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allsm [11]
3 years ago
7

2. Here is triangle ABC.

Mathematics
1 answer:
rusak2 [61]3 years ago
8 0
Triangle abc is a regular triangle
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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
QUICK 35 POINTS PLUS BRANLIEST. PLEASE ANSWER ALL THE QUESTIONS PROPERLY AND EXPLAIN HOW YOU GOT THEM. TRY TO ANSWER THEM BY TOD
Veronika [31]
  1. About 127.3(square root of 16,200, or 90√2)  Look at this problem like a right triangle.  Each leg is 90 feet, so the hypotenuse is the square root of 90^2 + 90^2
  2. About 52.3(square root of 2735.64)  Another right triangle problem!  Once again, with Pythagorean theorem (a^2 + b^2 = c^2) You can deduce that 60^2 = 29.4^2 + the width of the TV^2.
  3. About 11.6(Square root of 134.75)Another right triangle problem, you can deduce that 9.5^2 + The pool length^2 = 15^2

Hope it helps <3

(If it does, please give brainliest, only need one more for rank up :) )

7 0
3 years ago
Read 2 more answers
Lulu wants to get fit. She started with 50 laps a day and she intends to add 10 laps every week. Write a mathematical expression
vlabodo [156]

Answer: 10x + 50

Step-by-step explanation:

lets say that x is equal to the amount of weeks that she runs. She starts off the first week with 50

Then, since she is adding 10 every week, you would do 10x, or 10 times the amount of weeks that she runs.

Since you originally started with 50, you have to add the 50 to the 10x.

So you get...

<h3>10x + 50</h3>

For example

on week 2, if you plug in 2 to x you get

10(2) +50

20 + 50

70 laps after the second week

7 0
2 years ago
HELP does anyone get these three questions?
Tom [10]

Step-by-step explanation:

since we have the relation (inches/dollars)

4.3 inches down per dollar

per 10 dollars 43 inches down

per half a dollar 2.15 inches down

per 63.60 dollars 273.48 inches down

8 0
3 years ago
In what quadrant is the point (-7, -16)?<br><br> Help!!!!!
svp [43]

Answer:

quadrant 3

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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