Category: Mathematics

The India is very big country in this world . Madhya Pradesh is a state of india . Madhya Pradesh government are not success to found mines like petrol , diesel , iron , etc.

What is integer

La condicin necesaria para que una funcin sea diferenciable en un punto es que la funcin sea continua en ese punto.

Let the numbers be x and y

x+y=10…(1)

x=10-y…(2)

xy=24….(3)

Put eqn (2) in eqn (3)

(10-y)y=24

10y-y^2=24

y^2-10y-24=0

The coefficient of y multiply by twenty four

y^2-6y-4y+24=0

y(y-6)-4(y-6)=0

(y-4) (y-6)

y=4 or6

Problem 1:

A man (the system) walks inside an isolated room for 5 hours and does $W=1250\text{J}$W=1250J of work. The internal energy decreases by $U=2250\text{J}$U=2250J. Determine the heat $Q$Q (with sign).

Follow-up:

If the system instead gains

$3000\text{J}$3000J of heat while performing the same work ($W=1250\text{J}$W=1250J), what is the change in internal energy?

---

Problem 2:
At constant pressure $p=2.5{10}^5\text{Pa}$p=2.5105Pa, the system does $W=4500\text{J}$W=4500J of work. Find the change in volume $V$V.

---

Problem 3:
An isothermal compression of an ideal gas: $n=4$n=4 moles, initial temperature $T=375\text{K}$T=375K. The gas is compressed to one-fifth of its initial volume ($V_f=V_i/5$Vf=Vi/5). How much heat is removed during the compression?

---

Problem 4:
A car engine with efficiency $=30.0\%$=30.0% produces $W=4000\text{J}$W=4000J of work. How much heat is rejected by the engine?

---

Problem 5:
A Carnot (ideal) heat pump heats a house kept at $T_H=300\text{K}$TH=300K; outside temperature is $T_C=265\text{K}$TC=265K. How much work must the pump do to deliver $Q_H=5000\text{J}$QH=5000J of heat into the house?

Give Answer

Mathematics

• Definition: The study of numbers, shapes, patterns, and logical reasoning.
• Purpose: Provides tools to solve problems and explain real-world phenomena.
• Main Areas:
  • Arithmetic basic operations (addition, subtraction, multiplication, division).
  • Algebra using symbols and equations to represent relationships.
  • Geometry shapes, angles, space, and measurement.
  • Statistics & Probability analyzing data and predicting outcomes.
  • Calculus studying change, motion, and rates.
• Applications in Science:
  • Physics formulas for motion, energy, and forces.
  • Biology statistics for genetics and population studies.
  • Earth Science measurements for earthquakes, planetary motion, and climate models.
  • Ecology mathematical models for ecosystems and food chains.

y2x-yx2 y, find dydx by implicit differentiation y2x-yx2 y, ` (x^(2)+y^(2)) dx -2xy dy = 0`, solve 2(y+3)-x y dy/dx=0, 1+x2+y2 dydx, (x2 y2)dx + 2xy dy = 0, dy/dx=y2-2xy/x2-xy, dy/dx = (x2-y2)/(xy), solve dy/dx = (x2-y2)/(xy), x^2 y” – 2xy’ – 4y = 0, double integrate 1+x2+y2 dydx, 1+x2+y2 dydx double integrate, (x^2-y^2 )dx+2xydy=0, dy/dx=y^2-2xy/x^2-xy, solve dy/dx=y^2-2xy/x^2-xy, `(x^(2)-y^(2))dx+2xy dy=0`, 1+x^2+y^2 dydx, find dy dx by implicit differentiation, : (x^2 + y^2)dx+2xy dy = 0

A train travels 60 km in 1 hour, how far in 3 hours?