ago

Explain the slope and y-intercept from the equation y=mx+b.

Mathematics

1 answer:

SIZIF [17.4K]2 years ago

7 0

Answer:

The variable "m" is the variable for SLOPE, and the variable "b" is the variable for the Y-INTERCEPT.

Hope this helps!

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I need help with this problem!! I need it answered by 11:59 tonight.

tino4ka555 [31]

OOP sorry did you get it

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3 years ago

How many paychecks do you get a year if you're paid semimonthly?

hjlf

Semi --> twice
semimonthly --> occuring twice a month

Thus:
You are paid twice a month

12 months in a year

12 x 2 = 24 paychecks an year

6 0

2 years ago

Find the maximum and minimum values attained by f(x, y, z) = 5xyz on the unit ball x2 + y2 + z2 ≤ 1.

Allushta [10]

Check for critical points within the unit ball by solving for when the first-order partial derivatives vanish:
$f_x=5yz=0\implies y=0\text{ or }z=0$
$f_y=5xz=0\implies x=0\text{ or }z=0$
$f_z=5xy=0\implies x=0\text{ or }y=0$

Taken together, we find that (0, 0, 0) appears to be the only critical point on $f$ within the ball. At this point, we have $f(0,0,0)=0$ .

Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian

$L(x,y,z,\lambda)=5xyz+\lambda(x^2+y^2+z^2-1)$

with partial derivatives (set to 0)

$L_x=5yz+2\lambda x=0$
$L_y=5xz+2\lambda y=0$
$L_z=5xy+2\lambda z=0$
$L_\lambda=x^2+y^2+z^2-1=0$

We then observe that

$xL_x+yL_y+zL_z=0\implies15xyz+2\lambda=0\implies\lambda=-\dfrac{15xyz}2$

So, ignoring the critical point we've already found at (0, 0, 0),

$5yz+2\left(-\dfrac{15xyz}2\right)x=0\implies5yz(1-3x^2)=0\implies x=\pm\dfrac1{\sqrt3}$
$5xz+2\left(-\dfrac{15xyz}2\right)y=0\implies5xz(1-3y^2)=0\implies y=\pm\dfrac1{\sqrt3}$
$5xy+2\left(-\dfrac{15xyz}2\right)z=0\implies5xy(1-3z^2)=0\implies z=\pm\dfrac1{\sqrt3}$

So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of $\left(\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3}\right)$ , at which points we get a value of either of $\pm\dfrac5{\sqrt3}$ , with the maximum being the positive value and the minimum being the negative one.

5 0

3 years ago

HELP PLEASE

nasty-shy [4]

Answer:

Part A: -2.5

Part B: -1

Part C: 1

Part D: 2.5

5 0

2 years ago

What is 8 times -8/9

LuckyWell [14K]

When you multiply a whole number by a fraction, multiply the whole number by the numerator ( top number) and then divide by the denominator (bottom number).

8 x -8/9 = (8 *-8)/9 = -64/9 = -7 1/9 = -7.1

5 0

3 years ago

Read 2 more answers