Mathematical Modeling | MCQs

Explanation

2x + 7 = 19

2x = 19 - 7

2x = 12

x = 12/2

x = 6

Explanation

x^2 > y^2

This implies that the absolute value of x is greater than the absolute value of y.

Explanation

7x - 1 = 4x + 8

Add 1 to both sides:

7x = 4x + 9

Subtract 4x from both sides:

3x = 9

Divide both sides by 3:

x = 3

So, the value of x is 3.

Explanation

Let's start by calling the two numbers we are looking for x and y.

x + y = 80

x - y = 20

x - y = 20

x = 20 + y

x + y = 80

20 + y + y = 80

20 + 2y = 80

2y = 60

y = 30

x + y = 80

x + 30 = 80

X = 50

Sum: 50 + 30 = 80

Difference: 50 - 30 = 20

Explanation

Let the numbers be a, b and c Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131 (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400 ⇒ (a + b + c) = 400−−−√ = 20

Explanation

12 men took to 6 hours to complete the work.

It means there is 12 x 6= 72 units of work

Now 12men done work for one hour. So 12 x 1 =12 units of work completed.

Remaining work = 72-12= 60 units

Now the no of men=12+8= 20

So 60 units of work have to complete by 20 men

Therefore 60/20= 3 hours

Explanation

8 men can do work = 20 days 

1 man can do this work = 8*20

10 men can do that work = [8*20]/10

                                              =16 days 

Explanation

To solve the separable differential equation:

(1 + x)dy - ydx = 0

Rearrange the equation:

(1 + x)dy = ydx

Separate the variables:

dy/y = dx/(1 + x)

Integrate both sides:

∫(dy/y) = ∫(dx/(1 + x))

ln(y) = ln(1 + x) + C

y = e^(ln(1 + x) + C)

= e^C * e^(ln(1 + x))

= c(1 + x)

Explanation

Given y = 5x and dx/dt = 2, find dy/dt:

dy/dt = d(5x)/dt

= 5(dx/dt)

= 5(2)

= 10

Explanation

Since the population growth is exponential, the population P can be modeled as:

P = P0 x (1 + r)^t

where P0 is the initial population, r is the growth rate, and t is the time (in years).

Given that the initial population P0 = 20 and the population grew to 25 after 2 years, we can find the growth rate r:

25 = 20 x (1 + r)^2

Dividing both sides by 20:

1.25 = (1 + r)^2

Taking the square root:

1 + r = √1.25 = 1.125

Subtracting 1 from both sides:

r = 0.125

Now we can write the exponential growth function:

P = 20 x (1 + 0.125)^t

P = 20 x (1.25)^t