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maw [93]
3 years ago
8

Each day a runner trains for a 10km race. On the fisrt day she runs 1000m, and then increases the distance by 250m on each subse

quent day.
a) On which day does she run a distance of 10km in training?

b) What is the total distance she will have run in training by the end of that day?
Mathematics
1 answer:
anyanavicka [17]3 years ago
7 0
I think the answer is b
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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
Tom rolls 2 fair dice and adds the results from each.
o-na [289]

Answer:

1/6

Step-by-step explanation:

8 0
3 years ago
There are 12 appetizers; 4 are soups, 6 contain meat, and 2 do not. In how
Ahat [919]
72 different orders, each soup can have a different meat and other* so take 4* 6* 3 because that is how many different combanations you can do
7 0
3 years ago
Read 2 more answers
A blueprint shows the mater bedroom to be 5 inches long and 3 inches wide. The scale on the blueprint is 2 in : 11 ft. What is t
Anna35 [415]

Answer:

453.75 sq. feet

Step-by-step explanation:

In this question, we are going to calculate the area of a room given the blue print measurement and the actual measurements with the answer being in the actual measurement.

To correctly do this, it is best if the measurements are converted to the actual.

The measurements we’ll be trying to convert is 5 inches by 3 inches with a scale of 2in to 11ft ( same as 1 in to 5.5 ft)

The 5 inches blueprint measurement will be 5 * 5.5 = 27.5 ft

The 3 inches blueprint measurement will be 3 * 5.5 = 16.5 ft

The area in sq. feet will be length * width = 27.5 * 16.5 = 453.75 sq feet

7 0
3 years ago
It is estimated that the population of the world is increasing at an average rate of 1.09%. The population was about 7,632,819,3
morpeh [17]

Answer:

The equation that represents the population after T years is

P_{t}  = 7,632,819,325 [1 +\frac{1.09}{100} ]^{T}

Step-by-step explanation:

Population in the year 2018 ( P )= 7,632,819,325

Rate of increase R = 1.09 %

The population after T years is given by the formula

P_{t}  = P [1 +\frac{R}{100} ]^{T} -------- (1)

Where P = population in 2018

R = rate of increase

T = time  period

Put the values of P & R in above equation we get

P_{t}  = 7,632,819,325 [1 +\frac{1.09}{100} ]^{T}

This is the equation that represents the population after T years.

6 0
3 years ago
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