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3 years ago

Find the pair of numbers whose sum is 46 and whose product is a maximum.

1 answer:

7 0

To solve this problem you must apply the proccedure shown below:

1. Let's call:

x the first number and and the other number 46-x

2. Then, the product of both numbers is:

y=x(46-x)

3. When you apply the distributive property, you obtain:

y=46x-x^2

4. As you can see, the coefficient of x^2 is negative, this means that the maximun value is at the vertex of the parabola.

5. Then, you have:

h=-b/2a
h=-46/2(-1)
h=23 (x coordinate)

6.Then:

y=46x-x^2
y=46(23)-(23)^2
y=529

Therefore the answer is: 23 and 529.

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Marsha sees an airplane flying overhead. The spot on the ground that is directly under the plane is 3,600 feet from Marsha's hou

Rudiy27

The elevation of the plane is 3600 ft

Let

h = elevation of plane,
d = distance from Marsha's house to spot on ground below plane = 3600 feet and
Ф = angle of elevation of plane = 45°

From the triangle, we have the trigonometric ratio

tanФ = h/D

<h3>Elevation of the plane</h3>

Making h subject of the formula, we have

h = DtanФ

substituting the values of the variables into the equation, we have

h = DtanФ

h = 3600 ft × tan45°

h = 3600 ft × 1

h = 3600 ft

So, the elevation of the plane is 3600 ft

Learn more about elevation of the plane here:

brainly.com/question/26380084

7 0

2 years ago

DO ANYONE KNOW HOW TI FIND THE AREA OF A REGULAR POLYGON?? ill give brainlest and points

zloy xaker [14]

Answer:

see explanation

Step-by-step explanation:

The area (A) of a regular decagon ( 10 sided ) is calculated as

A = 0.5 × perimeter × apothem

Here side length = 3.25, hence perimeter = 10 × 3.25 = 32.5 m, thus

A = 0.5 × 32.5 × 5 = 81.25 m²

7 0

3 years ago

Read 2 more answers

arts academy requires there to be 6 teachers for every 144 students and 3 tutors for every 24 students. How many students does t

jonny [76]

Answer:

the teachers would have 24 students per teacher. 10 students per tutor. There would need to be 11 tutors

Step-by-step explanation:

each tutor would have 10 students then if you do 11 times 10 you get 11

(hope this helps can I pls have brainlist (crown)☺️)

4 0

2 years ago

The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there a

Anettt [7]

Answer:

1) The size of the colony after 4 days is 6553 mosquitoes

2) After $t = 4.9\ days$

Step-by-step explanation:

To answer this question you must use the growth formula

$N = N_0e ^ {kt}$

Where

$N_0$ is the initial population of mosquitoes = 1000

t is the time in days

k is the growth rate

N is the population according to the number of days

We know that when t = 1 and $N_0=1000$ then N = 1600

Then we use these values to find k.

$1600 = 1000e ^{k(1)}\\\\\frac{1600}{1000} = e ^ k\\\\ln(\frac{1600}{1000}) = k\\\\k = 0.47$

Now that we know k we can find the size of the colony after 4 days.

$N = 1000e ^ {0.47(4)}\\\\N = 6553\ mosquitoes$

To know how long it should take for the population to reach 10,000 mosquitoes we must do N = 10000 and solve for t.

$10000 = 1000e ^ {0.47t}\\\\10 = e ^ {0.47t}\\\\ln(10) = 0.47t\\\\t = \frac{ln(10)}{0.47}\\\\t = 4.9\ days$

6 0

3 years ago

Use the drop-down menus to describe the key aspects of the function f(x) = –x2 – 2x – 1.

Margaret [11]

Answer: The vertex is the minimum value

The function is increasing when x<1

The function is decreasing when x>1

The domain of the function is all real numbers

The range of the function is all numbers less than it equal to 0

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers