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SpyIntel [72]
3 years ago
5

Leroy's backyard is a rectangle that is three times as long as it is wide. What is the perimeter and the area of the yard? First

draw a diagram to help you solve the problem. Let a be the width of Leroy's yard. The perimeter is a+3a+a+3a or 8a. The area is l×w; so the backyard area is a×3a or 3a^2. Suppose you know the area of the yard 7,500 square feet how can you find the value of a?
Mathematics
1 answer:
spayn [35]3 years ago
7 0
3a^2=7500
a^2=7500/3
a^2=2500
square root of a^2=square root of 2500
a=50
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tresset_1 [31]

100g of ammonia releases 271.18 kJ of heat.

<u>Explanation:</u>

Given:

N₂ reacts with H₂

The reaction is:

2N₂ + 3H₂ → 2NH₃ + 92.2 kJ

According to the balanced reaction:

2 X 17g of ammonia releases 92.2 kJ of heat

34g of ammonia releases 92.2 kJ of heat

100g of ammonia will release = \frac{92.2}{34} X 100 kJ of heat

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Therefore, 100g of ammonia releases 271.18 kJ of heat.

8 0
3 years ago
4&gt; Solve by using Laplace transform: y'+5y'+4y=0; y(0)=3 y'(o)=o
harina [27]

Answer:

y=3e^{-4t}

Step-by-step explanation:

y''+5y'+4y=0

Applying the Laplace transform:

\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0

With the formulas:

\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)

\mathcal{L}[y']=s\mathcal{L}[y]-y(0)

\mathcal{L}[x]=L

s^2L-3s+5sL-3+4L=0

Solving for L

L(s^2+5s+4)=3s+3

L=\frac{3s+3}{s^2+5s+4}

L=\frac{3(s+1)}{(s+1)(s+4)}

L=\frac3{s+4}

Apply the inverse Laplace transform with this formula:

\mathcal{L}^{-1}[\frac1{s-a}]=e^{at}

y=3\mathcal{L}^{-1}[\frac1{s+4}]=3e^{-4t}

7 0
3 years ago
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tangare [24]
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4 0
3 years ago
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Delvig [45]

Answer:The equation that models the solution will be

33 = 22k / 6

Step-by-step explanation:

The two types of variation involved in this problem are direct variation and inverse variation.

In direct variation, when one item changes in the positive or negative direction, the other item also changes in the positive or negative direction.

In inverse variation, when one item changes in the positive or negative direction, the other item also changes in the negative or positive direction.

From the information given,

c varies directly with b

If we introduce a direct proportionality constant, k, then,

c = kb

c also varies inversely with a

If we introduce an inverse proportionality constant, k, then,

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Therefore, c = kb / a

When a=6 , b=22 and c=33.

The equation that models the solution will be

33 = 22k / 6

8 0
3 years ago
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Dimas [21]

Answer:

30

Step-by-step explanation:

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5 0
2 years ago
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