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Natalka [10]
3 years ago
5

Phil has drawn some house plans in which the lounge room will be 9.5 m long when it is built. This length has been drawn as 19cm

on the house plan. What scale did Phil use for his house plans?
Mathematics
1 answer:
Monica [59]3 years ago
7 0

Answer:

1:50 scale

Step-by-step explanation:

9.5m * 100 = 950cm

950/19 = 50

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a famer has 120 feet of fencing with whcih to enclose two adjacent rectangular pens as shown. what dimeensions should be used th
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The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Let the area be y .

Area = (base) × (height)

Base = 2x

Height = h

Let the area of the rectangular pens be y .

∴ y = 2xh

Perimeter of all the fencing = 4x+3h

∴ 4x+3h = 120

now we solve for h

3h = 120-4x

h = 40 - 4/3 x

Now we will substitute this value in the above first equation:

y = 2xh

or, y = 2x (40 - 4/3 x)

or, y = 80x - 8/3 x²

Now for the maximum area we have to find the first order differentiation of y

now,

dy /dx = 80 - 16/3 x

At dy/dx = 0 we get the value of x for which y is maximum.

80 - 16/3 x = 0

or, - 16/3 x = -80

or, x = 15 feet

Hence height =  40 - 4/3 x = 40 - 20 = 20feet

Maximum area = 2xh = 2×15×40 = 1200 square feet

The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.

Disclaimer : The missing figure for the question is attached below.

To learn more about area visit:

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6 0
1 year ago
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3 years ago
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2 years ago
Can someone help me figure out the answer?
Ahat [919]

Answer:

You will break even on the car wash when you buy 13.5 gallons. As long as you buy that or more, it is cheaper to get the car wash.

Step-by-step explanation:

In order to find this, we need to create equations for both situations. If we let x equal the amount of gallons purchased, we can model the first equation as:

f(x) = 3.35x

And the second equation as:

f(x) = 3.05x + 4.05

Then to find when they equal each other, we can set the two equations equal to each other and solve for x.

3.35x = 3.05x + 4.05

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This means once you buy 13.5 gallons, the prices will be the same. Any amount over that and the car wash will be cheaper

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