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tresset_1 [31]
2 years ago
8

Fill in the blanks to complete the sentence

Mathematics
1 answer:
user100 [1]2 years ago
4 0

Answer:

You would use the cos function because you are given the adjacent side and you are finding the opposite side.

Step-by-step explanation:

SOH CAH TOA

Sin = O/H

Cos = A/H

Tan = O/A

O is the Opposite side

H is the Hypotenuse

A is the adjacent side

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Find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y, z) = xy2z2 has a maximum value.
irina1246 [14]
Lagrange multipliers:

L(x,y,z,\lambda)=xy^2z^2+\lambda(x+y+z-5)

L_x=y^2z^2+\lambda=0
L_y=2xyz^2+\lambda=0
L_z=2xy^2z+\lambda=0
L_\lambda=x+y+z-5=0

\lambda=-y^2z^2=-2xyz^2=-2xy^2z

-y^2z^2=-2xyz^2\implies y=2x (if y,z\neq0)

-y^2z^2=-2xy^2z\implies z=2x (if y,z\neq0)

-2xyz^2=-2xy^2z\implies z=y (if x,y,z\neq0)

In the first octant, we assume x,y,z>0, so we can ignore the caveats above. Now,

x+y+z=5\iff x+2x+2x=5x=5\implies x=1\implies y=z=2

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of f(1,2,2)=16.

We also need to check the boundary of the region, i.e. the intersection of x+y+z=5 with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force f(x,y,z)=0, so the point we found is the only extremum.
4 0
3 years ago
What is the slope of the line that passes through the points (6, 2) and (4, 10)?
drek231 [11]

Answer:

-4

Step-by-step explanation:

Slope = y2 - y1/x2 - x1

Given

x1 = 6

y1 = 2

x2 = 4

y2 = 10

Therefore

Slope = 10 - 2/4 - 6

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3 years ago
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The sum of twice a number and 6 is the same as 3 subtracted from the number itself
rusak2 [61]
3+3=6
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Find the constant of proportionality given s = kt,<br> and s = 60 when t = 6.
Alinara [238K]

Answer:

sln

s=kt

60=k6

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