Problem to To Convert the Given Polar CoOrdinates to Rectangular CoOrdinates

Topic : Convertion of polar coordinates to rectangular coordinates

Question : Convert the given polar co ordinates to rectangular co ordinates.

Solution :

Simple Problem on Solving a Linear Equation

Topic : Linear Equation
Problem : Solve for x, x + 1 = 3
Answer :
x + 1 = 3
x = 3 -1
x = 2
So Value of x = 2
For verification you can substitute value of x in linear equation given.
Since 2 + 1 = 3 the value obtained is correct.

Verifying Continuity of a function r(t)

Topic : Limits and Continuity

Question : Determine whether r(t) is continuous at 0. Explain your reasoning.

r(t) = e^t(i) + j + Cosec t (k)

Solution :

r(t) is continuous at 0, if each of its components are continuous at 0 then,

Problem on Factorization

Topic : Factorization

Problem : Factorise -2w^4 +1250

Solution :
-2w^4 +1250
taking -2 as common
-2(w^4 -625)
-2[(w^2)^2 - (25)^2]
Applying the formula
a^2-b^2 = (a+b)(a-b)
we get -2[(w^2+25)(w^2-25)]
-2[(w^2+25)(w^2-5^2)]
Again applying the formula
for (w^2-5^2)
we get
-2[(w^2+25)(w+5)(w-5)]

Question on Equilibrium using Trignometric Expressions

Topic : Equilibrium of Suspended Strings

Question : A particle A, of weight W, is suspended by two strings AB and AC. AB is inclined at 30degrees to the vertical and AC at angle P to the vertical. The tension in AB and AC are 40N and 60N respectively. Calculate the value of W and P.

Solution :

Since the system is in equilibrium,
60 Sin P = 40 Sin 30º ------- (1)
and 60 Cos P + 40 Cos 30º = W-----(2)

From (1) we get,
60 Sin P = 40 *(1/2)

60 Sin P/60 = 20/60
Sin P = 1/3

P = Sinˉ¹(1/3)

P= 19.469º


From (2) we get,
W = 60 Cos P + 40 Cos 30º

= 60 Cos (19.469º) + 40 Cos 30º

= 60 . 0.943 + 40 . 0.866

= 56.58 + 34.64

= 91.22N

So P = 19.469º

W = 91.22N

Problem on Finding Geometrical Figure's unknown Quantity

Topic : Geometrical Figure





Question : Find the area of triangle ABC where
angle ABC = 35 degrees
angle BCA = 110 degrees
angle CAB = 35 degrees
AND, length BC = 4 cm



ANSWER:





















Description Step1 : b = AC = BC because triangle ABC is isosceles
Triangle ABC are isosceles because angle ABC=angle BAC=35 degree



Description Step2 : sin 70 degrees = h/4
0.9369=h/4
h = 0.9369*4 = 3.759



Step3: Area = 0.5*b*h = 0.5*(4)(3.759) = 7.518 cm2

Definition of Expanded Form of any Numbers

Topic : Expanded Form

Question : Definition for Expanded Form, Explained with an Example.

Answer :

Expanded form is a way to write a number that shows the sum of values of each digit of a number.

Expanded form is a way of writing numbers so that all that is hidden

about them comes out into the open.

The simplest way to write numbers in expanded form is to write them

sort of in English.

For 4,017, this becomes 4 thousands and 0 hundreds and 1 ten and 7

ones. This can be made to look like math by changing the words to math

symbols.The expanded form for 4,017, then, is:

4 x 1000 + 0 x 100 + 1 x 10 + 7 x 1

The expanded form shows what each digit is worth (for example, the 4

is worth 4 x 1000, which is the same as 4 thousands, which equals

4000).

Here is another example.

12,345 becomes 1 ten thousand and 2 thousands and 3 hundreds and 4 tens

and 5 ones. Changing the words to math symbols, 12,345 in expanded form

is:

1 x 10,000 + 2 x 1,000 + 3 x 100 + 4 x 10 + 5 x 1

Standard form is the reverse of expanded form. You begin with expanded

form and change it to the way we normally write numbers.

For example, 3 x 1,000 + 5 x 100 + 7 x 10 + 4 x 1 can be changed to

3 thousands and 5 hundreds and 7 tens and 4 ones. This becomes:

3000 + 500 + 70 + 4