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3 years ago

Jaylen is making pancakes. He has 1 liter of pancake mixture. If Jaylen is using

Mathematics

1 answer:

Finger [1]3 years ago

4 0

He can make 4 pancakes with the whole mixture.

Step-by-step explanation:

It is given that,

Jaylen has a total of pancake mixture = 1 liter.
The amount of pancake mixture he uses to make 1 pancake = 1/4 liter.

You need to find the number of pancakes he can make using the 1 liter of pancake mixture.

To find the number of pancakes :

let us take 'N' be the number of pancakes he can make using 1 liter of mixture.

⇒ Total mixture = amount of mixture needed for 1 pancake × N

⇒ 1 liter = 1/4 liter × N

⇒ 1 = N/4

Cross multiply the denominator 4 to the other side, to find N

⇒ 1 × 4 = N

⇒ N = 4 pancakes

Therefore, he can make 4 pancakes with the whole mixture.

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Step-by-step explanation:

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3 years ago

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

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

Find the area of the rectangular playground

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

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

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