Calculus

2x + 3x = 5x

-2x + 3y = -7

3x + y = 16

simultaneous equations.

Elimination a letter. Arbitrarily select 'y'

Hence multiply the bottom eq'n by ' -3'

Hence

-2x + 3y = -7

-9x - 3y = -48

Add the eq'ns/

-11x = =55

x = -55/-11 = 5

When x = 5 , substitute into either eq'n for 'y'

-2(5) + 3y = -7

-10 + 3y = -7

3y = 3

y = 1

Hence answer in ( x,y) fpr, is ( 5,1).

3x + y = 5

There is no answer for 'x' ^ 'y' as there are two unknowns, and no comparable values.

However. it is a linear equation, and can be rearranged into the straight line form .

y = -3x + 5

Hence

Gradient/slope is '-3' and the y0intercept is '5'.

p + 2 = 2 - 3p

Subtract '2' from both sides

p = -30

Subtract 'p' from both sides

0 = -2p

Hence 2p = 0

It folllows p = o

-x -2 = 1 - 2x

Add 'x' to both sides ( preserve equality ; balance)

-2 = 1 - x

Add '2' to both sides

0 = 3 -x

Add 'x' to both sides

x = 3 The Answer !!!!!

NB When said as 'adding/subtracting etc., to both sides', this is to preserve equality (=), so the eq'n remains 'balanced', just like a weigh scales.

e.g. with numbers.

5 = 3 + 2 , however, 5 - 2 = 3 ( same difference!!!!!).

0.4226 (not rounded) all you do is type in your number then press sin if you are doing these calculations on the computer but if you are on a calculator then you would press sin and then the number.

Just learned trig in my geometry class, its fun and easy.

Glad I could help out with this.

Thanks,

Kayla

x - a = y -6

Subtract 'x' from both sides.

-a = y - 6 - x

Multiply both sides by ;-1;

a = -y + 6 + x Solved.

x is equals to 0 or 1.

How is it solved? ....

x.x =x

x.x - x = 0 which can be solved by the usual formula for quadratic equations, or..

x.(x-1)=0

x= 0 or x-1 =0

x=0 or x=1

5y - y = 4y

-6

6

3x = x + 10

Subtract 'x' from both sides.

2x = 10

divide both sides by '2'

x = 5

yees because if you divide everything by 8 to get y=7/8+3x/8 which is a linear function since it fits the equation y=mx+b

6x - 13 = 47

Add '13' to both sides

Hence

6x + 13 - 13 = 47 + 13

6x = 60

Divide both sides by '6'

6x/6 = 60 /6

Cancel down

x = 10 The answer!!!!!

Remember ' Csc(Cosecant)' = 1 /sin

Hence

Cos X 1/Sin = Cos/Sin = Cot (Cotangent)

Do NOT confuse with Tan = Sin /Cos. Notice the positions of trig. functions in the ratios.

-3x + 10x = (+)7x

NB Think of it as

10x - 3x = 7x

log(10)x = 3

Antilog

x = 10^(3) = 1000

Ask Einstein , or read his research papers on the subject.

However, notice the parallel for kinetic energy (KE)

KE = m v^(2)

Where

KE is the Kinetic Energy

m is the mass ( much greater than the differential mass of Einstein).

v is the velocity (much less than the speed of light).

v^(2) is the velocity squared.

KE deals with large objects moving at slow speeds.

40 mm

1 cm = 10 mm

1 mm = 0.1 cm

Rational numbers are those that can be expressed as a ratio of two integers. So 2, which can be expressed in such a way, for example, (-2) / 1 or 2 / (-1) is a rational number.

Solution manuals for "Thomas' Calculus" (9th edition) and "Fundamentals of Physics" by Walker, Resnick, and Halliday (6th and 7th editions) can often be found on various educational websites, online marketplaces like Amazon or eBay, and sometimes through university resources or libraries. Additionally, platforms like Chegg and Course Hero may offer access to these solution manuals for a subscription fee. However, it's important to use these resources ethically and in accordance with copyright laws.

Well, isn't that a happy little math problem! When you have 3 times a number and you divide that by the same number, you're left with just 3. It's like painting a beautiful landscape with just three simple colors - simple and harmonious.

y = x^(3)

When x = 2

Substitute

y = 2^(3)

y = 8

No, y=8 is a fixed value. A linear equation would look something like y=x+8 - That would produce a straight line graph if the values of x & y were plotted against each other on a graph.

Nothing!!!! It is the use of two different letters to indicate the point on the y-axis were the straight 'crosses'.