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Airida [17]
3 years ago
5

The perimeter of a rectangular is 86 m. If the width were doubled and the length were increased by 22 m, the perimeter would be

166 m. What are the length and width of the rectangle?
Mathematics
1 answer:
Zina [86]3 years ago
3 0
Write them as system of equations:
x=length, y=width
2x+2y=86
4x+2y+22=166


when you solve, then x=length=7, y=width=36
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Newton’s law of cooling states that dx/dt= −k(x − A) where x is the temperature, t is time, A is the ambient temperature, and k
Vadim26 [7]

Answer:

(a) The solution to the differential equation is x = A_0Coswt + Ce^(-kx)

(b) The initial condition t > 0 will not make much of a difference.

Step-by-step explanation:

Given the differential equation

dx/dt= −k(x − A); t > 0, A = A_0Coswt

(a) To solve the differential equation, first separate the variables.

dx/(x - A) = -kdt

Integrating both sides, we have

ln(x - A) = -kt + c

x - A = Ce^(-kt) (Where C = ce^(-kt))

x = A + Ce^(-kx)

Now, we put A = A_0Coswt

x = A_0Coswt + Ce^(-kx) (Where C is constant.)

And we have the solution.

(b) Since temperature t ≠ 0, the initial condition t > 0 will not make much of a difference because, Cos(wt) = Cos(-wt).

It is not any different from when t < 0.

7 0
3 years ago
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7 0
3 years ago
Which expression has a value of StartFraction 1 Over 36 EndFraction? (StartFraction 1 Over 108 EndFraction) cubed (StartFraction
IrinaVladis [17]

Answer:

(1/6)^2

Step-by-step explanation:

We want to find the fraction that is equivalent to 1/36.

Let us look at each of them individually:

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b. (\frac{1}{9})^4 =  \frac{1}{6561}

c. (\frac{1}{6})^2 =  \frac{1}{36}

d. (\frac{1}{5})^2 = \frac{1}{25}

Therefore, the correct answer is c.

4 0
3 years ago
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svlad2 [7]
Hello,
p=>q  is equivalent to ~q → ~p


p-------q-------p=>q--~q ----- ~p----~q → ~p
0-------0-------1-------1 ------- 1------- 1
0-------1-------1-------0-------  1------- 1
1-------0-------0-------1-------  0-------0
1-------1-------1-------0-------  0-------1

Column 3= column 6 ==>equivalent


Answer B


























3 0
3 years ago
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What is the prime factorization of 144?<br> A) 4 x 36<br> OB) 2x6<br> C) 2x32<br> OD 12x12
mezya [45]

Answer:

12x12

Step-by-step explanation:

12x12=144

3 0
3 years ago
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