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MrRissso [65]
2 years ago
12

If A = { a, b, c, d, e, f ) B-{ b, c, d, f, g) an C = {a,e,i,o,u), show that. A U (BnC) = (AUB) n (AUC)​

Mathematics
1 answer:
Setler79 [48]2 years ago
4 0

B\cap C=\emptyset\\A\cup(B\cap C)=\{a,b,c,d,e,f\}\\A\cup B=\{a,b,c,d,e,f,g\}\\A\cup C=\{a,b,c,d,e,f,i,o,u\}\\(A \cup B)\cap (A \cup C)=\{a,b,c,d,e,f\}

As you can see A\cup(B\cap C)=(A \cup B)\cap (A \cup C)

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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
3 years ago
Please help i keep getting the wrong answers
Mrrafil [7]

Answer:

10 inches

Step-by-step explanation:

Surface Area = π R² + π R L [ L is Slant Height ]

200 π = π (10)² + π (10) L

200 π = π (100) + π (10) L

200 π - 100 π = 10 π L

100 π = 10 π L

100 π / 10 π = L

10 = L

L = 10 inches

Hope this Helps......

3 0
3 years ago
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In one foot, there are 0.33 yards.
Therefore, you need to multiply 26 by 0.33
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6.6+1.98= 8.58
Therefore, in a 26' long painting, there are 8.58 yards
Hope this helps :) 
3 0
3 years ago
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Calcule a segunda derivada )a y=√x
serious [3.7K]
The answer to this question would be x=a2y2
6 0
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Which expression represents four less than half a number, n? (show your work)
ikadub [295]
The answer is 1/2n-4

Multiplying a number n by 1/2 is the same as dividing that number by 2.
5 0
2 years ago
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