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2 years ago

9

John is travelling to another country.

1 answer:

Svetllana [295]2 years ago

7 0

Answer: The total distance is 8370 km

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Find the greatest solution for x+y when x^2+y^2 = 7, x^3+y^3=10

damaskus [11]

Answer:

4

Step-by-step explanation:

set

$f(x,y)=x+y\\$

constrain:

$g(x,y)=x^2+y^2 = 7\\h(x,y)=x^3+y^3=10$

Partial derivatives:

$f_{x}=1\\f_{y} =1 \\g_{x}=2x \\g_{y}=2y\\h_{x}=3x^2 \\h_{y}=3y^2$

Lagrange multiplier:

$grad(f)=a*grad(g)+b*grad(h)\\$

$\left[\begin{array}{ccc}1\\1\end{array}\right]=a\left[\begin{array}{ccc}2x\\2y\end{array}\right]+b\left[\begin{array}{ccc}3x^2\\3y^2\end{array}\right]$

4 equations:

$1=2ax+3bx^2\\1=2ay+3by^2\\x^2+y^2=7\\x^3+y^3=10$

By solving:

$a=4/9\\b=-2/27\\x+y=4$

Second mathod:

Solve for x^2+y^2 = 7, x^3+y^3=10 first:

$x=\frac{1}{2} -\frac{\sqrt{13}}{2} \ or \ y=\frac{1}{2} +\frac{\sqrt{13}}{2} \\x=\frac{1}{2} +\frac{\sqrt{13}}{2} \ or \ y=\frac{1}{2} -\frac{\sqrt{13}}{2} \\x+y=-5\ or\ 1 \or\ 4$

The maximum is 4

6 0

2 years ago

How many 1/3 pounds serving in 4 2/3 pound of cheese

Marysya12 [62]

Change 4 and 2/3 to an improper fraction.
4 + 2/3 = 14/3
There are 14 of the 1/3 lb serving in 4 and 2/3 pounds of cheese.

3 0

3 years ago

Which represents the probability (p) of a given chance event occurring? A) p > 0 B) p = 1 C) 0 < p < 1 D) 0 ≤ p ≤ 1

elixir [45]

Answer:

D) 0 ≤ p ≤ 1

Probability is 0 when there's no chance of occurrence

Probability is 1 when the event is certain to happen

5 0

2 years ago

Read 2 more answers

If rectangle ABCD is dilated by a scale factor of 3 with a center of dilation at vertex D, what is the perimeter of A'B'C'D?

kramer

The ans is C) 90 units

5 0

2 years ago

Fernando factored 45y^6 as (9y^3)(5y^3).

marishachu [46]

Answer:

They both factored it correctly

Step-by-step explanation:

To find the one that was factored correctly, we expand the two of them and compare with $45y^6$ .

Fernando

$(9y^3)(5y^3)$

= $9 * 5 * y^3 * y^3$

= $45y^6$

Salma

$(3y)(15y^5)$

= $3 * 15 * y * y^5$

= $45y^6$

As we can see, they both factored it correctly.

4 0

2 years ago