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devlian [24]
2 years ago
14

Evaluate each expression ​

Mathematics
1 answer:
choli [55]2 years ago
6 0

Answer:

below

Step-by-step explanation:

  • c = 8 and  d = -3

c^{2} + d^{3} \\8^{2} + (-3)^{3} \\64 + (-27) \\64 - 27 \\37

  • r = -3  and   s = -4

( r -  s)^{3} + r^{2}\\(-3 -(-4))^{2} + (-3)^{2} \\(-3+4)^{3} + 9+ \\1^{3} + 9\\1 + 9 \\10

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I don't understand this question. Could anyone excplain to me what it wants me to do and what the answer is?
Hatshy [7]
The answer is 18.2
I got the answer by solving it
7 0
3 years ago
Read 2 more answers
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
Imaginen que un maratonista corre toda una carrera a una velocidad constante. Después de dos horas lleva recorridos 22 km
saw5 [17]

For this case we have:

If after 2 hours the marathon runner has traveled 22 kilometers we have:

2h -----------> 22km

Applying a rule of three, we can know the time it takes to run 42km. So, we have:

2h -----------> 22km

x -------------> 42km

Where "x" is the time it takes to travel 42km. Resolving we have:

x = \frac {(42 * 2)} {22}

x = \frac {84} {22}

x = \frac {42} {11}

x = 3.82 hours

Thus, after 3.82 hours the marathon runner will travel 42km.

Answer:

3.82 hours


6 0
2 years ago
Justin solved this problem.
aleksklad [387]
The answer is A, yes his answer is reasonable because 6 times 0.74 is 44.4
4 0
2 years ago
Read 2 more answers
kayden paddled a canoe to an island. the island is 8 miles from the shore. his trip to the island took two hours while paddling
Andrew [12]

Answer:

2\text{ mph}

Step-by-step explanation:

GIVEN: kayden paddled a canoe to an island. the island is 8 miles from the shore. his trip to the island took two hours while paddling against the current. he paddles 6 mph with no current.

TO FIND: what was the speed of the current.

SOLUTION:

distance of island from the shore =8 miles

total time taken by Kayden =2 hours

speed of Kayden in still water =6\text{ mph}

Let the speed of current be x

Speed of Kayden against current =6-x\text{ mph}

As,

\text{Time}=\frac{\text{Distance}}{\text{speed}}

2=\frac{8}{6-x}

12-2x=8

x=2\text{ mph}

Hence speed of current is 2\text{ mph}

7 0
3 years ago
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