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Mademuasel [1]
3 years ago
15

Once a commercial plane reaches the desired altitude,

Mathematics
1 answer:
lesantik [10]3 years ago
4 0

Answer:nd gk

Step-by-step explanation:bx cm

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A school wishes to enclose its rectangular playground using 480 meters of fencing.
Harlamova29_29 [7]

Answer:

Part a) A(x)=(-x^2+240x)\ m^2

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

P=2(L+W)

we have

P=480\ m\\L=x\ m

substitute

480=2(x+W)

solve for W

240=x+W\\W=(240-x)\ m

<u><em>Find the area of the rectangular playground</em></u>

The area is given by

A=LW

we have

L=x\ m\\W=(240-x)\ m

substitute

A=x(240-x)\\A=-x^2+240x

Convert to function notation

A(x)=(-x^2+240x)\ m^2

Part b) What side length x gives the maximum area that the playground can have?

we have

A(x)=-x^2+240x

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

A(x)=-x^2+240x

Factor -1

A(x)=-(x^2-240x)

Complete the square

A(x)=-(x^2-240x+120^2)+120^2

A(x)=-(x^2-240x+14,400)+14,400

A(x)=-(x-120)^2+14,400

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

x=120\ m

W=(240-120)=120\ m

The playground is a square

A=120^2=14,400\ m^2

8 0
3 years ago
If, for all x, f'(x)=(x-2)^4(x-1)^3, it follows that funtaion f has
Elenna [48]

Answer:

We say that f(x) has an absolute (or global) minimum at x=c if f(x)≥f(c) f ( x ) ≥ f ( c ) for every x in the domain we are working on. We say that f(x) has a relative (or local) minimum at x=c iff(x)≥f(c) f ( x ) ≥ f ( c ) for every x in some open interval around x=c .

4 0
3 years ago
4. 46 is what percent of 69?
sergij07 [2.7K]

Answer:

66%(technically 0.66 repeating)

Step-by-step explanation:

We need to figure out what percentage of 69 equates to 46. In other words, we need to figure out what percentage <u>times</u> 69 equals 46:

percentage*69 = 46

Now that we formed this equation, we can solve for the percentage as if it was x.

First lets simplfy:

percentage*69 = 46 -- > 69percentage = 46

Now we can solve for x just by getting x alone, which means we must remove the coefficent. We can do this by dividing both sides of the equation by 69:

percentage = \frac{46}{69}

=

percentage=0.66

Putting this into the form of percentage, we must multiply by 100. Since, the percentage form of a decimal is 100 times bigger(moved up 2 decimal places):

percentage = 0.66*100

=

percentage = 66%

Hope this helps! :3

4 0
2 years ago
1 2 3 4 5 6 7 8 9 10 The two conditional relative frequency tables below show the results of a survey asking students whether th
Yuki888 [10]
B (:  


cuz i saw it on this other website and i am like 50% sure its correct 










7 0
3 years ago
Read 2 more answers
The weekly cost (c) of manufacturing (x) number of remotes is given by the equation below. what is the cost to manufacture 2500
IRISSAK [1]
C= 2000 + 3(2500)
C= 2000 + 7,500
C= $9,500
6 0
3 years ago
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