Answer:
471 cm^2
Explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "3.14" was replaced by "(314/100)".
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
t*t-((314/100))=0
Step by step solution :
STEP
1
:
157
Simplify ———
50
Equation at the end of step
1
:
157
t2 - ——— = 0
50
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 50 as the denominator :
t2 t2 • 50
t2 = —— = ———————
1 50
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
t2 • 50 - (157) 50t2 - 157
——————————————— = ——————————
50 50
Trying to factor as a Difference of Squares:
2.3 Factoring: 50t2 - 157
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 50 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Equation at the end of step
2
:
50t2 - 157
—————————— = 0
50
STEP
3
:
When a fraction equals zero :
3.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
50t2-157
———————— • 50 = 0 • 50
50
Now, on the left hand side, the 50 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
50t2-157 = 0
Solving a Single Variable Equation:
3.2 Solve : 50t2-157 = 0
Add 157 to both sides of the equation :
50t2 = 157
Divide both sides of the equation by 50:
t2 = 157/50 = 3.140
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
t = ± √ 157/50