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Tresset [83]
3 years ago
15

For every hour that passes, the temperature drops by 6. What is the temperature change after 4 hours

Mathematics
2 answers:
Ber [7]3 years ago
8 0

Answer:

24

Step-by-step explanation:

1 hour = 6

So, 6 times 4 equals 24 which is how much temperature that changed.

choli [55]3 years ago
7 0

Answer: 24

Step-by-step explanation:

1 hour = 6

So, 6 times 4 equals 24 which is how much temperature that changed.

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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
Please help fast will give brainliest
antoniya [11.8K]

Answer:

THE ANSWER IS C

Step-by-step explanation:

8 0
3 years ago
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Please help and I'll love you foreverrrrr no joke!!!
spin [16.1K]
Only like sedans: 25- 15 = 10

Only like hatchbacks: 40-15 = 25

Like both: 15

Like none of them: 100-10-25-15 = 50

Dislike sedans: 100 - 10-15 = 75

Dislike hatchbacks: 100-25-15 = 60

So dislikes: sedans>hatchbacks
4 0
3 years ago
Suppose f(x)= 4x/3+5 and g(x) = x/3 +1. solve for x when f(x)=g(x)
yuradex [85]
\bf \begin{cases}
f(x)=\cfrac{4x}{3}+5\\\\
g(x)=\cfrac{x}{3}+1
\end{cases}\qquad f(x)=g(x)\implies \cfrac{4x}{3}+5=\cfrac{x}{3}+1

solve for "x" then
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What is the answer for this
ella [17]

Answer:

Grids b and c have 25% shaded

Step-by-step explanation:

a) shaded = 5/16 = 31.25%

b) shaded = 4/16 = 25%

c) shaded = 5/20 = 25%

d) shaded = 3/10 = 30%

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3 years ago
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