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natulia [17]
3 years ago
13

Round 3.44570830811 to the nearest hundred-thousandth,

Mathematics
1 answer:
Alika [10]3 years ago
4 0

Answer:

3.44571

Step-by-step explanation:

look at the number to the right of the decimal. if the number is higher than or is 5 round the number up, but if the number is less than 5 it will stay the same.

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The product of five and a number, b<br> Please help
Verdich [7]

Answer:5x

Step-by-step explanation:

4 0
3 years ago
The height of a triangle is 5 m less than its base. The area of the triangle is 42 m².
SCORPION-xisa [38]
A = (1/2) b * h
h = b - 5
42 = (1/2) * b * (b - 5)
42 = (1/2) * b^2 - 5b
multiply both sides by 2 to clear the fraction (1/2)
2(42) = 2(1/2) *b^2 - 5b
84 = b^2 -5b
Since this is a quadratic equation, subtract 84 from both sides so that it is set = to zero.
b^2 - 5b - 84 = 0
Now factor.
(b - 12)(b + 5) = 0
b - 12 = 0; b = 12
b + 5 = 0; b = -5
You can't have a negative length so the answer is 12m
To check the answer:
A = (1/2) * 12* 7
A = 42 m^2
4 0
3 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
Someone help me with this math problem pleasee
Mekhanik [1.2K]

Answer:

0.012

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
The probability that an event will occur is 2/3 what is the best answer of this event likely occurring
Oduvanchick [21]
It's likely that the event will occur.
6 0
3 years ago
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