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melamori03 [73]
3 years ago
9

Simplify. 4*3 · 4*4

Mathematics
1 answer:
viktelen [127]3 years ago
4 0
A)4*16

because 4*3•4*4•4*9
you have to add the exponents

3+4+9=16
keep the number

so 4*16 is the answer
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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
Delia earns $10.50 per hour working at a restaurant. On Friday she spent 1 3/4 hours cleaning . 2 1/3 hours doing paperwork, and
DIA [1.3K]
Friday:
She earns $10.5×1 3/4=$18.375 for cleaning, 10.5×2 1/3=$24.5 for doing paper work, 10.5×1 5/12=$14.875 for serving costumes. As a result, Delia earns $57.75 in total. Hope it help!
6 0
3 years ago
When do we say that the computed solution or root of a quadratic equation is<br>extraneous?<br><br>​
scoray [572]

Answer:

raising both sides of the equation to a certain power in order to eliminate radicals may result in the creation of extraneous roots

Step-by-step explanation:

7 0
3 years ago
A baby bird jumps from a tree branch and flutters to the ground. The function "f" models the bird's height (in meters) above the
AURORKA [14]

The answer to this question will depend on the function f itself. Basically you will find the height in meters above the ground of the bird when it jumped when the time t=0s. This is substsitute every t in the function for a value of zero and that way you will get the bird's height at the time it jumped. If you were given a graph for this function, you can find the y-intercept of the graph and that will be the answer as well. The question could be written like this:

A baby bird jumps from a tree branch and flutters to the ground. The function "f(t)-4.9t^{2}+25" models the bird's height (in meters) above the ground as a function of time (in seconds) after jumping. What is bird's height above the ground when it jumped.

Answer:

25m

Step-by-step explanation:

Once your function is given, you can substitute t=0 since 0s is the time measured at the moment the bird jumped. So our function will be:

f(0)=-4.9(0)^2+25

f(0)=25m

So the height of the bird above the ground when it jumped is 25m in this particular function.

8 0
2 years ago
Answer for any of these will help with work as well
Orlov [11]
13. 81.64
14. 803.84
15. 153.83
16. 753.6


you just use circumference and area formulas for a circle
8 0
3 years ago
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