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Citrus2011 [14]

3 years ago

5

On average,ea rectangular garden ha an area of 144 meter square. During a redesign of the garden center, the dimension of the re

ctangular garden are altered but the area is unchanged .The width is doubed and length is decreased by 12m.

1 answer:

aksik [14]3 years ago

5 0

Answer:

New dimensions are; Width = 12m and Length = 12m

Step-by-step explanation:

Let length of rectangle be L

Let width be W

Area of rectangle has a formula;

Area = Length x Width = LW

We are given the area = 144 m²

So,

LW = 144 - - - (eq1)

Now, we are told that width is doubled and length is decreased by 12m but area remains the same.

Thus, we have;

Width as 2W and Length as L - 12.

Area = 2W(L - 12)

So,

2W(L - 12) = 144 - - - (eq2)

Equating eq 1 and 2,we have;

LW = 2W(L - 12)

W will cancel out to give;

L = 2(L - 12)

L = 2L - 24

2L - L = 24

L = 24m

From equation 1, LW = 144

Thus; W = 144/L = 144/24

W = 6m

So new design of rectangle now has a dimension of;

Width = 2W = 2 × 6 = 12m

Length = L - 12 = 24 - 12 = 12m

So, new dimensions are; Width = 12m and Length = 12m

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The linear equation in slope intercept form

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$y=100(120)+300=\$12,300$

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For x=24 months

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$y=100(24)+300=\$2,700$

Part 5) What type of exponential model is Sally’s situation?

we know that

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$A=P(1+\frac{r}{n})^{nt}$

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A is the Final Investment Value

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n is the number of times interest is compounded per year

in this problem we have

$P=\$6,000\\ r=7\%=0.07\\n=1$

substitute in the formula above

$A=6,000(1+\frac{0.07}{1})^{1*t}\\ A=6,000(1.07)^{t}$

therefore

Is a exponential growth function

Part 6) Write the model equation for Sally’s situation

see the Part 5)

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For t=10 years

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3 years ago