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3 years ago

A shopkeeper had a profit of ₹ 50 on Monday , a loss of ₹ 20 on Tuesday and of loss of

Mathematics

1 answer:

Oliga [24]3 years ago

4 0

Answer:

Step-by-step explanation:

Remark

I can't use a symbol for the currency. I'll just get the answer in numbers. You can add the symbol.

Solution

First day: 50

Second day: - 20

Third day: - 18

50 - 20 - 18 = 12

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(6x-5y+4)dy+(y-2x-1)dx=0

Len [333]

(6x - 5y + 4) dy + (y - 2x - 1) dx = 0

(6x - 5y + 4) dy = (2x - y + 1) dx

dy/dx = (2x - y + 1) / (6x - 5y + 4)

Let X = x - a and Y = y - b. We want to find constants a and b such that

dY/dX = (a rational function)

where the numerator and denominator on the right side are free of constant terms. Substituting x and y in the equation, we have

dY/dX = (2 (X + a) - (Y + b) + 1) / (6 (X + a) - 5 (Y + b) + 4)

dY/dX = (2X - Y + 2a - b + 1) / (6X - 5Y + 6a - 5b + 4)

Then we solve for a and b in the system,

2a - b + 1 = 0

6a - 5b + 4 = 0

==> a = -1/4 and b = 1/2

With these constants, the equation reduces to

dY/dX = (2X - Y) / (6X - 5Y)

Now substitute Y = VX and dY/dX = X dV/dX + V :

X dV/dX + V = (2X - VX) / (6X - 5VX)

The equation becomes separable after some simplification:

X dV/dX + V = (2 - V) / (6 - 5V)

X dV/dX = (2 - V) / (6 - 5V) - V

X dV/dX = (2 - V - (6 - 5V)) / (6 - 5V)

X dV/dX = (4V - 4) / (6 - 5V)

- (5V - 6) / (4V - 4) dV = 1/X dX

Integrate both sides:

-5/4 V + 1/4 ln|4V - 4| = ln|X| + C

Extract a constant from the logarithm on the left:

-5/4 V + 1/4 (ln(4) + ln|V - 1|) = ln|X| + C

-5/4 V + 1/4 ln|V - 1| = ln|X| + C

-5V + ln|V - 1| = 4 ln|X| + C

Get this back in terms of Y :

-5Y/X + ln|Y/X - 1| = 4 ln|X| + C

Now get the solution in terms of y and x :

-5 (y - 1/2)/(x + 1/4) + ln|(y - 1/2)/(x + 1/4) - 1| = 4 ln|x + 1/4| + C

With some manipulation of constants and logarithms, and a bit of algebra, we can rewrite this solution as

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|x + 1/4| + 4 ln(4) + C

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| - ln|4x + 1| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| = 5 ln|4x + 1| + C

8 0

3 years ago

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–

polet [3.4K]

The expression (21 + 5i) + (-1 + i) demonstrates the commutative property of addition for (-1 + i) + (21 + 5i)

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more number and variables.

Given the expression:

(-1 + i) + (21 + 5i)

Using the commutative property of addition, we get:

(21 + 5i) + (-1 + i)

The expression (21 + 5i) + (-1 + i) demonstrates the commutative property of addition for (-1 + i) + (21 + 5i)

Find out more on equation at: brainly.com/question/2972832

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3 0

2 years ago

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Can someone please help me with 44. And 45?

Angelina_Jolie [31]

Problem 44

The term "bisect" means "cut in half".

Since BD bisects angle ABC, this means the smaller angles ABD and DBC are congruent.

angle ABD = angle DBC

x+15 = 4x-45

15+45 = 4x-x

60 = 3x

3x = 60

x = 60/3

x = 20

<h3>Answer: x = 20</h3>

========================================================

Problem 45

We use the same idea as the previous problem

angle ABD = angle DBC

2x+35 = 5x-22

35+22 = 5x-2x

57 = 3x

3x = 57

x = 57/3

x = 19

<h3>Answer: x = 19</h3>

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2 years ago

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In two or more complete sentences, describe how you would draw the graph of the solution set for the following inequality.

vovikov84 [41]

Answer:

Step-by-step explanation:

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3 years ago

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20 POINTS! HELP PLEASE!

nevsk [136]

Answer:

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Step-by-step explanation:

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3 years ago

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