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3 years ago

10

Can someone help me out on this please?

1 answer:

asambeis [7]3 years ago

6 0

Answer:

Alexis: 2.5x

Gary: x

James: x + 18

Total: (2.5x) + (x) + (x + 18)

= 4.5x + 18

Bonus:

4.5x + 18 = 1206

4.5x = 1188

x = 264

Alexis: 2.5(264) = 660

Gary: 264

James: 264 + 18 = 282

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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

Identify the y-intercept of the following line: <br> y=3x-5

Cerrena [4.2K]

Y intercept is -5....

8 0

3 years ago

Find the volume of the following compound shape.<br>

Bess [88]

<h3>Given:</h3>

Cone
Cylinder

<h3>Volume of the cone:</h3>

$v = \frac{1}{3} \pi {r}^{2} h$

$v = \frac{1}{3} \times \pi \times {10}^{2} \times 10$

$v = 1047.20 \: {cm}^{3}$

<h3>Volume of the cylinder:</h3>

$v = \pi {r}^{2} h$

$v = \pi \times {10}^{2} \times 10$

$v = 3141.59 \: {cm}^{3}$

<h3>Total volume:</h3>

$v = 1047.20 + 3141.59$

$v = 4188.79 \: {cm}^{3}$

<u>Hence</u><u>,</u><u> </u><u>the</u><u> </u><u>volume</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>given</u><u> </u><u>cone</u><u> </u><u>shape</u><u> </u><u>is</u><u> </u><u>4188.7</u><u>9</u><u> </u><u>cubic</u><u> </u><u>centimeters</u><u>.</u>

5 0

2 years ago

Read 2 more answers

A and b are positive integers and a–b = 3. Evaluate the following:

yulyashka [42]

1/27

1/27

125

Step-by-step explanation:

Given that,

a - b = 3

9^(1/2b) /3^a = 3^(2/2b) /3^a

= 3^b/3^a

= 3^(b-a)

= 3^(-3)

= 27^(-1)

= 1/27

27^(1/3b) /9^(1/2a) = 3^(3/3b) /3^(2/2a)

= 3^b/3^a

= 3^(b-a)

= 3^(-3)

= 27^(-1)

= 1/27

125^(1/3a) /25^(1/2b) = 5^(3/3a) /5^(2/2b)

= 5^a/5^b

= 5^(a- b)

= 5^3

= 125

6 0

3 years ago

PLEASE HELP ME THANK YOU IF U DO

Andrews [41]

Answer:

B (r= 1/6s)

Step-by-step explanation:

If you just work out each option, you'll see that "s" multiplied by 1/6 gets r.

5 0

3 years ago