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11Alexandr11 [23.1K]
3 years ago
10

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

Mathematics
1 answer:
damaskus [11]3 years ago
6 0

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

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icang [17]

Answer:

13

Step-by-step explanation:

Use PEMDAS

2(3+2x5)÷2

first you would do the parenthesis

2 times 5 is 10

so now you have:

2(3+10)÷2You still have parenthesis so you would add 3+10 because that is inside the parenthesis

2(13)÷3

next you would do 2 times 13 which is 26:

so now you have 26÷2 which is 13

so the answer is 13

4 0
3 years ago
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Laurie was scuba diving. Each time she dove 5 feet deeper, she would stop and clear her ears. After Laurie had checked her instr
Leona [35]

Complete question :

Answer:

(-5) * (20) * (3)

Step-by-step explanation:

Diving 5 feets deeper = descent = negative 5 Feets

Each time instrument is checked = (60/3) = depth of 20 feets

Number of times instrument is checked = 3

Hence, maximum depth :

Diving 5 feets deeper * Each time instrument is checked = depth of 20 feets * Number of times instrument is checked

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3 years ago
I dont understand how to answer this. I tried to find the second derivative. ​
Orlov [11]

Answer:

(B) π/12 + π/6 k

Step-by-step explanation:

Points of inflection are where f"(x) = 0 and changes signs.

f(x) = cos²(3x)

f(x) = (cos(3x))²

f'(x) = 2 (cos(3x))¹ × -sin(3x) × 3

f'(x) = -6 sin(3x) cos(3x)

Using double angle formula:

f'(x) = -3 sin(6x)

f"(x) = -3 cos(6x) × 6

f"(x) = -18 cos(6x)

0 = -18 cos(6x)

0 = cos(6x)

6x = π/2 + 2πk or 6x = 3π/2 + 2πk

We can simplify this to:

6x = π/2 + πk

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4 years ago
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Genrish500 [490]

Answer:4.3

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3 years ago
I need to find what b is with all steps <br> Thank you
Mnenie [13.5K]

Answer:

b ≈ 148.5

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan68° = \frac{opposite}{adjacent} = \frac{b}{60}

Multiply both sides by 60 to clear the fraction

60 × tan68° = b, thus

b ≈ 148.5 ( to 1 dec. place )

8 0
3 years ago
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