1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sever21 [200]
3 years ago
11

A rectangle is constructed with its base on the​ x-axis and two of its vertices on the parabola y equals = 100 100 minus −x squa

red 2. What are the dimensions of the rectangle with the maximum​ area? What is that​ area?
Mathematics
1 answer:
masha68 [24]3 years ago
5 0

Answer:

Step-by-step explanation:

Given that a rectangle is constructed with its base on the x axis and two of its vertices on the parabola

y=100-x^2

This parabola has vertex at (0,100) and symmetrical about y axis.

Any general point above x axis can be written as (a,b) (-a,b) since symmetrical about yaxis.  

Hence coordinates of any rectangle are

(a,0) (-a,0), (a, 100-a^2), (-a, 100-a^2)

Length of rectangle = 2a and width = 100-a^2

Area of rectangle = lw = 2a(100-a^2)=200a-400a^3

To find max area, use derivative test.

A' = 200-800a^2\\A"=-1600a

Hence maxima when first derivative =0

i.e. when a =2

Thus we find dimensions of the rectangle are l =4 and w = 96

Maximum area = 4(96) = 384

You might be interested in
In a certain test, the number of successful candidates was three times than that of unsuccessful candidate, if there had been 16
Natali5045456 [20]

Answer:

The number of candidates is 136.

Step-by-step explanation:

3 0
3 years ago
3x−(2x+1) for x=7 5/13
marusya05 [52]

Answer:

83/13 or 6.3846

Step-by-step explanation:

i subsituted for x and used a calculator

8 0
3 years ago
Three populations have proportions 0.1, 0.3, and 0.5. We select random samples of the size n from these populations. Only two of
IRINA_888 [86]

Answer:

(1) A Normal approximation to binomial can be applied for population 1, if <em>n</em> = 100.

(2) A Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50 and 40.

(3) A Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50, 40 and 20.

Step-by-step explanation:

Consider a random variable <em>X</em> following a Binomial distribution with parameters <em>n </em>and <em>p</em>.

If the sample selected is too large and the probability of success is close to 0.50 a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

  • np ≥ 10
  • n(1 - p) ≥ 10

The three populations has the following proportions:

p₁ = 0.10

p₂ = 0.30

p₃ = 0.50

(1)

Check the Normal approximation conditions for population 1, for all the provided <em>n</em> as follows:

n_{a}p_{1}=10\times 0.10=1

Thus, a Normal approximation to binomial can be applied for population 1, if <em>n</em> = 100.

(2)

Check the Normal approximation conditions for population 2, for all the provided <em>n</em> as follows:

n_{a}p_{1}=10\times 0.30=310\\\\n_{c}p_{1}=50\times 0.30=15>10\\\\n_{d}p_{1}=40\times 0.10=12>10\\\\n_{e}p_{1}=20\times 0.10=6

Thus, a Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50 and 40.

(3)

Check the Normal approximation conditions for population 3, for all the provided <em>n</em> as follows:

n_{a}p_{1}=10\times 0.50=510\\\\n_{c}p_{1}=50\times 0.50=25>10\\\\n_{d}p_{1}=40\times 0.50=20>10\\\\n_{e}p_{1}=20\times 0.10=10=10

Thus, a Normal approximation to binomial can be applied for population 2, if <em>n</em> = 100, 50, 40 and 20.

8 0
3 years ago
Drag values to complete each equation.
Alex777 [14]

Answer:

1. A. 1

2. D. 17^9

Step-by-step explanation:

Properties used:

  • Power of a Power Property
  • Product Property
  • Quotient Property
  • Zero Exponent Property

1. First, let's deal with the numerator.

(17^3)^6 can be turned into 17^1^8 by using the Power of a Power Property.

And then use the Product Property, (17^1^8)(17^-^1^0) = 17^8

So now, our fraction is this: \frac{17^8}{17^8}

All number over itself in a fraction is equal to 1. But you can also do this the mathmatic way using the Quotient Property: \frac{a^m}{a^n} = a^m^-^n or \frac{1}{a^(^n^-^m^)}. Which then you plug the numbers in: \frac{17^8}{17^8} = 17^8^-^8 = 17^0. And since we know that in Zero Exponent Property: a^0 = 1, we can see that 17^0 = 1. So either way, we get 1.

So the answer is 1, which is A

2. Power of a Power Property: (a^m)^n = a^m^n

So plug the numbers in the property: (17^{6}) ^3= 17^1^8

Product Property: (a^m)(a^n) = a^m^+^n

We plug the equation in with (17^{6}) ^3 turned into 17^1^8 ---

(17^1^8)(17^-^9) = 17^1^8^-^9 = 17^9

So the answer is 17^9, which is D

I hope this helps!
Please give Brainliest!

Have a great day!

7 0
2 years ago
Read 2 more answers
V-3/-10= -4 please answer step by step
Triss [41]

See the pic above!

Hope it helps!

5 0
3 years ago
Other questions:
  • Find the magnitude of WX for W(-2, 8, -3) and X(1, 4, -1)
    9·2 answers
  • What is the value of five in 3156
    12·2 answers
  • Solve for x. Use the completing the squares
    14·1 answer
  • What is 1745÷8 equals
    12·2 answers
  • Write a fraction that is equivalent to 3/12
    13·2 answers
  • Plzzz help !!
    6·1 answer
  • What is 10 2/3 in inproper numbers
    6·1 answer
  • Last year there were two hundred and forty seven thousand, three hundred and seventy two weddings in the UK.
    7·2 answers
  • Why do we wait until night to 'call it a day?'
    14·2 answers
  • Juanita has saved 30% of the money that she needs to buy a new bicycle.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!