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Tpy6a [65]
3 years ago
13

An Olympic runner set a record for the 100m dash.

Mathematics
1 answer:
DiKsa [7]3 years ago
5 0
10.62 seconds

ignore:
(i am writing this bc i need at least 20 characters)
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3.) The height of the baseball can be modeled by the function Hs= -16s2+96s where s represents the time in seconds the ball is i
Aleks04 [339]

Answer:

what's the topic hahhahahahah

3 0
3 years ago
The local office supply store charges $0.08 per page to make photocopies. Lionel paid $20.00 for a set of copies. How many pages
Darina [25.2K]

Answer:

250

Step-by-step explanation:

You do 20/.08 to get 250.

5 0
3 years ago
Read 2 more answers
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
Melons cost $.56 per pound how many pounds can be bought with $5.60
Reptile [31]
You can buy 10 pounds of melons
5 0
2 years ago
If z = 2, find the value of: a. 6z2–2z+5<br> b. 64–5z
Ludmilka [50]

Answer:

25 and 54

Step-by-step explanation:

(a)

6z² - 2z + 5 ← substitute z = 2

= 6(2)² - 2(2) + 5

= 6(4) - 4 + 5

= 24 - 4 + 5

= 20 + 5

= 25

(b)

64 - 5z ← substitute z = 2

= 64 - 5(2)

= 64 - 10

= 54

4 0
2 years ago
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