All categories

4 years ago

Find two numbers x and y such that their sum is 60 and x2y is maximized.

1 answer:

3 0

X + y = 60
P = x^2 y

From first equation y = 60 - x

P = x^2(60 - x)
P = 60x^2 - x^3
Finding the derivative of P and equating to zero:-
P' = 120x - 3x^2 = 0
-3x ( x - 40) = 0
x = 40
This makes y = 20
So maximum values of x^2y = 40^2 * 20 = 32,000.

You might be interested in

Jason has a credit card that charges 2% interest on unpaid balances each month. He spent $300, but only makes the minimum paymen

likoan [24]

$201.08 is the answer

8 0

4 years ago

My bro needs help with this plz help

bearhunter [10]

Answer:

28 jelly beans

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A survey of 100 people asked if they have a dog or a cat. The answers were: 56 people answered yes for dog and 51 people answere

den301095 [7]

Answer: The maximum number of people who could answer yes for both cat and dog is 7.

Step-by-step explanation: Given that a survey of 100 people asked if they have a dog or a cat.

Out of those 100 people, 56 people answered yes for dog and 51 people answered yes for cat. Some people may own neither and some people may own both animals.

We are to find the maximum number of people that could answer yes for both cat and dog.

Let A and B represents the set of people that answered Yes for dog and Yes for cat respectively.

Then, according to the given information, we have

$n(A)=56,~~n(B)=51.$

From Set Theory, we have

$n(A\cup B)=n(A)+n(B)-n(A\cap B)\\\\\Rightarrow n(A\cup B)=56+51-n(A\cap B)\\\\\Rightarrow n(A\cup B)=107-n(A\cap B)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Since the total number of people is 100, so we get

$n(A\cup B)\geq 100.$

Therefore, from equation (i), we get

$107-n(A\cap B)\geq 100\\\\\Rightarrow n(A\cap B)\leq 107-100\\\\\Rightarrow n(A\cap B)\leq 7.$

Thus, the maximum number of people who could answer yes for both cat and dog is 7.

4 0

3 years ago

Read 2 more answers

Adding and Subtracting Fractions Solve each problem. Write your answer as a mixed number(if possible) 1. 2 1/9 - 7/6= 2. 2/3 + 2

AleksandrR [38]

1) 1 1/6
2) 1 1/6
4) 5 1/ 18

hope you got your answer i didn't know what number 3 was so i did the rest

5 0

3 years ago

Which two values of X are roots of the polynomial below 4x^2-6x+1

PtichkaEL [24]

$4x^2-6x+1=0\\\\a=4,\ b=-6,\ c=1\\\\\Delta=b^2-4ac\\\\\Delta=(-6)^2-4(4)(1)=36-16=20\\\\\sqrt\Delta=\sqrt{20}=\sqrt{4\cdot5}=\sqrt4\cdot\sqrt5=2\sqrt5\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a},\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\x_1=\dfrac{-(-6)-2\sqrt5}{2\cdot4}=\dfrac{3-\sqrt5}{4}\\\\x_2=\dfrac{-(-6)+2\sqrt5}{2\cdot4}=\dfrac{3+\sqrt5}{4}$

5 0

4 years ago