Help show work <br> assig 8

If 3x+2y=18 find x and y for which the product xy takes its maximum value

grin007 [14]

Answer:

(x, y) = (3, 4.5)

Step-by-step explanation:

You want to find x and y such that xy is a maximum subject to the constraint that 3x+2y=18.

<h3>Objective function</h3>

The objective function f(x, y) = xy is most easily maximized if it can be written in terms of one variable only. Solving the constraint equation for y, we have ...

3x +2y = 18

2y = 18 -3x

y = 1/2(18 -3x) = (3/2)(6 -x)

Then the objective function is ...

f(x) = x(3/2)(6 -x)

<h3>Maximum</h3>

We recognize this as the equation of a parabola that opens downward, and has zeros at x=0 and x=6. Its line of symmetry is halfway between those, at x = 3. That is the location of the maximum of the objective function.

The corresponding y-value is ...

y = (3/2)(6 -3) = 9/2 = 4.5

The values of x and y that maximize their product are (x, y) = (3, 4.5).

__

<em>Additional comment</em>

In the attached graph, the larger the product, the farther away the curve is from the origin. The product is maximized subject to the constraint when the curves are tangent to each other. That point of tangency is (x, y) = (3, 4.5).

5 0

1 year ago

PLEASE HELP!! The amount a string stretches varies linearly with the mass applied to the spring, as can be seen in the video. In

Aleksandr [31]

Hello there!

d(m) = k*m
<span>d(m) = 0.096 x m = 30.6 - 21.7
= (30.6 - 21.7)/0.096 = 92.7 grams
The answer is 92.7 to one decimal place

</span>Hope This Helps You!
Good Luck :)

7 0

3 years ago

Read 2 more answers

A toy manufacturer estimates that 6% of its products are defective.If it produces 550 toys in one day,then how many will be defe

Roman55 [17]

Answer:33

Step-by-step explanation:550*.06=33

4 0

3 years ago

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads).

Crank

Answer:

The standard deviation for this distribution is 0.8660.

Step-by-step explanation:

For each coin toss, there are only two possible outcomes. Either it is heads, or it is tails. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

In this problem, we have that:

In each toss, heads or tails are equally as likely, since the coin is fair. So $p = \frac{1}{2} = 0.5$

Three throws, so $n = 3$

What is the standard deviation for this distribution?

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{3*0.5*0.5} = 0.8660$

The standard deviation for this distribution is 0.8660.

7 0

3 years ago

on a coordinate grid, her house is located at (1,2) and the park at (5,5) what is the shortest distance from her house to the pa

nadya68 [22]

To solve, use the distance formula: $d= \sqrt{(x_1+x_2)^2+(y_1+y_2)^2}$ . Using your values of x and y, you get $d= \sqrt{(1+5)^2+(2+5)^2} = \sqrt{6^2+7^2} = \sqrt{36+49} = \sqrt{85}$ , which is approximately 9.22. This means your shortest distance is √85≈9.22

3 0

3 years ago

Help show work assig 8